Revision sheets in English

1. 1
   Types, conversion and conditions 9 traps traps exercises

   What loses marks on the first chapter of COMP 202 and the gesture that avoids each loss: input left as a string, int where float was needed, == between floats, not misread, elif in the wrong order.

2. 2
   Loops and the patterns they carry 9 traps traps exercises

   What costs marks on loops in COMP 202: the while whose body never touches the tested variable, the continue that skips the update, the counter reset inside its own loop, and break read as an exit from every loop.

3. 3
   Strings and text processing 8 traps traps exercises

   What loses marks on strings in COMP 202: the method result thrown away, the character assigned by index, the window s[i:3] that never slides, the comparison '10' < '9', the vowels counted as a substring, print where the autograder wanted return. Eight traps with their cost, a decision tree, a traced example and the checks to run before submitting.

4. 4
   Functions, scope and program design 8 traps traps exercises

   What loses marks on functions in COMP 202: the print that hands None to the autograder, the global read instead of the parameter, UnboundLocalError, the shared default list, and the trace drawn without its frames.

5. 5
   Lists, dictionaries and the structure to choose 9 traps traps exercises

   What loses marks on lists, dictionaries, sets and tuples in COMP 202: the result of append stored as None, the copy that stops one level down, the grid built from one row, the missing key read with brackets, the dictionary deleted from while it is iterated, and the membership test that makes the autograder time out.

6. 6
   Files, exceptions and real data 9 traps traps exercises

   What costs marks on files and exceptions in COMP 202: the mode that empties a file, the open inside its loop, the field compared before its strip, the handle read twice, the bare except, the missing value turned into 0.

7. 7
   Recursion, and when a loop is the better answer 9 traps traps exercises

   The missing return, the call handed the same argument, the base case that misses the empty list, the mid index left inside a binary search, the memo default argument: each with its cost and the line to write instead.

8. 8
   Classes and objects 10 traps traps exercises

   What costs marks on classes in COMP 202: the header without self, the counter that hides the class attribute, the list shared by every object, the __str__ that prints, == on objects, and super forgotten.

1. 1
   Units, measurement and vectors 10 traps traps exercises

   What actually loses marks on the first chapter of PHYS 101 at McGill, and the gesture that avoids each loss: the conversion factor that has to be cubed, the calculator display copied out instead of the digits the data earned, the order of magnitude read off the wrong exponent, the cosine used for the horizontal component when the angle was measured from the vertical, the calculator left in radian mode, the arctangent trusted for a direction it cannot know, the triangle's angle put into the law of cosines of the formula sheet, and a formula trusted because its number looks plausible. The dot product and the law of cosines of the formula sheet, ten traps with their cost in marks, a decision tree, a worked resultant step by step, and the five second checks to run before handing the paper in. No calculus, as the course demands.

2. 2
   Motion in a straight line 10 traps traps exercises

   What actually costs marks in the first mechanics chapter of PHYS 101, and the gesture that avoids each loss: the axis written on the first line, the four equations chosen by the quantity that is missing, a negative acceleration that speeds an object up, a velocity of zero at the top of a throw with an acceleration that is not zero, the area under a velocity-time graph read as a displacement and not as a distance, an instantaneous velocity obtained as the slope of a tangent, a motion in two phases whose top comes after the motors stop, and an answer in letters checked by its dimensions and a limit case.

3. 3
   Projectile motion and relative velocity 10 traps traps exercises

   What actually costs marks on the projectile chapter of PHYS 101: calling the velocity zero at the top of the flight, using the symmetric time of flight when the landing height differs from the launch height, reading the parabolic path as a graph against time, dividing a river width by the ground speed, reversing the subscripts of a relative velocity, and thinking that keys dropped in a moving tram fall straight down for the platform. Ten traps written as a student writes them, two decision trees, a fully annotated example and the five second checks to run before handing in the paper. No calculus, exactly as the course requires.

4. 4
   Newton's laws and free-body diagrams 8 traps traps exercises

   What costs marks on the dynamics question of a PHYS 101 midterm, and the gesture that avoids each loss: the arrow with no source, the normal force copied as the weight on a tilted surface, the two members of an action and reaction pair added in the same equation, the tension taken as the hanging weight while the system accelerates, the sine and cosine swapped on an incline, and the contact force between two pushed crates taken as the whole push. Eight traps with their cost, a table of the normal force case by case, two decision trees on the choice of axes, the habit of answering in letters with its three checks, and one worked problem with a cord over a pulley.

5. 5
   Friction, circular motion and gravitation 9 traps traps exercises

   What actually costs marks on the hardest chapter of PHYS 101, and the gesture that avoids each loss. Nine traps written as a student writes them, with the correct line to copy and the price of the error: static friction set equal to its ceiling on a block that is merely at rest, an invented centripetal arrow added to a diagram that was already complete, the incline formula for the normal force carried over to a banked curve where the acceleration is horizontal, friction pointed the wrong way on a banked ramp taken below its design speed, an altitude fed into the law of gravitation in place of a distance from the centre, a square root taken where Kepler's third law calls for a cube root, and weightlessness in orbit blamed on an absence of gravity that is not there. Artificial gravity in a spinning habitat, two decision trees, a table of the three friction cases, a full worked curve problem step by step, and four five-second checks to run before handing the paper in.

6. 6
   Work, energy and power 11 traps traps exercises

   What actually costs marks on the energy chapter of PHYS 101 at McGill: the cosine that disappears, the slope length used as a height, the reference level nobody writes down, friction added instead of subtracted, kinetic energy treated as proportional to the speed, minutes left inside a power calculation, the normal force on a slope taken as the weight, a spring compression that forgets the last stretch of sliding, and a constant force read as a constant power. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs. No calculus anywhere, as the course requires.

7. 7
   Momentum, impulse and collisions 10 traps traps exercises

   The sheet for the chapter where one equation is always true and the other one has to be earned. The signed components that make a recoil visible, the impulse read as an area of triangles and rectangles, the airbag that divides the force by five without touching the impulse, the grid of the four collision types with a worked number under every row, the elastic line of the formula sheet with its three limit cases, the same impulse that never means the same energy, the two stage ballistic pendulum, and the five second checks to run before handing in the paper.

8. 8
   Torque, rotation and equilibrium 12 traps traps exercises

   The chapter where marks are lost on a geometry question dressed as a physics one: the lever arm measured to the point of application instead of to the line of the force, a moment of inertia quoted without its axis, a rolling body given only half of its kinetic energy, the friction that makes it roll counted as a loss, a race ranked by mass, a cord over a pulley given a tension equal to the weight, and kinetic energy conserved where only angular momentum survives. With what the formula sheet does and does not give, the decision tree that names the right equation from the shape of the question, and the static case worked on a hinged sign beam, step by step.

9. 9
   Oscillations and simple harmonic motion 11 traps traps exercises

   What actually loses marks on the oscillations chapter of PHYS 101, and the exact gesture that avoids each loss. Eleven traps taken from real scripts, among them the phase constant of the formula sheet's A sin(ωt + φ), two decision trees that pick the right formula from the shape of the question, three write-ups a marker expects, seven five-second checks, the reference circle that gives the maximum speed and acceleration, and a full vertical-spring laboratory worked through step by step. No calculus anywhere, as in the course itself.

10. 10
    Waves and sound 9 traps traps exercises

    What costs marks in the waves and sound chapter of PHYS 101 at McGill, and the gesture that avoids each loss: reading a period off a snapshot graph, doubling a tension expecting to double a frequency, letting the frequency change at a boundary or when a swell turns toward a beach, giving a closed pipe the even harmonics it does not have, adding decibel levels instead of intensities, reading a doubled amplitude as 3 decibels, using the moving source formula when it is the listener who moves, and forgetting to halve the round trip time of an echo. Nine traps with their cost, a decision tree that picks the formula from the shape of the question, a method written in four steps, a full sonometer example, and a figure on eight of the nine traps. Algebra only, no calculus, as the course requires.

11. 11
    Refraction and dispersion, with a look ahead to lenses 9 traps traps exercises

    What actually costs marks on the light chapter of PHYS 101, and the gesture that avoids each loss. First what the formula sheet gives: the angle measured from the surface instead of the normal, the speeds put on the wrong side of the sheet's refraction law, the critical angle hunted in the direction where it does not exist or taken in the wrong medium, the inverse sine taken too early. Then mirrors and lenses, a look ahead to PHYS 102: the minus sign erased from an image distance, the outgoing side of a mirror confused with that of a lens, the focal length left in centimetres inside a power in diopters. Two decision trees, a worked example and the five second checks to run before handing in.

12. 12
    Wave optics, interference and diffraction 10 traps traps exercises

    Not a summary of the lecture, a list of what costs marks on this chapter and the exact gesture that avoids each loss. Ten traps with the wrong line and the line to write instead, a grid that counts the reflection flips of a thin film before any formula is chosen, two decision trees, the wording a marker expects on a double slit answer and on a film answer, six five second checks, and a full worked example that puts the two slit fringes inside the single slit envelope. Refraction written with the wave speeds, as on the formula sheet, and the double slit under water. No calculus anywhere, as PHYS 101 requires.

Linear systems and matrices

1. 1
   Systems of linear equations and Gaussian elimination 8 traps traps exercises

   What actually costs marks on the first chapter of MATH 133 at McGill: a variable copied into the wrong column, a row replaced by a combination that no longer contains it, a division by k minus 2 that erases a whole case, a zero row read as infinitely many solutions, a free variable declared before the consistency test, and a pivot variable used as a parameter. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

2. 2
   Homogeneous systems and the rank theorem 8 traps traps exercises

   What actually costs marks on the second chapter of MATH 133 at McGill: subtracting the number of equations instead of the rank, reading the theorem on homogeneous systems backwards, counting parameters on a system with no solution, a product Ax with the wrong number of entries, adding two solutions and expecting a third, and rejecting a basic solution because it was scaled. Every trap is a wrong line next to the line to write instead, with the marks it costs.

3. 3
   Matrix algebra and the matrix product 10 traps traps exercises

   What actually costs marks on the matrix algebra chapter of MATH 133 at McGill: products multiplied entry by entry, sizes never checked, a transpose taken without reversing the order, the square of a matrix computed by squaring its entries, a matrix declared zero because its square is, symmetric matrices whose product is assumed symmetric, and the second product in a commuting question never actually computed. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs. No calculator anywhere, as the course requires.

4. 4
   Matrix inverses and elementary matrices 9 traps traps exercises

   What actually costs marks on the inverse chapter of MATH 133 at McGill: the solution of XA = B written on the wrong side, the inverse of a product left in the original order, entries inverted one by one, a zero on the diagonal taken for a dead end, a pivot divided before its zero case is set aside, and a product of elementary matrices read backwards. Every trap is a wrong line from a real paper next to the line to copy instead, with the mark it costs.

Determinants

1. 5
   Determinants and cofactor expansion 8 traps traps exercises

   What actually costs marks on the determinant chapter of MATH 133 at McGill: the minus sign that starts row 2, the minor handed in where the cofactor was asked, a swap never recorded, a factor pulled out of a row and then lost, the operation 3R2 minus R1 taken for a harmless replacement, and det(2A) written as twice det A. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs. No calculator, as the course requires.

2. 6
   Determinants, inverses and Cramer's rule 8 traps traps exercises

   What actually costs marks on determinants, inverses and Cramer's rule in MATH 133 at McGill: the power n forgotten in the determinant of kA, the scalar inside or outside an inverse, the negative branch dropped, a division by a determinant that may be zero, the swapped indices of one entry of the inverse, and a zero determinant read as no solution. Every trap is a wrong line from a real paper, next to the line to copy instead, with the mark it costs. No calculator, as on the exam.

