Q: Confusing displacement and distance when integrating velocity functions in kinematics.

Remember that distance is the integral of speed (the absolute area under the velocity-time graph). Check if the velocity crosses the t-axis; if so, integrate the positive and negative regions separately and sum their absolute values.

Q: Writing the hypotheses for statistical hypothesis tests in terms of the sample mean or sample proportion instead of the population parameter.

Always state H0 and H1 using the population parameters 'p' (for binomial proportion) or 'mu' (for normal mean), never 'p-hat' or 'x-bar'.

Q: Sign errors in the factor theorem: assuming that f(a) = 0 implies (x + a) is a factor instead of (x - a).

Remember that if f(a) = 0, then x = a is a root, which means (x - a) is the linear factor.

Question 1

Failing to write down a complete, continuous chain of mathematical steps in 'show that' questions, assuming some algebraic simplifications are 'obvious'.

Accepted Answer

Explicitly state every step of your algebra. If factorising, show the factored expression; if simplifying fractions, show the common denominator explicitly before combining.

Question 2

Omitting the constant of integration (+ C) when performing indefinite integration, particularly inside larger multi-step problems.

Accepted Answer

Always write '+ C' immediately upon removing the integration sign, and use initial/boundary conditions to solve for its value if given.

Question 3

Losing the second solution in trigonometric quadratic equations (e.g. from sin^2(x)) or failing to find all solutions inside the specified interval.

Accepted Answer

Always check the domain, adjust it for any transformed arguments (like 2x or x-30), and use the unit circle or wave symmetry to identify all possible solutions.

Question 4

Failing to verify the nature of a stationary point (maximum vs minimum) when solving optimization or calculus problems.

Accepted Answer

Find the second derivative, evaluate it at the stationary point, and formally state: since d^2y/dx^2 < 0, the point is a local maximum.

Question 5

Confusing displacement and distance when integrating velocity functions in kinematics.

Accepted Answer

Remember that distance is the integral of speed (the absolute area under the velocity-time graph). Check if the velocity crosses the t-axis; if so, integrate the positive and negative regions separately and sum their absolute values.

Question 6

Writing the hypotheses for statistical hypothesis tests in terms of the sample mean or sample proportion instead of the population parameter.

Accepted Answer

Always state H0 and H1 using the population parameters 'p' (for binomial proportion) or 'mu' (for normal mean), never 'p-hat' or 'x-bar'.

Question 7

Sign errors in the factor theorem: assuming that f(a) = 0 implies (x + a) is a factor instead of (x - a).

Accepted Answer

Remember that if f(a) = 0, then x = a is a root, which means (x - a) is the linear factor.

試験	時間	配点	問題数	配点比率	出題形式
Paper 1 (Pure & Mechanics)	1時間 30分	80	18	50%	Objective, Short structured, Multi-step / show that, Structured mechanics
Paper 2 (Pure & Statistics)	1時間 30分	80	18	50%	Objective, Short structured, Multi-step / optimisation, Structured