Vector geometry in space

1. 7
   Geometric vectors and lines in space 8 traps traps exercises

   What actually costs marks on vectors and lines in MATH 133 at McGill: the same parameter letter used for two lines, the third equation never checked, proportional directions read as the same line, skew lines called parallel, a symmetric form divided by zero, and the weight put on the wrong end of a ratio. Each trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

2. 8
   Dot product, projections and planes 8 traps traps exercises

   What actually costs marks on the dot product chapter of MATH 133 at McGill: the projection divided by the length instead of its square, the projection taken for the distance to a line, the distance to a plane without its denominator, parallel planes compared before their normals match, a zero dot product read as perpendicular, and the obtuse angle given for two planes. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

3. 9
   Cross product, areas and volumes 8 traps traps exercises

   What actually costs marks on the cross product chapter of MATH 133 at McGill: the minus sign lost on the middle component, the half forgotten in a triangle area, position vectors used instead of edges, a zero cross product patched into an equation, one third instead of one sixth for a tetrahedron, and a distance never divided by the length of the direction. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

Subspaces, transformations and eigenvalues

1. 10
   Subspaces, span and independence 8 traps traps exercises

   What actually costs marks on subspaces, span and linear independence in MATH 133 at McGill: a no without a numerical counterexample, a yes checked on two examples, the zero test taken as the whole test, span decided by looking for multiples, the trivial solution mistaken for a dependency, and a pivot containing k divided away. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

2. 11
   Basis, dimension and the fundamental subspaces 8 traps traps exercises

   What actually costs marks on the basis and dimension chapter of MATH 133 at McGill: the column space copied from the reduced matrix, rows of A trusted after a row swap, rank plus nullity counted on the rows, zero rows mistaken for free variables, equations counted instead of independent equations, and three coordinates given to a vector of a plane. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

3. 12
   Linear transformations and their matrices 8 traps traps exercises

   What actually costs marks on linear transformations in MATH 133 at McGill: the images written as rows, a composition multiplied in reading order, the rotation with its sine in the wrong place, the missing one over one plus m squared in a reflection, data on other vectors used as columns, and a projection treated as invertible. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

4. 13
   Eigenvalues and eigenvectors 9 traps traps exercises

   What actually costs marks on the eigenvalue chapter of MATH 133 at McGill: eigenvalues read off a row reduced matrix, the zero vector given as an answer, a negative eigenvalue thrown away, a cubic expanded along the wrong row, opposites instead of reciprocals for the inverse, and the transpose assumed to share its eigenvectors. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

5. 14
   Diagonalization and its applications 8 traps traps exercises

   What actually costs marks on the diagonalization chapter of MATH 133 at McGill: the double root declared defective without a rank, one eigenvector per eigenvalue whatever the multiplicity, D listed in a different order from the columns of P, A written as the inverse of P times D times P, powers taken entry by entry, shared invariants taken as proof of similarity, and a steady state never scaled to the total. Every trap is a wrong line from a real paper, next to the line to copy instead, with the marks it costs.

Functions and limits

1. 1
   Functions, graphs and transformations 8 traps traps exercises

   What actually costs marks on the review of functions that opens MATH 140 at McGill: a shift in the wrong direction, f(2x + 4) read as a shift of 4, an outside order reversed, a domain read on a simplified formula, a range taken from the two ends, a candidate kept outside its piece, a symmetry proved with one point, and a composition treated as a product. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

2. 2
   Exponential, inverse, log and inverse trig functions 9 traps traps exercises

   What actually costs marks on exponential, logarithmic and inverse functions in MATH 140 at McGill: a log equation whose negative root is kept, ln of x squared turned into 2 ln x, the logarithm of a sum split in two, an arcsin answer outside its range, the second solution the calculator never shows, a triangle trusted for a sign, and an inverse written as a reciprocal. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

3. 3
   Limits and the limit laws 8 traps traps exercises

   What actually costs marks on the first limit chapter of MATH 140 at McGill: the value of the function given as its limit, 0 over 0 answered 1, one side of an absolute value forgotten, the square root of a square taken without its absolute value, the product law used on a factor with no limit, and a squeeze between bounds that do not meet. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

4. 4
   Continuity and the IVT 8 traps traps exercises

   What actually costs marks on continuity in MATH 140 at McGill: a discontinuity classified by the wrong criterion, a seam computed by plugging into zero over zero, a parameter equation with its second root forgotten, the IVT applied across a point where the function is undefined or without its hypotheses written, and uniqueness read into an existence theorem. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

5. 5
   Limits at infinity and asymptotes 8 traps traps exercises

   What actually costs marks on infinite limits and asymptotes in MATH 140 at McGill: a nonzero number over zero answered infinity without a side, an asymptote declared where the factor cancels, the minus sign of the square root of x squared forgotten at minus infinity, infinity minus infinity answered zero, the wrong dominant exponential, and an oblique asymptote read off the leading terms. Every trap is a wrong line next to the line to copy, with the mark it costs.

The derivative and its rules

1. 6
   The derivative as a limit 8 traps traps exercises

   What actually costs marks on the definition of the derivative in MATH 140 at McGill: substituting h equal to zero, expanding f of x plus h wrongly, using the power rule when the question says by the definition, calling a continuous function differentiable, taking a chord for a tangent, and reading a rate as an amount. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

2. 7
   Differentiation rules 10 traps traps exercises

   What actually costs marks on the first differentiation rules of MATH 140 at McGill: a product or a quotient differentiated factor by factor, the power rule applied to e to the x or to a constant, a fraction not rewritten as a power, the quotient rule with its terms swapped, a tangent line with f prime of x left unevaluated, the wrong normal, and a tangent through a point off the curve. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

3. 8
   Trigonometric derivatives 9 traps traps exercises

   What actually costs marks on the trigonometric derivatives of MATH 140 at McGill: the limit of sin 3x over x answered 1, one minus cosine over x answered 1, a slope computed in degrees, the lost minus sign of cosecant or cotangent, the derivative of tangent taken as a quotient of derivatives, a 99th derivative read on parity, and solutions lost by dividing by sine. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

4. 9
   The chain rule 9 traps traps exercises

   What actually costs marks on the chain rule in MATH 140 at McGill: the missing inner factor, the derivative placed inside the cosine, the outer derivative read from the wrong row of a table, the power rule applied to an exponential, e to the x squared taken as its own derivative, a false chain rule for second derivatives, and degrees used where calculus needs radians. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

5. 10
   Implicit differentiation 9 traps traps exercises

   What actually costs marks on implicit differentiation in MATH 140 at McGill: the missing dy/dx on a y-term, the product rule skipped on xy, a slope given for an x instead of a point, a line given as the answer to a horizontal-tangent question, 0 over 0 read as a vertical tangent, y'' computed with y frozen, the sign of the square root in the arcsin proof, and the inverse function derivative taken at the wrong point. Every trap is a wrong line next to the line to copy instead, with the mark it costs.

6. 11
   Logarithmic differentiation and growth 10 traps traps exercises

   What actually costs marks on the logarithm chapter of MATH 140 at McGill: the derivative of ln(5x) written 5 over x, a log in base b without its ln b, the square of ln confused with the ln of a square, a derivative evaluated outside the domain, ln y taken where y is negative, the last multiplication by y forgotten, x to the x treated as a power, and k taken for a percentage in a growth problem. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

7. 12
   Related rates 8 traps traps exercises

   What actually costs marks on related rates in MATH 140 at McGill: numbers substituted before differentiating, a minus sign dropped, the radius of a cone frozen instead of eliminated, a diameter put where the radius goes, degrees in a trigonometric derivative, speeds added on perpendicular roads. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs, and every relation comes with its figure.

8. 13
   Linear approximation and differentials 8 traps traps exercises

   What actually costs marks on linear approximation in MATH 140 at McGill: the factor (x - a) dropped from the tangent line, a centre chosen far from the target or where the derivative does not exist, degrees fed to sin x close to x, a side announced without the second derivative, dy confused with Delta y, and a relative error carried unchanged through a cube. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

Applications of the derivative

1. 14
   Maximum and minimum values 8 traps traps exercises

   What actually costs marks on section 4.1 of MATH 140 at McGill: an endpoint called a local maximum, a corner or a cusp missed because only f prime equal to zero was solved, a vertical asymptote counted as a critical number, a candidate kept outside the interval, forgotten endpoints, the method applied across a discontinuity, and a horizontal tangent taken for an extremum. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

2. 15
   Rolle's theorem and the Mean Value Theorem 8 traps traps exercises

   What actually costs marks on Rolle's theorem and the Mean Value Theorem in MATH 140 at McGill: the hypotheses skipped or checked on the wrong interval, a value of c kept at an endpoint, a function with zero derivative declared constant on two pieces, c computed where it should only be bounded, exactly one root claimed from the Intermediate Value Theorem alone, and Rolle read backwards. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

3. 16
   Shape of a graph 8 traps traps exercises

   What actually costs marks on section 4.3 of MATH 140 at McGill: an extremum declared wherever the derivative is zero, an inflection point wherever the second derivative is zero, a cusp forgotten in the list of critical numbers, signs alternated across a double root, the graph of f' read as the graph of f, and a silent Second Derivative Test taken for a no. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

4. 17
   L'Hospital's rule 8 traps traps exercises

   What actually costs marks on L'Hospital's rule in MATH 140 at McGill: differentiating a form that is not indeterminate, the quotient rule used by mistake, one round too many, the wrong factor put downstairs, infinity minus infinity answered 0, 1 to the infinity answered 1, the limit of the logarithm given as the answer, and a limit declared nonexistent because the rule was silent. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

5. 18
   Curve sketching 8 traps traps exercises

   What actually costs marks when sketching a graph in MATH 140 at McGill: an interval of increase written across an asymptote, an inflection point placed where the function is undefined, a hole taken for an asymptote, the square root of x squared taken for x at minus infinity, the critical number of a cusp forgotten, and L'Hospital's rule applied to a form that is not indeterminate. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

6. 19
   Optimization problems 8 traps traps exercises

   What actually costs marks on the optimization chapter of MATH 140 at McGill: answering with the critical number, a second derivative test that only proves a local maximum, a critical number outside the domain, a capacity that moves the optimum to an endpoint, the closed interval method used on an open domain, and the squared distance given as the distance. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

7. 20
   Antiderivatives 8 traps traps exercises

   What actually costs marks on antiderivatives in MATH 140 at McGill: the constant dropped before an initial condition, the power rule applied to 1 over x, the product of two antiderivatives, the missing factor of a linear inside function, one constant forced across a gap, the same constant used twice for a second derivative, and an antiderivative read as increasing because f increases. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

The definite integral

1. 1
   Riemann sums and the definite integral 9 traps traps exercises

   What actually costs marks on the first chapter of MATH 141 at McGill: the left end dropped from the sample point, a constant summed once instead of n times, the wrong leading term of a sum of squares, the midpoint sum taken for an average, the left sum assumed to underestimate, and an integral of zero reported as an area of zero. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the marks it costs.

2. 2
   The Fundamental Theorem of Calculus 8 traps traps exercises

   What actually costs marks on the Fundamental Theorem chapter of MATH 141 at McGill: the missing chain rule factor on a moving bound, the constant bound subtracted, F(b) minus F(a) computed across a discontinuity, an antiderivative that jumps, displacement reported as distance, and product or quotient rules invented for integrals. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

3. 3
   The substitution rule 8 traps traps exercises

   What actually costs marks on the substitution chapter of MATH 141 at McGill: dividing by a variable to manufacture du, keeping the old bounds, reordering reversed bounds and keeping the minus sign, freezing a stray x, the sign of the integral of tan x, a dropped absolute value, and symmetry quoted on the wrong interval. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

Techniques of integration

1. 4
   Integration by parts 7 traps traps exercises

   What actually costs marks on integration by parts in MATH 141 at McGill: the integral of a product taken as the product of the integrals, a choice of u that raises the power, the minus sign of v lost, table signs that do not alternate, a cyclic integral that turns into I = I, and a definite integral whose second half loses its bounds. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

2. 5
   Trigonometric integrals 8 traps traps exercises

   What actually costs marks on the trigonometric integrals of MATH 141 at McGill: the factor saved from the even power, the wrong sign in a half-angle formula, the integral of sine squared written as a cube, the bound sec 0 taken as 0, the lost half in the integral of secant cubed, the sign of a product-to-sum formula, and a square root that silently flips a cosine. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

3. 6
   Trigonometric substitution 8 traps traps exercises

   What actually costs marks on trigonometric substitution in MATH 141 at McGill: the substitution chosen from the letters instead of the sign under the root, a forgotten dx, limits that did not move, the root of the secant taken positive on the negative branch, a triangle read without its hypotenuse, a double angle treated as linear, and a completed square with the wrong sign. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

4. 7
   Partial fractions 8 traps traps exercises

   What actually costs marks on the partial fractions chapter of MATH 141 at McGill: an improper fraction decomposed without its long division, the factor one over p forgotten in front of a logarithm, the lower power of a repeated factor left out, a squared factor integrated into a logarithm, a splitting quadratic taken for an irreducible one, and du over u lost after u equals e to the x. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

5. 8
   Strategy for integration 9 traps traps exercises

   What actually costs marks when the integral arrives without a chapter title on a MATH 141 exam: substituting when the derivative is not there, forgetting to rewrite dx or the bounds, splitting into partial fractions before dividing, clearing one root out of two, writing the square root of sine squared as sine, and dividing by the derivative of the inner function. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

6. 9
   Improper integrals 8 traps traps exercises

   What actually costs marks on the improper integrals chapter of MATH 141 at McGill: infinity substituted into an antiderivative, the Fundamental Theorem used across an asymptote, two infinities added into a number, the principal value taken for the integral, the p-rule applied on the wrong interval, a comparison in the direction that proves nothing, and infinity times zero written as zero. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

Applications of integration

1. 10
   Areas between curves and average value 9 traps traps exercises

   What actually costs marks on areas between curves and average value in MATH 141 at McGill: one integral across a crossing, the absolute value put outside the integral, an intersection lost by dividing, x-bounds on a dy integral, the wrong branch of a sideways parabola, the endpoint average taken for the average value, and a c kept outside the interval. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

2. 11
   Volumes: disks and washers 8 traps traps exercises

   What actually costs marks on volumes by slicing in MATH 141 at McGill: pi times (R minus r) squared instead of the washer, the height of a curve taken for a radius about y = k, outer and inner radii swapped when the axis is above, a vertical axis integrated in x, x limits in a dy integral, and a half-chord under a known cross-section. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

3. 12
   Volumes by cylindrical shells 8 traps traps exercises

   What actually costs marks on cylindrical shells in MATH 141 at McGill: a radius written as a coordinate and a negative volume, the dropped radius, pi instead of two pi, vertical strips about the x-axis, the curve taken for the height of a horizontal strip, an axis that cuts the region, and the inner branch forgotten when washers are used as a check. Every trap is a wrong line from a real paper, next to the line to copy, with the mark it costs.

4. 13
   Work 9 traps traps exercises

   What actually costs marks on the work chapter of MATH 141 at McGill: the final force of a spring multiplied by the stretch, a length taken for a stretch, every piece of a cable lifted the full length, the distance of a layer written y by reflex, the similar triangle read upside down, g applied to pounds, and half full taken for half the work. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

5. 14
   Arc length and surface area 8 traps traps exercises

   What actually costs marks on arc length and surfaces of revolution in MATH 141 at McGill: one plus f prime instead of the root, the minus sign kept when the square opens, the secant without its absolute value, bounds in x with dy, the volume reflex 2 pi y dx for an area, the wrong radius, and a finite volume taken for a finite area. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

6. 15
   Moments, centres of mass and hydrostatic force 9 traps traps exercises

   What actually costs marks on section 8.3 in MATH 141 at McGill: the x-axis moment built from x, the difference squared instead of the difference of squares, the average of two centroids, the depth measured from the bottom, the pressure taken at the deepest point, the slant forgotten on an inclined plate, and Pappus with the wrong distance. Every trap is a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

7. 16
   Probability density functions 9 traps traps exercises

   What actually costs marks on probability density functions in MATH 141 at McGill: a height read as a probability, the constant k inverted, a density checked for area but not for sign, a cumulative distribution function restarted on each piece, the median taken at the middle, the exponential median confused with its mean, and a mean given by symmetry when it does not exist. Every trap is a wrong line from a real paper, next to the line to copy instead.

Sequences and series

1. 17
   Sequences 9 traps traps exercises

   What actually costs marks on the sequences chapter of MATH 141 at McGill: L'Hôpital applied to a sequence, the converse of the function theorem, 1 to the infinity answered 1, infinity minus infinity answered 0, a squeeze between bounds that do not share their limit, the first terms trusted over the tail, and a recursion solved before its limit was shown to exist. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

2. 18
   Series: geometric, telescoping, divergence test 8 traps traps exercises

   What actually costs marks on the first series chapter of MATH 141 at McGill: one over one minus r applied to a series that starts at n equals 1, a ratio misread behind a doubled exponent, convergence concluded from terms that tend to zero, a telescoping sum split into two divergent series, the wrong number of surviving terms, and brackets inserted into a divergent series. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

3. 19
   The integral and comparison tests 8 traps traps exercises

   What actually costs marks on sections 11.3 and 11.4 in MATH 141 at McGill: the decrease never checked, the integral read as the sum, a comparison in the useless direction, a limit comparison against the wrong benchmark, an exponent that is not constant, and the remainder bounds swapped. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

4. 20
   Alternating series 8 traps traps exercises

   What actually costs marks on alternating series in MATH 141 at McGill: the decrease never checked, a decrease proved by the denominator grows, divergence declared because the test fails, the error bounded by the wrong term or given the wrong sign, terms counted from the wrong index, and converges written where absolutely or conditionally was asked. Each trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

5. 21
   Ratio and root tests 9 traps traps exercises

   What actually costs marks on the ratio and root tests in MATH 141 at McGill: a ratio below 1 for every n taken for a limit below 1, L = 1 read as a verdict, a factorial that gains one factor instead of two, the form 1 to the infinity read as 1, conditional convergence looked for after L above 1, and the test chosen before the form of the term was read. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

6. 22
   Power series 8 traps traps exercises

   What actually costs marks on the power series chapter of MATH 141 at McGill: the open interval given as the answer, an endpoint tested with the ratio test, the centre of (2x - 3) to the n read as 3, a missing factor in the series of 1/(2 + x), the constant of integration forgotten, a number differentiated instead of a function, a derived series assumed to keep its endpoints, and a series evaluated outside its interval. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

7. 23
   Taylor and Maclaurin series 8 traps traps exercises

   What actually costs marks on the Taylor series chapter of MATH 141 at McGill: the n factorial forgotten when a derivative is read from a coefficient, the centre lost, a series used outside its interval, the interval not rescaled after a substitution, series multiplied coefficient by coefficient, a composition expanded too short, a limit expansion stopped before anything survives, and a convergent series taken for its function. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

8. 24
   Taylor polynomials and error bounds 7 traps traps exercises

   What actually costs marks on the last chapter of MATH 141 at McGill: M taken at the centre instead of the worst point, the first omitted term used on a series of positive terms, the sine polynomial of degree 3 not used as degree 4, degrees plugged into a formula in radians, an error bound read as correct decimals, and a polynomial centred at 0 by habit when a nearer centre was available. Every trap is written as a wrong line from a real paper, next to the line to copy instead, with the mark it costs.

Functions and limits

1. 1
   Functions, trigonometric and exponential functions 8 traps traps exercises

   What actually costs marks in the review chapter that opens MATH 203 at Concordia: a shift read before the inside is factored, an arc length computed in degrees, a sign copied from a triangle, a calculator left in degree mode, solutions deleted by dividing by cos x, a doubled interval forgotten, half a period taken for a period, and a negative exponent turned into a negative number. Every trap is written as the wrong line next to the line to copy instead, with the marks it costs.

2. 2
   Inverse functions and logarithms 8 traps traps exercises

   What actually costs marks on inverse functions and logarithms in MATH 203 at Concordia: an inverse formula with x still on both sides, a plus or minus left in the answer, a forgotten restriction, ln of a sum split in two, the square of a logarithm turned into twice the logarithm, a change of base upside down, a root kept that makes a logarithm negative, and a valid negative root thrown away. Every trap is a wrong line next to the line to copy, with the mark it costs.

3. 3
   Rates of change and limit laws 8 traps traps exercises

   What actually costs marks on the first limit chapter of MATH 203 at Concordia: a rate computed upside down, a tangent estimated from one side only, the value of the function given as its limit, 0 over 0 read as no limit, a negative exponent turned into a minus sign, the square root of a sum split in two, and a calculator table trusted after it rounded to zero. Every trap is a wrong line next to the line to write instead, with the mark it costs.

4. 4
   One-sided limits 9 traps traps exercises

   What actually costs marks on one-sided limits in MATH 203 at Concordia: an absolute value opened with the wrong sign, a split where nothing changes, the square root of a square taken without its absolute value, the floor of 2x read on x, a jump price read on the wrong step, and the limit of sine over its angle quoted when the angle does not match. Each trap is written as a wrong line next to the line to copy instead, with the mark it costs.

5. 5
   Limits involving infinity and asymptotes 8 traps traps exercises

   What actually costs marks on limits involving infinity and asymptotes in MATH 203 at Concordia: a numerator divided term by term only halfway, a negative exponent taken for the dominant one, the square root of x squared written as x at minus infinity, a root split over a sum, an asymptote declared where the factor cancels, an exponent law misapplied, and a long division without its placeholder. Every trap is a wrong line next to the line to copy, with the mark it costs.

6. 6
   Continuity 8 traps traps exercises

   What actually costs marks on continuity in MATH 203 at Concordia: a factorization stopped halfway, a repeated factor cancelled once and called removable, a complex fraction cleared with the wrong sign, an absolute value split on one side only, the IVT applied across a hole, and a bisection run in degree mode. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

The derivative and its rules

1. 7
   The derivative at a point and as a function 8 traps traps exercises

   What actually costs marks on the definition of the derivative in MATH 203 at Concordia: a minus sign that reaches only half of a square, a complex fraction subtracted without its common denominator, a conjugate forgotten under a root, f prime of 3 read as the derivative of a number, a continuous function called differentiable, and a rate read as an amount. Each trap is a wrong line next to the line to write instead, with the mark it costs.

2. 8
   Differentiation rules 9 traps traps exercises

   What actually costs marks on the differentiation rules of MATH 203 at Concordia: a coefficient moved with the power, one added to a negative exponent, the minus sign of the quotient rule stopped after one term, a complex fraction differentiated as it stands, an excluded value kept after cancelling, a tangent line without its shift, a zero velocity taken for a turn, and the price taken for the marginal revenue. Every trap is a wrong line next to the line to copy, with the mark it costs.

3. 9
   Trigonometric derivatives 8 traps traps exercises

   What actually costs marks on the trigonometric derivatives of MATH 203 at Concordia: a minus sign lost on cosecant or cotangent, the power rule applied to secant squared, a term cancelled instead of a factor, the quotient rule written in the wrong order, a calculator left in degrees, the single angle returned by inverse cosine, and solutions lost by dividing. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

4. 10
   The chain rule 8 traps traps exercises

   What actually costs marks on the chain rule in MATH 203 at Concordia: the forgotten inside derivative, the exponent computed in the wrong direction, a reciprocal differentiated as one over the derivative, a factorisation taken at the higher power, a table read in the wrong row, the power rule applied to 2 to the minus x, points where the derivative does not exist, and the product rule skipped in a second derivative. Every trap is a wrong line next to the line to copy instead.

5. 11
   Implicit differentiation 8 traps traps exercises

   What actually costs marks on implicit differentiation in MATH 203 at Concordia: the sign lost when a term crosses the equal sign, the dy/dx forgotten on the other side, the fraction with a square root not cleared, a negative exponent turned upside down, a line given as the answer to a horizontal-tangent question, the complex fraction of y'' multiplied on one floor only, a parameter left in a slope, and a calculator that refuses a cube root. Every trap is a wrong line next to the line to copy, with the mark it costs.

6. 12
   Derivatives of inverse functions and logarithms 9 traps traps exercises

   What costs marks on section 3.8 in MATH 203 at Concordia: the slope of an inverse read at the wrong point, the logarithm of a sum split like a product, the domain lost when a logarithm is expanded, the ln a forgotten in a base other than e, the power rule applied to 2 to the x, logarithmic differentiation of a sum, and a yearly percentage taken for a relative rate. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

7. 13
   Inverse trigonometric functions 8 traps traps exercises

   What actually costs marks on the inverse trigonometric functions in MATH 203 at Concordia: an angle outside the range, the wrong sign in the reference triangle, the degree mode, the absolute value dropped in the derivative of arcsec, a chain factor lost, a square applied to half of 3x, and one constant claimed for two intervals. Every trap is a wrong line next to the line to copy instead, with the mark it costs.

Applications of the derivative

1. 14
   Related rates 8 traps traps exercises

   What actually costs marks on related rates in MATH 203 at Concordia: not the chain rule, but the algebra around it. A square root of a difference split in two, a diameter used for a radius, a fraction squared on top only, the derivative of a product or of a reciprocal invented, a negative rate written positive, hours left where minutes were asked. Every trap is a wrong line next to the line to copy, with the mark it costs.

2. 15
   Linearization and differentials 8 traps traps exercises

   What actually costs marks on linearization in MATH 203 at Concordia: a negative exponent read as a negative number, the rule (1 + x) to the k applied without factoring, the sign of the increment lost, degrees fed to the tangent function, the side of the error announced backwards, a relative error written as the wrong percentage, and the error of a diameter put on the radius. Every trap is a wrong line next to the line to copy, with the mark it costs.

3. 16
   L'Hôpital's Rule 8 traps traps exercises

   What actually costs marks on L'Hôpital's Rule in MATH 203 at Concordia: the rule used on a form that is not indeterminate, the two factors of a product differentiated, a factor sent downstairs without flipping its exponent, a complex fraction cleared upside down, infinity minus infinity answered 0, 1 to the infinity answered 1, the limit of the logarithm given as the answer, and one round too many after the form became c over 0. Every trap is a wrong line next to the line to copy instead, with the marks it costs.

4. 17
   Extreme values of functions 7 traps traps exercises

   What actually costs marks on section 4.1 of Thomas in MATH 203 at Concordia: a critical point lost by dividing by a factor, a negative exponent left in f prime, an endpoint called critical, a calculator that reads minus two to the fourth as minus sixteen, an error message on a fractional power of a negative number, degree mode, and a table of f prime instead of f. Every trap is a wrong line next to the line to write instead, with the mark it costs.

5. 18
   Monotonic functions and the First Derivative Test 8 traps traps exercises

   What actually costs marks on section 4.3 of Thomas in MATH 203 at Concordia is rarely the test itself: it is the algebra before it. A minus sign of the quotient rule applied to one term, a cos x divided away, a lowest power never factored out, a number outside the domain read as a maximum, an inequality multiplied by a denominator of unknown sign. Every trap is written as a wrong line next to the line to copy, with the mark it costs.

6. 19
   Concavity and curve sketching 8 traps traps exercises

   What actually costs marks on concavity and curve sketching in MATH 203 at Concordia: a second derivative expanded instead of factored, a zero of the second derivative taken for an inflection point, a point where it does not exist forgotten, a fractional power given the wrong sign, a silent second derivative test read as no extremum, and a cusp called an inflection point. Every trap is written as a wrong line next to the line to copy instead, with the mark it costs.

7. 20
   Applied optimization 8 traps traps exercises

   What actually costs marks on the applied optimization chapter of MATH 203 at Concordia: a lost minus sign on a negative exponent, a fraction divided in one term only, a critical number deleted by dividing by x, a root created by squaring, a decimal rounded too early, and an optimum pushed to an endpoint by a cap. Every trap is a wrong line next to the line to copy instead, with the mark it costs.

Functions and limits

1. 1
   Functions, domains and operations 10 traps traps exercises

   The opening chapter of differential calculus, the one students rush through because it looks like review. The only three restrictions that build a domain, the inequality that becomes strict when the root moves to the denominator, the zeros of the denominator to remove from an intersection, composition and its domain built in two steps, the square root of x squared that equals the absolute value, the direction of the shift in a transformation, the range interval reversed by a negative coefficient, and the physical domain that decides whether an optimization answer is acceptable.

2. 2
   Limits and continuity 12 traps traps exercises

   What costs marks on the first differential calculus test: confusing the limit with the value of the function, handling infinity as a number, cancelling without a condition, the square root that produces two horizontal asymptotes, and the Intermediate Value Theorem written up without its hypotheses. With the tables of limit laws, one line per case and a worked numerical example every time, the decision tree for indeterminate forms and a two-parameter piecewise function taken apart step by step.

The derivative

1. 3
   The derivative and its rules 10 traps traps exercises

   What costs marks in the most mechanical chapter of differential calculus: a product differentiated factor by factor, the inside derivative forgotten in the chain rule, the order of the numerator in the quotient rule, the derivative function confused with the derivative at a point when writing the tangent line, the belief that continuity implies differentiability, the power rule applied to a variable exponent, and the forgotten y prime factor in implicit differentiation. With the decision tree that picks the rule from the form, the expected write-up for the equation of a tangent line, and an implicit differentiation taken apart step by step.

2. 4
   Derivatives of transcendental functions 10 traps traps exercises

   What costs marks on the second differential calculus test: the u prime factor forgotten at every layer, the power confused with the exponential, cos(x²) taken for cos²x, the domain of the logarithm checked too late, the absolute value forgotten in arccos(3/x), the missing sign on arccosine and the extra sign on the hyperbolic cosine. With the tg, cotg and cosec notation of French-language Quebec textbooks, the logarithms that simplify like ln(sec x + tan x), the decision tree that picks the rule from the FORM of the expression, logarithmic differentiation written out step by step, and a quotient of three factors taken apart down to the numerical check.

3. 5
   Implicit differentiation 8 traps traps exercises

   What costs marks on curves defined by an equation: the factor y prime forgotten as soon as a term contains y, the product rule skipped on x y, the lower branch lost by solving for y before differentiating, the vertical tangent announced without looking at the numerator, and the second derivative computed without differentiating y prime again. With the decision tree that reads the quotient according to what vanishes, the tangent line written up for the marker, and a conic worked through all the way to its points with a horizontal tangent.

Applications of the derivative

1. 6
   Related rates 7 traps traps exercises

   The chapter where differentiating costs almost nothing and translating the problem costs everything: substituting a value before differentiating, missing the similarity relation that leaves two unknowns for one equation, confusing the length of the shadow with the position of its tip, differentiating an angle in degrees, taking a negative rate for a sign error, and treating a varying quantity as a constant. With the six-step method, the write-up the marker expects and a shadow problem taken apart.

2. 7
   Differentials and linear approximation 7 traps traps exercises

   The shortest chapter of differential calculus, and the one where exam papers mix things up the most: the differential and the actual change, absolute and relative error, a base point chosen far from the target value, the direction of the error according to concavity, and the approximation used well beyond its range of validity. With the decision tree that picks the base point, the expected write-up for an error propagation and a cube root estimate taken apart step by step.

3. 8
   Applications of the derivative 7 traps traps exercises

   The chapter of theorems, where students lose marks on the hypotheses rather than on the computations: Rolle's Theorem applied to a function that is not differentiable at a point, a critical number taken for an extremum although the derivative does not change sign, displacement confused with distance travelled in a motion that changes direction, L'Hôpital's rule applied to a form that is not indeterminate, and Newton's method started from a point that makes it diverge. With the decision tree that picks the theorem from the verb of the question.

4. 9
   Rectilinear motion 8 traps traps exercises

   What costs marks on the kinematics application of the derivative: a negative acceleration read as slowing down, the displacement given instead of the total distance travelled, a zero velocity taken for a turnaround, the velocity graph read as if it were the position graph, and an acceleration believed to be zero at the top of a free fall. With the decision tree that says which function to look at depending on the verb of the question, the distance travelled written up step by step and a complete motion over four seconds worked through.

5. 10
   Rolle's theorem and the mean value theorem 8 traps traps exercises

   What costs marks on the mean value theorems: a hypothesis skipped because it seemed obvious, uniqueness claimed when the theorem only gives existence, an invented value of c, a function declared constant on a domain in two pieces, and the mean value inequality applied with a local bound. With the tree that picks the theorem from the verb of the question, the write-up the marker expects and an example worked out down to the exact value of c.

6. 11
   Bisection, Newton's method and fixed-point iteration 8 traps traps exercises

   What costs marks when solving equations numerically: Newton's method started without checking that the derivative is nonzero, convergence taken for granted while the sequence cycles, the number of bisection iterations confused with the number of decimals, the rewrite x equals g of x chosen without looking at the derivative, and a stopping criterion based on the value of f alone. With the decision tree that picks the method from the data, the write-up the marker expects and a cubic equation worked through all the way to a certified bracket.

7. 12
   L'Hôpital's rule and indeterminate forms 8 traps traps exercises

   The chapter as differential calculus meets it, and what costs marks: the rule applied to a limit that was not indeterminate, the quotient rule confused with differentiating the top and the bottom separately, the indeterminate form not checked again at the second round, a special limit proved again with the derivative it helped build, an exponential form where you forget to go back to the exponential, and a base that tends to one taken for a base equal to one. With the decision tree of indeterminate forms, the expected write-up sentence and the five-second checks before handing in.

8. 13
   Function analysis and curve sketching 8 traps traps exercises

   The long question of the last Differential Calculus exam, the one where every forgotten step costs two marks: the oblique asymptote looked for when the degrees rule it out, the zero denominator that does not always give an asymptote, the critical number taken for an extremum without a sign change, the inconclusive second derivative test, the zero second derivative taken for an inflection point, and the sketch that contradicts the table without anyone noticing. With the order of the eight steps and a complete analysis taken apart step by step.

9. 14
   Applied optimization 8 traps traps exercises

   The long, heavily weighted problem of the differential calculus final exam. What costs marks: the constraint confused with the function to optimize, two variables kept for lack of a substitution, the physical domain forgotten or taken as closed when it is open, the extremum announced without justification, the endpoint of a closed interval never tested, and the question that asked for the dimensions answered with the value of the maximum. With the six-step method, the decision tree of justifications and a box problem worked through in detail.

Integration

1. 15
   Elementary integration 10 traps traps exercises

   The chapter that closes the differential calculus course, handled with the only tools of the semester: the table of derivatives read from right to left, and checking by differentiation. The sheet takes on what really costs marks: the forgotten constant, the constant set to zero because the initial position is zero, the missing factor you try to pull out of the integral, the exponent lowered instead of raised, the minus one case treated as a power, the absolute value lost in the logarithm and the sign errors on transcendental functions. With the three-column table read backwards, the tree that sorts between reading, rewriting and substituting, the count of constants in a problem with two integrations, and a cart problem taken apart line by line.

Antiderivatives and integration techniques

1. 1
   Antiderivatives and the indefinite integral 8 traps traps exercises

   The first chapter of integral calculus, the one where students invent rules: the forgotten constant, the product and the quotient supposedly integrable term by term, the dx lost while substituting, the antiderivative of one over x written without an absolute value, a substitution forced when the inner derivative is missing, and the forgotten return to the original variable. With the tree that recognizes a substitution form, the check by differentiation, and a stubborn substitution taken apart step by step.

2. 2
   Partial fraction decomposition 9 traps traps exercises

   The chapter where marks are lost without a single computing error: the form of the decomposition is read from the denominator, and it is set up before anything else. The sheet gives the required order, how many terms each kind of factor opens, the role of the discriminant, the exact limits of the cover-up method, and the numerical check that catches almost every mistake.

3. 3
   Integration techniques 8 traps traps exercises

   The longest chapter of integral calculus, where the costly mistake is not computing badly but choosing badly: an integration by parts launched on an obvious substitution, the wrong choice of u in integration by parts, the polynomial long division forgotten before partial fractions, a repeated factor decomposed with a single fraction, the reference triangle never drawn after a trigonometric substitution, and the sign lost in the integration by parts formula. With the decision tree that chooses from the form, and a trigonometric substitution taken apart step by step.

4. 4
   Substitution, parts and partial fractions 11 traps traps exercises

   The three techniques that carry all of CEGEP integral calculus, with the errors that come back on every exam. Limits of integration not changed after a substitution. The dx forgotten in the change of variable. The choice of u made against LIATE. The boundary term evaluated at a single limit. The improper fraction decomposed without dividing first. The repeated factor written only once. The constant numerator put over an irreducible quadratic. With the tree that recognizes the form, the step-by-step decomposition method, and a rational function integrated from start to finish.

5. 5
   Trigonometric integrals 10 traps traps exercises

   The part of integral calculus where you know the technique and still lose marks, for not seeing it through. The return to x never made after a trigonometric substitution. Bounds left in x on an integral in theta. The square root of x squared minus a squared written without an absolute value. Two even exponents attacked with a substitution that cannot work. A quadratic substituted without first completing the square. With the tree that picks the substitution from the root, the three reference triangles, and a definite integral carried through to the end.

6. 6
   Integration tricks: Weierstrass, King's rule, Wallis 10 traps traps exercises

   The techniques of the last question of a final exam, the ones that come in when the four methods of the course have failed. King's rule used as a computation rather than as an equation. The Weierstrass substitution applied across a discontinuity, which cancels the integral. Parity invoked without checking that the function is odd. The Wallis recurrence started without its two base cases. The factor one over x squared forgotten in the substitution that swaps x and its reciprocal. With the tree that recognizes when each trick applies, and an integral folded onto itself in three lines.

Indeterminate forms and improper integrals

1. 7
   Indeterminate forms and L'Hôpital's rule, 201-SN3-RE (201-NYB) 8 traps traps exercises

   The chapter where a very simple rule is misapplied one time in two: the derivative of the quotient computed instead of the quotient of the derivatives, the rule used on a form that is not indeterminate, product, difference and power forms never rewritten as a quotient, the logarithm forgotten in a one-to-the-infinity form, and the rule repeated mechanically on a limit where it goes in circles. With the decision tree of the seven forms, the growth rates and an exponential form taken apart step by step.

2. 8
   Definite and improper integrals, 201-SN3-RE (201-NYB) 8 traps traps exercises

   The central chapter of integral calculus, where marks are lost on questions of definition rather than computation: the integral confused with the area when the function changes sign, the singularity hidden inside the interval that makes an integral improper without anyone noticing, the limit never written before the computation, the two pieces of a doubly improper integral handled together, and the Comparison Test used the wrong way round. With the p-test, the expected write-up and a doubly improper integral worked step by step.

Applications of the integral

1. 9
   Area between curves, 201-SN3-RE (201-NYB) 8 traps traps exercises

   The chapter where the antiderivative is almost never the difficulty. What costs marks: the integral handed in instead of the area when the function changes sign, bounds looked for anywhere but in the intersection equation, the top curve decided by guesswork rather than by a test point, the split forgotten when the roles switch, three vertical integrals where a single horizontal one was enough, and a negative result fixed by redoing the whole computation. With the decision tree for the direction of the strips and a region in horizontal strips worked through step by step.

2. 10
   Numerical integration, 201-SN3-RE (201-NYB) 8 traps traps exercises

   The chapter where you hand in a number without knowing what it is worth. What costs marks: the error bound never computed, the number of subintervals confused with the number of points, the factor h/2 or h/3 left out, Simpson applied with an odd number of subintervals, the maximum of the derivative looked for in the wrong place, and Simpson's coefficients alternating in the wrong order. With the decision tree for the methods, the direction of the error given by concavity and an error bound worked through step by step.

3. 11
   Applications of integration, 201-SN3-RE (201-NYB) 8 traps traps exercises

   The chapter of long formulas, where marks are lost by reciting them instead of rebuilding them: the radius taken equal to the function when the axis of rotation is elsewhere, the washer treated as a solid disk, shell and disk mixed up for not looking at the direction of the slice, arc length computed without squaring the derivative, the average value taken without dividing by the length of the interval, and depth measured from the bottom instead of the surface. With the slice method and a volume worked out step by step.

Parametric curves and polar coordinates

1. 12
   Parametric curves 8 traps traps exercises

   The chapter where you forget that the parameter is a time: the curve treated as the graph of a function although it crosses itself, the second derivative taken as the derivative of the slope with respect to the parameter, the vertical tangent line confused with a cusp, the orientation never shown, the arc length computed without both derivatives, and the parameter eliminated without carrying over the restrictions on the domain. With the decision tree for special tangent lines and one arch of the cycloid worked through step by step.

2. 13
   Polar coordinates, 201-SN3-RE (201-NYB) 8 traps traps exercises

   The chapter where one point has infinitely many names, which sets traps in the simplest questions: the negative radius treated as impossible, the pole forgotten in an intersection because the system does not give it, the polar area written without the factor one half or without the square, bounds taken over a full turn when a single loop is asked for, the number of petals of a rose guessed instead of counted, and the tangent confused with the derivative of the radius. With the decision tree for symmetry and the area of a cardioid worked through step by step.

Sequences and series

1. 14
   Sequences, 201-SN3-RE (201-NYB) 8 traps traps exercises

   The pivot chapter of integral calculus, the one that opens series and that students rush through. What costs marks: the sequence confused with the series it generates, a sequence differentiated like a function without going through the associated function, convergence concluded from monotonicity alone without a bound, the limit of a recursive sequence computed without proving that it exists, the fixed point taken as a proof of convergence, and the converse of the step through the function used as if it were true. With the decision tree of methods and a recursive sequence taken apart step by step.

2. 15
   Infinite series, 201-SN3-RE (201-NYB) 8 traps traps exercises

   The most heavily weighted chapter at the end of the term, and the one where the wrong test gets applied: a general term that tends to zero taken as proof of convergence, the ratio test used on a p-series where it never concludes, comparison used in the wrong direction, an alternating series declared convergent without checking that the terms decrease, the sum of a geometric series computed with the wrong first term, and convergence confused with the value of the sum. With the decision tree of the tests and an integral test worked through step by step.

3. 16
   Series with sin, cos, exp and ln terms, 201-SN3-RE (201-NYB) 11 traps traps exercises

   Series whose general term contains a transcendental function, and the mistakes that come back on every final exam. A general term tending to zero taken as proof of convergence. The ratio test applied despite a limit equal to one. An equivalent used on a difference whose first-order terms cancel. The three conditions of the Alternating Series Test reduced to one. Convergence confused with absolute convergence. With the decision tree that chooses the test, the method for bounding the remainder, and an alternating series with a logarithm worked from start to finish.

4. 17
   Advanced tests: root, condensation, Raabe, Abel, 201-SN3-RE (201-NYB) 11 traps traps exercises

   The tests that come in when the four from the course have failed, and the pitfall that comes with all of them. The equivalent applied to a series whose terms change sign. Condensation used on a sequence that is neither positive nor decreasing. Raabe's test invoked when the ratio does not tend to one. The Cauchy product formed without absolute convergence. The boundary terms forgotten in a telescoping sum. The series of one over n log n believed to converge because its terms are small. With the complete decision tree and the Bertrand family handled by condensation.

5. 18
   Power series and Taylor series, 201-SN3-RE (201-NYB) 8 traps traps exercises

   The last chapter of the semester, the one where equalities get written without saying where they hold. What costs marks: the interval of convergence never given, the two endpoints never tested after the Ratio Test, the factorial forgotten in the denominator, the expansion recomputed from scratch when a substitution into a known series was enough, the centre of the expansion confused with zero, and the remainder never bounded when the question asks for a given precision. With the decision tree of the standard expansions and a substitution worked step by step.

Differential equations

1. 19
   Differential equations 8 traps traps exercises

   The end-of-semester chapter where the constant decides everything. What costs marks: the constant placed after the exponential instead of becoming a factor, the initial condition used before the solving is finished, the absolute value of the logarithm dropped without discussion, the integrating factor applied to an equation not put in standard form, the constant solution lost by dividing, and exponential growth confused with the logistic model. With the decision tree of methods and a cooling problem worked step by step.

Vectors and geometry in space

1. 1
   Vectors in space: the three products 8 traps traps exercises

   What costs marks on products of vectors: the arrow written over a dot product, the half forgotten on the area of a triangle, the sixth forgotten on the volume of a tetrahedron, the cross product treated as if it were commutative, and the projection divided by the wrong power of the norm. With the decision tree that picks the product from what the question asks.

2. 2
   Lines and planes in space 8 traps traps exercises

   What costs marks in the analytic geometry of space: the normal vector taken for a direction vector, the point read off the denominators of the symmetric equations, skew lines mistaken for intersecting ones, the same parameter used for two lines, and the angle between a line and a plane computed with a cosine. With the decision tree of relative positions and a line-plane intersection worked step by step.

Matrices and linear systems

1. 3
   Matrices, systems and determinants 8 traps traps exercises

   What costs marks in matrix algebra: a product set up when it does not exist, the order of the factors reversed, a factor declared zero because a product is zero, the transpose of a product written the wrong way round, the real-number identity applied as is, and division by a matrix, which does not exist. With the recipe for the 2x2 inverse and a system solved in two ways.

2. 4
   Linear systems, Gauss and Gauss-Jordan 8 traps traps exercises

   What costs marks on Gaussian elimination: a row multiplied by zero, two rows replaced at once, a zero row taken for a contradiction, free parameters counted on the equations instead of the pivots, a row echelon form read as if it were reduced, and a homogeneous system declared impossible. With the decision tree of the three cases and a parabola fitted step by step.

3. 5
   Determinants and Cramer's rule 8 traps traps exercises

   What costs marks on determinants: the sum distributed as if on matrices, a common factor taken out once instead of as a power, the checkerboard sign forgotten, the effect of row operations ignored, the transpose forgotten in the adjugate, and a row replaced instead of a column in Cramer's rule. With an order four determinant taken apart step by step.

Vector spaces

1. 6
   Linear combinations, linear dependence and bases 8 traps traps exercises

   What costs marks on the first linear algebra test: a dependent set mistaken for collinear vectors, a combination read by eye without setting up the system, standard components copied as coordinates relative to another basis, and two independent vectors promoted to a basis of space. With the right-hand-side decision tree, the count that settles a question without any computation, and a change of basis worked step by step.

2. 7
   Vector spaces and subspaces 8 traps traps exercises

   What costs marks on the most abstract chapter of 201-SN4-RE: a line that misses the origin promoted to subspace, closure checked on an example instead of proved, the union of two subspaces, the number of spanning vectors taken for the dimension, and the rank-nullity theorem applied to the codomain. With the decision tree that settles on the FORM of the definition and a complete study of a kernel and an image.

Linear transformations and eigenvalues

1. 8
   Linear transformations of the plane 8 traps traps exercises

   What loses marks on transformations of the plane: a composition written in the wrong order, the minus sign of the rotation matrix, the single angle confused with the double angle of a reflection, a zero determinant taken to mean no transformation, and a matrix built from vectors that are not the standard basis. With the catalogue of standard matrices and their determinants.

2. 9
   Eigenvalues and diagonalization 8 traps traps exercises

   What costs marks on diagonalization: the zero vector mistaken for an eigenvector, lambda subtracted somewhere other than the diagonal, an eigenspace reduced to a single vector, the geometric multiplicity assumed equal to the algebraic one, P and D in orders that do not match, and complex eigenvalues mistaken for no eigenvalues at all. With a complete diagonalization and the computation of a power.

3. 10
   Matrix models: Markov, Leontief, Leslie 8 traps traps exercises

   What costs marks on matrix models: the row convention taken for the column convention, the product written in the wrong order, the power of a matrix computed entry by entry, the steady state sought by solving the wrong system, the forgotten normalization, the Leontief inverse replaced by a plain multiplication, and the population wave taken for the stable structure. With the tree that recognizes the model, the write-up of a steady state and a three-program chain worked through from start to finish.

Complex numbers and applications

1. 11
   Complex numbers and De Moivre's theorem 8 traps traps exercises

   What costs marks on complex numbers: the argument chosen with the tangent alone, without looking at the quadrant, division without the conjugate, the modulus distributed over a sum, De Moivre's theorem applied to the algebraic form, a single nth root given out of n, and the square root of a negative number handled as if it were real. With the six sixth roots of 64 worked through step by step.

2. 12
   Applications in science 10 traps traps exercises

   What costs marks in this chapter is never Gaussian elimination, it is the setup. The sheet gives the three-step protocol: name one unknown per unknown quantity, write one equation per constraint, arrange the coefficients in an augmented matrix. It then teaches you to read the rank as a diagnosis of the problem: unique solution, missing constraint, or physically impossible situation. Ten traps with their cost in marks, including the junction rule written once too often, the torque taken about a second point that adds no rank, the confusion between the dot product and the cross product, and the consistent system that nevertheless has no admissible solution.

Describing data

1. 1
   Descriptive statistics 9 traps traps exercises

   When the mean lies and the median tells the truth, why the standard deviation of a sample is divided by n minus 1, how a z-score makes two marks on different scales comparable. Nine mistakes from 201-337 papers with their cost, two decision trees and the trap of the mean of means taken apart.

Probability models

1. 2
   Probability and distributions 9 traps traps exercises

   Mutually exclusive is not independent, a conditional probability cannot be turned around, and the binomial stops working as soon as there is no replacement. Nine errors from the 201-337 course with what they cost, the four counting cases sorted in a decision tree, the continuity correction and a quality control problem worked through step by step.

2. 3
   Continuous random variables and density 9 traps traps exercises

   The chapter where probability stops being a height and becomes an area, and where every reflex from the discrete case breaks down. The sheet sets discrete against continuous line by line, puts a price on the nine traps that cost marks, gives the decision tree that says which area to compute according to the shape of the density, and takes apart a complete example, from the normalizing constant to the centre of gravity. No integral anywhere: rectangles, triangles, trapezoids and the table are enough.

Statistical inference and regression

1. 4
   Estimation and hypothesis testing 10 traps traps exercises

   What a 95 percent interval really says, why the p-value is not the probability that the null hypothesis is true, and why making the sample four times larger only halves the margin. Ten errors from the 201-337 course with their cost, the complete write-up of a test and an election poll taken apart.

2. 5
   Correlation and linear regression 9 traps traps exercises

   Why two unrelated scatter plots can give the same coefficient, why r equal to 0.8 does not mean 80 percent, and what a single distant point does to the slope. Nine 201-337 mistakes with their cost, reading residuals, the two linearizations and a complete regression taken apart.

Logic and proof

1. 1
   Boolean and mathematical logic 9 traps traps exercises

   The implication that is false only once in four rows, the contrapositive confused with the converse, De Morgan applied the wrong way and Karnaugh groups that must hold a power of two cells. Nine 201-N11 errors with their cost, two decision trees and an access control system simplified step by step.

2. 2
   Proof techniques 12 traps traps exercises

   The five structures of the course outline, and above all the move that comes before them: reading the form of the statement to choose the structure before writing the first line. The contrapositive against the converse, which is the mistake of the chapter. Contradiction against the contrapositive, which look alike and are not written the same way. What induction requires instead of proving, and what the pigeonhole principle does not say. Twelve pitfalls with their cost, two decision trees, three model write-ups and an impossibility problem taken apart.

Numbers in a computer

1. 3
   Number systems in computing 9 traps traps exercises

   Remainders read from bottom to top, groups of four bits counted from the right, a two's complement that needs a plus one after the inversion, and an overflow that only shows in the sign bit. Nine 201-N11 mistakes with their cost, two decision trees and an overflowing addition, taken apart step by step.

2. 4
   Modular arithmetic 8 traps traps exercises

   What costs marks in mathematics for computer science: a remainder left negative because the calculator or the C language gives it that way, a congruence cancelled by a factor that is not relatively prime to the modulus, a division attempted where only the inverse exists, an exponent reduced modulo p instead of p minus 1, and Fermat applied to a modulus that is not prime. With the decision tree that says what you may do in a congruence, the modular inverse written up by the extended Euclidean algorithm and a linear congruence taken apart down to its two solutions.

Sets, relations and functions

1. 5
   Set theory and relations 9 traps traps exercises

   Membership confused with inclusion, the empty set that is a subset of everything without belonging to anything, and antisymmetry that is not the absence of symmetry. Nine errors from 201-N11 with their cost, two decision trees and a survey solved by inclusion-exclusion, region by region.

2. 6
   Injective, surjective and bijective functions 9 traps traps exercises

   The decision table of the chapter: a rule, a domain, a codomain, and the nature that comes out of them. The nine false sentences that cost the most marks, each one killed by a counterexample with numbers. The three standard write-ups, prove, prove, disprove, with the concluding sentence to copy. And the four arrow diagrams that give the answer in five seconds on a finite set.

Induction, graphs and counting

1. 7
   Induction and recursion 8 traps traps exercises

   What loses marks on proof by induction and on recursive algorithms: the induction hypothesis stated for every n instead of a fixed rank, the base case skipped because it looks obvious, a single base case for a two-step relation, a naive recursion believed to be linear, and memoization applied where the subproblems do not overlap. With the tree that chooses the form of induction, the one that reads the cost off the relation, and the Towers of Hanoi proved step by step.

2. 8
   Introduction to graphs and matrices 9 traps traps exercises

   The sum of the degrees that equals twice the number of edges, the k-th power that counts the paths of length exactly k, and the matrix product that changes meaning when the order is reversed. Nine mistakes from the 201-N11 course with their cost, two decision trees and a network analyzed matrix by matrix.

3. 9
   Counting and probability 8 traps traps exercises

   What loses marks in counting and probability: the selection model chosen without asking whether order matters, a conditional probability read backwards, equal likelihood assumed where it fails, a union computed without removing the intersection, independence confused with mutual exclusion, and the strength of a hash overestimated by a square. With the tree of the four models, the write-up of a Bayes calculation and the birthday paradox worked through to hash collisions.

Measuring and collecting data

1. 1
   Concepts, variables and measurement scales 8 traps traps exercises

   What costs marks on the first Quantitative Methods exam: the mean computed on codes that are only names, the “twice as much” written on a scale with no absolute zero, the negative item reversed with a minus sign, reliability mistaken for validity, and the conclusion drawn about individuals from data measured on regions. With the decision tree that settles the scale in three questions, the write-up expected when the question asks you to justify a type of variable, and a composite index built from start to finish.

2. 2
   Sampling and questionnaires 8 traps traps exercises

   What costs marks on the sampling chapter: size mistaken for representativeness, the margin of error believed to be proportional to the sample size, the stratified plan confused with quotas, the design effect forgotten in a cluster survey, the response rate mistaken for a measure of bias, and the double-barrelled question that no treatment will ever repair. With the tree that recognizes the plan described by a problem, the write-up of a justification of sample size and a student survey designed from start to finish.

Describing and comparing data

1. 3
   Frequency distributions and graphs 8 traps traps exercises

   What costs marks in the chapter on tables and graphs: cumulative frequencies placed on a variable with no order, the histogram with unequal classes drawn in frequencies instead of densities, the axis cut at 50 that makes a six-point gap look fourfold, the pictograph doubled in height that quadruples its area, the grouped mean computed on the limits instead of the midpoints, and the median read without interpolation. With the tree that picks the graph the scale allows and a raw data set taken all the way to the histogram.

2. 4
   Z scores, percentile ranks and the R score 8 traps traps exercises

   What costs marks in the chapter on standardization: the zero mean and unit standard deviation mistaken for a result, the percentile rank confused with a percentage of correct answers, ten percentile ranks believed equal everywhere, points added for the whole group supposed to raise the Z score, and the R score averaged by course instead of weighted by units. With the Z score and percentile rank correspondence to know by heart, the write-up of a comparison between two groups and a semester record calculated from start to finish.

3. 5
   Index numbers, rates and constant dollars 8 traps traps exercises

   What costs marks in the chapter on rates: successive changes added instead of multiplied, percentage points mistaken for percentages, the total increase divided by the number of years, two index numbers compared by their difference, dollars of two different years put side by side, and the unemployment rate read without looking at its denominator. With the tree that decides which operation to apply to a percentage, and twenty years of salary brought back to constant dollars.

Relationships between variables and polls

1. 6
   Cross-tabulations, chi-square and association 8 traps traps exercises

   What loses marks on the crosstab: the percentage computed in the wrong direction, the chi-square applied to percentages instead of counts, significance mistaken for strength, a failure to reject mistaken for proof of independence, degrees of freedom counted as rows times columns, and causation concluded from a simple cross. With the tree that decides the direction of the percentages, the complete write-up of a test and a 2 by 2 table taken from the chi-square to Cramér's V.

2. 7
   The margin of error of a poll 8 traps traps exercises

   What costs marks on the margin of error: the interval described as if it contained the true value with a 95% chance, the margin believed to cover every bias, the overall margin applied to a subgroup, the gap between two candidates compared with the ordinary margin, the overlap of two intervals taken for a tie, and a majority announced at 51%. With the tree that decides which margin to compute and an election night worked through from start to finish.

Research design

1. 8
   Research design and critical reading 8 traps traps exercises

   What costs marks in the chapter on the research process: the researcher's hypothesis believed to be proven directly, random sampling confused with random assignment, causation concluded from a cross-sectional design, regression toward the mean mistaken for a program effect, a before-and-after with no control group, and the twenty tests of which only the significant one is published. With the tree of the five designs, the write-up of a program evaluation and a peer tutoring program evaluated from start to finish.

Comparing groups

1. 1
   Comparing two groups: t-test and effect size 8 traps traps exercises

   What loses marks on the t-test: the p-value read as the probability that the null hypothesis is true, paired data treated as independent, the pooled variance used on very unequal variances, a failure to reject turned into proof of equivalence, significance mistaken for importance, and a one-tailed test chosen after seeing the data. With the tree that chooses the test, the complete write-up of a comparison and the evaluation of a workshop taken as far as power.

2. 2
   One-way analysis of variance 8 traps traps exercises

   What costs marks in analysis of variance: three t-tests run instead, F taken as an answer to which group differs, mean squares added up like sums of squares, eta squared confused with the p-value, a grand mean computed without weighting by the sample sizes, and post hoc comparisons run at the ordinary level. With the complete ANOVA table, the tree of what to do after a rejection and three teaching methods compared from start to finish.

Controlling for a variable

1. 3
   Multiple regression 8 traps traps exercises

   What costs marks in multiple regression: the partial coefficient read as a raw slope, two coefficients with different units compared directly, the coefficient of determination inflated by useless variables, as many dummy variables as categories, residual shape never looked at, and simple coefficients interpreted despite an interaction. With a decision tree for reading an output, the write-up of a complete interpretation and a term-grade model built from start to finish.

When the normal model fails: rank tests

1. 4
   Nonparametric tests 8 traps traps exercises

   What costs marks on rank tests: ties ranked in order of arrival instead of receiving an average rank, the larger U compared with the critical value instead of the smaller, the median tested without checking equal shapes, Wilcoxon applied to skewed differences, Spearman confused with Pearson, and the mean published after a test that threw it away. With the tree that chooses the rank test, the write-up of a complete Mann-Whitney and two small groups compared all the way to the probability of superiority.

Following a series over time

1. 5
   Time series and forecasting 8 traps traps exercises

   What costs marks on time series: a moving average whose order is not a multiple of the period, an even order never centred, seasonal indices never renormalized, seasonal adjustment done by subtraction in a multiplicative model, a quarter compared with the previous one rather than with the same quarter last year, and two series correlated because they share time. With the decision tree for the additive or multiplicative model and a quarterly forecast carried through from start to finish.

Functions, limits and continuity

1. 1
   Functions and their domain 8 traps traps exercises

   The only three restrictions, and why a root gives a non-strict inequality when a logarithm gives a strict one. The domain of a sum, a quotient and a composition, which is never read off the final formula. The inverse, which swaps domain and range. The three families of models in the course and the domain of validity, the one the paper forgets.

2. 2
   Limits and continuity 9 traps traps exercises

   The three questions asked at a single point, and why they have three different answers. The three tools that resolve an indeterminate form, chosen by its form and not by the topic. The two kinds of asymptote, only one of which is a barrier. The Intermediate Value Theorem, which proves an existence and never a uniqueness. And the piecewise benefit schedule, where continuity is a policy decision.

The derivative and its rules

1. 3
   The derivative and differentiation rules 9 traps traps exercises

   The secant and the tangent, two slopes separated by a single question. The basic rules, with a worked number under each one, and the rule that does not exist. The chain rule, whose inner layer is the number one oversight of the course. The tangent line in point-slope form, the units of the derivative, and what the second derivative really says.

2. 4
   Exponential and logarithmic functions 9 traps traps exercises

   Why the power rule never applies to an exponential, and what the forgotten chain-rule factor costs. The constant relative rate, signature of the exponential, and the doubling time that does not depend on the starting value. The rule of 70 and its range of validity. The semilog scale, which turns an exponential into a straight line.

3. 5
   Implicit differentiation 8 traps traps exercises

   The whole chapter rests on one factor that the chain rule drops at every y: forgetting it costs the entire question, and the wrong result stays plausible. A three-column table gives the derivative of each term and says which one leaves that factor behind. Eight pitfalls, each priced in marks, two decision trees that decide first on the form of the constraint and then on the word in the problem, the two expected write-ups and five figures: the indifference curve and its tangent, the curve carrying two opposite slopes above the same abscissa, the possibilities frontier and its two limiting tangents, the isoquant and the consumer's budget.

Applications of the derivative

1. 6
   Related rates 9 traps traps exercises

   The five steps of the method, in order, and why the fourth can never come before the third. The chain factor that every quantity other than time brings out. The short route of relative rates, which add for a product and subtract for a quotient. And the units, which on their own catch most of the mistakes.

2. 7
   Differentials and linear approximation 9 traps traps exercises

   The difference between the change along the tangent and the change along the curve, and the formula that puts a number on the gap. Why the sign of the second derivative says in advance whether you underestimate or overestimate. Relative errors, which add up for a product and add up again for a quotient, unlike changes. And the margin, below which you comment on nothing.

3. 8
   Curve sketching 9 traps traps exercises

   The seven steps of a study, in order, and why the sketch always comes last. The two independent readings of the table, direction and curvature, with the four shapes they produce. Why a zero derivative only makes a candidate, and why a zero second derivative does not make an inflection point. The three kinds of candidates for an absolute extremum, endpoints included, which students forget.

4. 9
   Applied optimization 9 traps traps exercises

   The five steps of the method, and the difference between the constraint, which eliminates a variable, and the domain, which decides the answer. The four standard forms of the program with their signature at the optimum, a free check on your work. The integer optimum, settled by the geometric mean and not by the midpoint. And the cost of a constraint, the one figure you bring to a negotiation.

Trigonometric functions

1. 10
   Trigonometric functions and their derivatives 9 traps traps exercises

   What costs marks in this chapter comes down to a few moves: answering the month of the peak when the question asks for the month of fastest growth, differentiating with a calculator left in degrees, forgetting the factor left by the inner layer, and confusing the amplitude with the maximum value. The sheet gives the method for reading the four parameters off a scatter plot, the table of derivatives with its numerical check, the two write-ups the marker expects and the quarter-period check.

Calculus in economics

1. 11
   Marginal analysis 8 traps traps exercises

   What costs marks on marginal analysis: marginal cost confused with average cost, marginal revenue mistaken for the price, revenue maximized in place of profit, a fixed cost assumed to move the optimal quantity, the second derivative never checked, and the inflection point of production mistaken for a maximum. With the tree that turns an economic statement into a calculation, the write-up expected for an optimization and a firm worked through from start to finish.

2. 12
   Elasticity and economic optimization 8 traps traps exercises

   What costs marks on elasticity: the slope mistaken for the elasticity when one is constant and the other is not, the forgotten sign, the price rise assumed to always pay, the optimum looked for in the inelastic range, the arc elasticity computed on the starting point, and the revenue of a tax assumed to grow forever. With the tree that decides the range, the write-up of a constrained optimization, and a pricing decision worked through from start to finish.

Measurement and atomic structure

1. 1
   Measurement, significant figures and uncertainty 8 traps traps exercises

   The two rounding rules and what sets them apart, exact numbers, loss of significant figures by cancellation, the tolerance of the five pieces of glassware, the propagation of uncertainties, accuracy against precision, and a titration carried through to the publishable concentration with its uncertainty.

2. 2
   Atomic structure and electron configuration 10 traps traps exercises

   A wavelength left in nanometres. The sign of the energy change, emission against absorption. Electrons of a cation removed from the d subshell instead of the s subshell. Light intensity wrongly believed able to eject an electron. An anion wrongly assumed smaller than its atom. With the decision tree that picks the right energy formula, the method for writing a configuration, and a complete calculation on the hydrogen lamp.

Bonding and molecular structure

1. 3
   Chemical bonding and molecular geometry 9 traps traps exercises

   The geometry of the domains is not the geometry of the molecule. The molecule declared polar because its bonds are. The expanded octet granted to a second-period atom. The lone pair placed in an axial position in a bipyramid. The formal charge calculated with the bonding electrons counted in full. Hydrogen bonding attributed to a hydrogen carried by a carbon. With the tree that deduces the shape from the number of domains, the Lewis method step by step, and two molecules with five and six domains analysed from start to finish.

2. 4
   Hybridization and the quantum model of bonding 10 traps traps exercises

   Pi bonds counted as directions. Lone pairs forgotten in the count, which makes the oxygen of water linear. A double bond taken for two sigma bonds. Rotation believed free about a double bond. Bond order calculated without dividing by two. Oxygen gas declared diamagnetic although a magnet attracts it. With the tree that deduces hybridization from the count, the method for analyzing an organic molecule, and acrylonitrile worked through atom by atom.

3. 5
   Organic molecules, functional groups and isomers 8 traps traps exercises

   Two class periods of organic chemistry in a general chemistry course, with no IUPAC nomenclature or stereochemistry. The seven functional groups and their characteristic groups, the three ways of writing, the valence of four, counting isomers, the two conditions of geometric isomerism, and going from functional group to boiling points and solubilities.

Stoichiometry and gases

1. 6
   Stoichiometry, limiting reactant and percent yield 10 traps traps exercises

   The limiting reactant named by its mass instead of by the ratio of its amount to its coefficient. Subscripts changed to balance an equation. Coefficients read as grams. The oxygen of a combustion analysis calculated from the dioxygen consumed. Successive yields added instead of multiplied. With the conversion map, the limiting reactant method, and an impure limestone analyzed from start to finish.

2. 7
   Gases: Dalton, kinetic theory and real gases 9 traps traps exercises

   Degrees Celsius left in a gas law. The gas constant taken in joules while the pressure is in kilopascals. The water vapour pressure forgotten on a gas collected over water. The mass fraction used in place of the mole fraction. The molar mass left in grams per mole in the root-mean-square speed. The ratio in Graham's law turned upside down. With the tree that picks the law from the data, the method for a gas collected over water, and a hydrogen evolution worked through from start to finish.

Reactions, nomenclature and the periodic table

1. 8
   Redox, oxidation numbers and nomenclature 9 traps traps exercises

   Naming a compound and counting electrons are the same skill. The three methods of nomenclature and how to choose between them, the oxyanion series and the acids, the six oxidation number rules in order with their three exceptions, the five reaction types, balancing by electron balance, and combustion.

2. 9
   Metals, nonmetals and metalloids 8 traps traps exercises

   The position of an element in the periodic table decides everything else. The staircase and the three families, physical states at 25 degrees, metallic bonding and what it explains, ion charges read from the column, the isoelectronic series, the activity series and its two landmarks, the halogens, semiconductor doping and the extraction of metals.

Solutions, energy and states of matter

1. 10
   Solutions and colligative properties 10 traps traps exercises

   Molarity used where molality is needed. The van't Hoff factor forgotten, which halves the effect of salt. Molality calculated on the mass of the solution instead of that of the solvent. The freezing point raised instead of lowered. The mole fraction of the solute used in Raoult's law in place of that of the solvent. The solubility of a gas believed to increase with temperature. With the tree that picks the right concentration, the complete colligative method, and an antifreeze compared with road salt.

2. 11
   Thermochemistry and the first law 10 traps traps exercises

   The heat of the calorimeter mistaken for that of the reaction. Bond energies subtracted the wrong way round. The physical state of water forgotten in an enthalpy of formation. The multiplying factor of an equation not carried over to its enthalpy. The heat capacity of the calorimeter left out. The difference between the internal energy measured in a bomb and the enthalpy measured at constant pressure. With the tree that chooses the calculation method, Hess's law written out step by step, and the combustion of methanol worked through by two independent routes.

3. 12
   States of matter and phase diagrams 10 traps traps exercises

   The specific heat used during a plateau of a phase change. Vapour pressure believed to depend on the amount of liquid. The boiling point taken for a constant of the substance. The melting slope of water lined up with that of other substances. The atoms of a unit cell counted without their fractions. With the heating curve read segment by segment, the full-balance method, and fifty grams of ice followed all the way to steam.

Measurement and reaction rates

1. 1
   Measurement, uncertainty and graphical analysis 10 traps traps exercises

   The coefficient of determination mistaken for a proof, the arc-shaped residuals it cannot see, the uncertainty of a slope looked for where it is not, propagation through a logarithm, the exponent that triples a relative uncertainty, and the systematic error that no repetition corrects. With the table of linearizable laws from the course and the table of propagation rules, each illustrated by a worked calculation.

2. 2
   Chemical kinetics 10 traps traps exercises

   Orders read off the coefficients of the equation. The half-life believed constant whatever the order. Arrhenius temperatures left in degrees Celsius. The catalyst supposed to shift the equilibrium. The rate law of a slow step left with its intermediate. The rate of one species confused with the rate of the reaction. With the tree that identifies the order from the data, the method of initial rates, and a reaction compared by heating it and by catalyzing it.

Equilibrium, acids and bases

1. 3
   Chemical equilibrium 10 traps traps exercises

   Shifting an equilibrium is not changing its constant. Pure solids written into the expression of K. Initial concentrations used in place of equilibrium ones. The small-x approximation used without its test. The RT factor forgotten between Kp and Kc. Total moles counted instead of moles of gas only. The catalyst credited with a better yield. With the tree that predicts the direction of change, the full ICE method, and a dissociation followed by its dilution.

2. 4
   Acids and bases 10 traps traps exercises

   The weak acid treated as a strong acid. The equivalence pH set at seven when the conjugate base pulls it upward. The Henderson ratio inverted. The buffer formula used outside the buffer region. The two ionizations of a polyprotic acid added together. The salt assumed neutral because it comes from a neutralization. With the tree that identifies the region, the buffer method, and an acetate buffer pushed until it breaks down.

3. 5
   Titrations and buffer solutions 6 traps traps exercises

   The equivalence point is almost never at pH 7, the half-equivalence point gives the pKa with no calculation, and diluting a buffer does not change its pH but divides its robustness. The six traps that cost marks, the tree that decides the method according to the nature of the acid and the base, and the worked example of the complete titration of acetic acid with its four regions.

Solubility and electrochemistry

1. 6
   Solubility and the solubility product 10 traps traps exercises

   Two solubility products compared when the salts do not have the same stoichiometry. The relation between Ksp and solubility written with s squared for every salt. The coefficient forgotten in the exponent or in the concentration. The dilution neglected before calculating the ion product. The effect of pH ignored on a salt whose anion is basic. With the tree that picks the relation, the method for selective precipitation, and two silver salts separated quantitatively.

2. 7
   Redox and electrochemistry 10 traps traps exercises

   The standard potential multiplied by a coefficient. The two potentials added instead of subtracted. The anode identified by its sign rather than by oxidation. The number of electrons taken from a single half-reaction. The Nernst quotient written upside down. Oxygen assumed to always have oxidation number minus two. With the tree that links potential, free energy and constant, the method of balancing by half-reactions, and a Daniell cell followed through to the mass consumed.

Thermodynamics and solutions

1. 8
   Chemical thermodynamics 11 traps traps exercises

   Kilojoules subtracted from joules. Temperature left in degrees Celsius. The standard entropy of an element set to zero. A spontaneous reaction mistaken for a fast one. Standard free energy used away from standard conditions. A crossover temperature sought where none exists. With the table of the four cases, the complete method for a spontaneity calculation, and a lime kiln that works well below the predicted temperature.

2. 9
   Solutions and colligative properties 8 traps traps exercises

   Enthalpy taken as the criterion for spontaneity, the van 't Hoff factor of a weak acid announced as two, total pressure slipped into Henry's law in place of partial pressure, the square of the charges forgotten in the ionic strength, a tabulated constant treated as a concentration, Raoult's law cut down to a single term when both liquids are volatile, and an extraction solvent poured in all at once instead of in portions. With the decision tree for colligative properties, the expected concluding sentence and the five-second checks before handing in.

Structure, isomerism and mechanisms

1. 1
   Nomenclature, unsaturation, Z/E and R/S 17 traps traps exercises

   Naming an alkane, an alkene or a ring, choosing the principal functional group, computing the degree of unsaturation, settling Z or E with the CIP rules, then chirality, R and S, the meso compound and optical rotation. Seventeen mistakes that cost marks on exams, four decision trees and the write-ups the marker expects.

2. 2
   Resonance and reaction mechanisms 9 traps traps exercises

   Resonance structures where only electrons move, the carbocation scale that decides everything, and the real Markovnikov rule, which is not a rhyme. Nine exam errors at the CEGEP level, with their cost, the decision tree between SN1, SN2, E1 and E2, and an addition with rearrangement worked through.

Hydrocarbons and alkyl halides

1. 3
   Hydrocarbons 9 traps traps exercises

   The ring that counts as a degree of unsaturation, the branching that lowers the boiling point, and the radical propagation that must regenerate a radical. Nine exam mistakes with their cost, two decision trees and a quantitative combustion worked through to the molecular formula.

2. 4
   Alkyl halides 9 traps traps exercises

   Fluorine, the most electronegative yet the worst leaving group, the aryl halides that refuse to react, and the Grignard reagent that inverts the polarity of carbon. Nine exam mistakes with their cost, the tree that decides between substitution and elimination, and a Grignard synthesis taken apart step by step.

3. 5
   Substitution and elimination: SN1, SN2, E1, E2 10 traps traps exercises

   Everything you need for substitution and elimination, starting from scratch: the vocabulary, the sp3 carbon where the reaction takes place, the table of leaving groups read from the pKa with its two exceptions, the four families of reagents. Then what costs marks: the arrows, the charge balance, the Z and E inventory of the products, the R or S letter you rank again, and a model example written out from start to finish.

Functional groups

1. 6
   Aromatic compounds 9 traps traps exercises

   The four Hückel conditions that get half-forgotten, the addition that is impossible on an aromatic ring, and the halogens that are deactivating yet direct ortho and para. Nine exam mistakes with their cost, the tree of directing effects and a synthesis where the order of the steps decides the isomer obtained.

2. 7
   Alcohols, phenols and ethers 9 traps traps exercises

   The ether that does not associate with itself, the phenol six orders of magnitude more acidic than an alcohol, the tertiary alcohol that refuses to oxidize, and the epoxide that opens on either side depending on the medium. Nine exam mistakes with their cost, two decision trees and two preparations compared on the same alkene.

3. 8
   Aldehydes and ketones 9 traps traps exercises

   The carbon you attack and the oxygen you do not, the aldehyde more reactive than the ketone for two cumulative reasons, and the four tests that tell the two families apart. Nine exam mistakes with their cost, two decision trees and an identification carried out test by test.

4. 9
   Carboxylic acids and derivatives 9 traps traps exercises

   The hierarchy deduced from the pKa of the leaving groups, the addition-elimination that is never a one-step substitution, and the esterification that stalls at two thirds where saponification goes all the way. Nine exam mistakes with their cost, two decision trees and a calculated equilibrium yield.

5. 10
   Amines 9 traps traps exercises

   The class counted on nitrogen and not on carbon, aniline a million times less basic than an ordinary amine, and the synthesis routes that add or remove a carbon. Nine exam mistakes with their cost, two decision trees and an amine preparation compared across three routes.

Spectroscopy and biomolecules

1. 11
   Spectroscopy and structure determination 9 traps traps exercises

   The oxygen that does not count in the degree of unsaturation, the isotope cluster that betrays a bromine at a glance, the exact position of the carbonyl that names the derivative, and the n plus one rule that counts NEIGHBOURS. Nine exam mistakes with their cost, two reading trees and a structure determined by cross-checking the four techniques.

2. 12
   Biomolecules 9 traps traps exercises

   The carbon that decides the series and is not the one you think, the rule for going from Fischer to Haworth, the reducing sugar that keeps one free anomeric carbon, and the amino acid that is never neutral in solution. Nine exam errors with their cost, two reading trees and a calculated isoelectric point.

Synthesis and the laboratory

1. 13
   Synthesis and retrosynthesis 8 traps traps exercises

   You no longer ask which product a reaction gives, you ask which reagents give the target. This sheet does not repeat the reaction toolkit, it carries the habit of working BACKWARD from the target, one bond at a time. The disconnections that pay off at the CEGEP level and the reaction that closes each one, the order of steps on an aromatic ring, where the chapter loses its marks, the overall yield that is a product and never an average, chemoselectivity and the price of a protection. Eight costed pitfalls, two decision trees and the synthesis of 4-bromoaniline taken apart step by step.

2. 14
   Laboratory techniques: purify, measure, report back 10 traps traps exercises

   Where the organic layer is, and why it is never always on top. Why bicarbonate separates what sodium hydroxide mixes. Why washing with hot solvent costs twenty-three times more than washing with cold solvent, and why cooling fast lowers the melting point. What a sharp melting point proves, and what it does not prove. The yield calculated in moles on the right reagent, and what a yield of one hundred and eight percent means.

Measurement and kinematics

1. 1
   Measurement, uncertainty and graph analysis in the lab 7 traps traps exercises

   Absolute uncertainties added in a product, the exponent of a square forgotten, calculator digits copied down, bounds paired the wrong way, consistency judged by eye.

2. 2
   Kinematics in one and two dimensions 9 traps traps exercises

   The acceleration declared zero at the top of a projectile's path, g taken positive on an upward axis, the four constant-acceleration equations applied to a varying acceleration, the forgotten constant of integration, the range formula used for a throw from a cliff. With the decision tree that picks the equation from the missing quantity, the step-by-step method for a projectile, and a throw from a roof worked through from start to finish.

3. 3
   Vector kinematics in two and three dimensions 8 traps traps exercises

   An angle read from the wrong axis, magnitudes added like numbers, the z-component forgotten in a magnitude, a zero velocity at the top of a projectile, an average of velocities used outside uniformly accelerated motion, a slowdown concluded from the sign of one component, and the minimum of a coordinate taken for that of the speed. With the decision tree, the expected write-up and a worked example.

Dynamics and conservation laws

1. 4
   Dynamics, Newton's laws and friction 9 traps traps exercises

   Centrifugal force invented in a curve, the normal force set equal to the weight as soon as a force is applied at an angle, static friction written at its maximum on a body that does not move, the two forces of an action-reaction pair added on the same body, terminal speed sought by setting the speed to zero instead of the acceleration. With the tree that picks the right friction, the one that says which body to isolate, and an inclined plane tied to a hanging mass solved from start to finish.

2. 5
   Work, energy and power 10 traps traps exercises

   The weight counted twice, as work and as potential energy. The height replaced by the length of the slope. The work of friction written as positive. The reference level moved between the start and the end. The loop approached with the height of the top instead of two and a half times the radius. With the tree that decides between energy and Newton, the balance written line by line, and a spring followed all the way up a slope.

3. 6
   Momentum and collisions 9 traps traps exercises

   Kinetic energy conserved in a collision where the bodies stick together. Momentum treated as a positive number when it changes sign with direction. The rebound whose change equals twice the momentum, not zero. The ballistic pendulum solved with a single balance. The billiard ninety-degree angle believed true in every circumstance. With the tree that picks the law according to the type of collision, the two-phase method, and a ballistic pendulum worked through in full.

Rotation, equilibrium and gravitation

1. 7
   Rotation of rigid bodies 9 traps traps exercises

   The moment of inertia used without saying about which axis. The sine forgotten in the torque. The pulley assumed massless when the statement gives it a mass, hence two different tensions. Rotational energy missing from the energy balance of a rolling object. Kinetic energy believed conserved when the skater pulls her arms in. With the decision tree that chooses between torque and energy, the method for a massive pulley, and an Atwood machine solved from start to finish.

2. 8
   Static equilibrium 9 traps traps exercises

   The second condition forgotten. The weight applied at the geometric midpoint of a beam that is not uniform. Friction written at its maximum when nothing is sliding. The smooth wall given a friction force. Tipping tested without sliding, or the reverse. With the tree that picks the pivot, the method for the ladder against a wall, and a loaded ladder problem solved from start to finish.

3. 9
   Universal gravitation 9 traps traps exercises

   Centripetal force, energy and conservation brought together to close mechanics. Altitude mistaken for the distance to the centre. Weightlessness believed to mean no gravity. The high school potential energy formula used at a thousand kilometres of altitude. The minus sign of that energy lost along the way. Escape speed confused with orbital speed. With the tree that chooses between force and energy, the method for putting a satellite into orbit, and a low-orbit satellite worked through from start to finish.

Measurement in the lab

1. 1
   Lab measurements, uncertainties and graphical analysis 8 traps traps exercises

   Absolute uncertainties added in a quotient, a square forgotten as doubling the relative uncertainty, a parallel combination treated as a product, a voltmeter that skews the reading however often you repeat it, a component tolerance confused with an uncertainty, a regression slope taken for a result with no uncertainty, and an internal resistance obtained by subtracting two almost equal voltages. With the decision rule, the conclusion sentence expected and the five-second checks before handing in.

Electrostatics

1. 2
   Electric charge, field and potential 8 traps traps exercises

   Fields added as plain numbers instead of components. The zero-field point searched for between two charges of opposite signs, where it cannot be. The sign of the charge forgotten in the potential. Pairs counted twice in the energy of a system. Zero flux mistaken for zero field. With the tree that decides between vector and scalar, the write-up expected for Gauss's law, and an electron gun solved from start to finish.

2. 3
   Gauss's law 6 traps traps exercises

   A zero flux does not mean a zero field, an outside charge does create a field on the surface, and the formula for a uniform sphere does not apply to a varying density. The six traps that cost marks, the tree that chooses the Gaussian surface according to the symmetry, and the worked example of the solid insulating sphere with the matching of its two regions.

3. 4
   Electric potential and capacitors 6 traps traps exercises

   Never confuse the vanishing of the potential with that of the field, never believe that capacitance depends on the charge, never apply the resistor combination rules to capacitors. The six traps that cost marks, the tree that picks the method according to the geometry, and the example of a network of four capacitors taken apart in both directions.

Direct-current circuits

1. 5
   Direct-current circuits 8 traps traps exercises

   The sum of reciprocals not inverted in parallel. The battery's terminal voltage taken as its emf while it delivers current. Resistor rules applied to capacitors, where everything is reversed. The negative Kirchhoff current that gets redone instead of interpreted. The capacitor believed charged after one time constant. With the folding tree, the write-up expected for Kirchhoff, and a complete network solved then checked with the power balance.

2. 6
   RC circuits in direct current 7 traps traps exercises

   The RC circuits of the revised Electricity and Magnetism course, and what costs marks there: kilohms and microfarads multiplied without conversion, a capacitor voltage that would jump at closing, the wrong resistance in the time constant, the charging formula used for a discharge, energy that would decay like the voltage.

Magnetism and induction

1. 7
   Magnetism and induction 8 traps traps exercises

   The sine forgotten when the velocity is parallel to the field. The right-hand rule applied as is to an electron. The magnetic force made to accelerate the particle. The cyclotron period believed to depend on the speed. The flux angle measured from the plane of the coil. The intense but constant field from which an emf is expected. With the decision tree of the paths, the write-up of Lenz's law, and the rod on rails checked by the power balance.

2. 8
   Electromagnetic induction 6 traps traps exercises

   A strong but constant field induces nothing, an induced current opposes the change and not the field, and an emf exists even without a closed circuit. The six traps that cost marks, the tree that decides which of the three causes of flux change is at work, and the worked example of a coil in a field that rises and then falls, where the emf vanishes exactly at the maximum.

3. 9
   Sources of the magnetic field 8 traps traps exercises

   Electrostatics reflexes carried over to where they do not apply. The field drawn radially when it circles. The formula for the whole loop applied to a semicircle. The total number of turns mistaken for the number per metre. The enclosed current confused with the total current in a coaxial cable. The finite wire treated as an infinite one. With the tree that chooses between Biot-Savart and Ampère, the write-up of Ampère's law, and a coaxial cable handled region by region.

Transients, oscillations and AC circuits

1. 10
   RC, RL and RLC circuits 9 traps traps exercises

   The time constant of an RL written like that of an RC. The inductor current made to jump at closing. The capacitor voltage made to jump too. The energy believed to be conserved in a transfer between two capacitors. The inductor voltage not allowed to exceed the source voltage. AC voltages added like plain numbers. With the tree of the two instants, the write-up of just before and just after, and a series resonance worked through from start to finish.

Geometric optics and lab work

1. 1
   Geometric optics and optical instruments 8 traps traps exercises

   Focal lengths added instead of powers. The intermediate image of a microscope forgotten. The real image of a mirror looked for behind the mirror. Nearsightedness corrected with a converging lens. Magnification confused with the sharpness of an instrument, which depends only on the diameter. With the tree for chaining two lenses, the write-up of an eye correction, and a microscope worked from start to finish.

2. 2
   Lab measurements, uncertainties and graphical analysis 8 traps traps exercises

   An angular uncertainty left in degrees in front of a sine derivative, a whole-number count taken for an exact measurement, a background averaged instead of subtracted, a square root you forget halves the uncertainty, resolving power confused with accuracy, a regression slope announced without an uncertainty, and a weak source declared active when its signal is smaller than its noise. With the decision rule, the expected concluding sentence and the five-second checks before handing in.

Oscillations, waves, sound and light

1. 3
   SHM and mechanical waves 8 traps traps exercises

   The wave speed confused with the speed of a point of the medium. The period believed to depend on the amplitude. The frequency supposedly changed by changing the string. The spring cut in half whose stiffness is divided instead of doubled. The power believed proportional to the amplitude when it goes as its square. With the decision tree of periods, a full reading of a wave equation, and an oscillator treated by energy from start to finish.

2. 4
   Sound and standing waves 8 traps traps exercises

   Two sources of sixty decibels that would give one hundred and twenty. The doubled distance that would halve the level. The closed pipe treated like an open pipe, with even harmonics that do not exist. The Doppler shift of a moving observer treated like that of a moving source. Nodes spaced one wavelength apart instead of a half. With the pipe decision tree, the write-up of a decibel calculation, and an organ pipe tuned by its beats.

3. 5
   Doppler effect: signs, radial component and echo 9 traps traps exercises

   The central move: decide whether the frequency must go up or down BEFORE writing down a single sign. The four simple cases in a grid, the general two-mover formula on an oriented axis, the radial component that vanishes at the moment of passing, the wind that moves the medium, the double shift of an echo, the harmonic mean of a rotating source and the cosine error of measuring instruments.

4. 6
   Wave optics 9 traps traps exercises

   The diffraction condition used as a condition for maxima. The narrow slit from which a narrow spot is expected. The reflection phase shift forgotten in a thin film. Malus's law applied to unpolarized light. The factor of two of the Michelson dropped along the way. With the tree that sorts interference from diffraction, the write-up of a thin film, and an antireflection coating worked from start to finish.

Modern physics

1. 7
   Modern physics 9 traps traps exercises

   The intense light from which faster electrons are expected. The threshold wrongly thought to be crossable by waiting. The negative energy levels subtracted the wrong way. The doubled temperature that would double the radiated power. The two half-lives after which nothing would be left. The atomic mass unit left in kilograms. With the decision tree that picks the relation, the write-up of a photoelectric problem, and an illuminated metal worked through from start to finish.

2. 8
   Quantum physics: photons, line spectra and duality 7 traps traps exercises

   The wavelength left in nanometres, intensity confused with photon energy, the Rydberg formula not inverted, the Bohr radius growing as n instead of n squared, forgetting Z squared and screening.

3. 9
   Nuclear physics and radioactivity 6 traps traps exercises

   Never judge stability by the total binding energy, never forget the two electron masses of beta-plus decay, never believe a source is extinguished after two half-lives. The six pitfalls that cost marks, the tree that picks the decay mode from the position of the nucleus, and the worked example of a complete alpha decay with its recoil.

4. 10
   Special relativity 6 traps traps exercises

   Spot the proper time and the proper length before any calculation, never combine dilation and contraction in the same story, refuse relativistic mass, and check every result with the invariant. The six traps that cost points, the tree that decides which formula to apply from what the problem gives, and the muon example worked in both reference frames.

Heat and climate

1. 11
   Heat, temperature and heat transfer 7 traps traps exercises

   Degrees Celsius under a fourth power, flows added in a wall instead of resistances, latent heat forgotten, Newton's law applied to the temperature instead of the difference, thickness left in centimetres.

2. 12
   Greenhouse effect, albedo and radiative forcing 6 traps traps exercises

   The climate issues of the new waves and modern physics course, and what costs marks there: the forgotten factor of 4, albedo mistaken for the absorbed fraction, CO₂ forcing treated as proportional, feedbacks multiplied instead of divided, equilibrium assumed to be instantaneous.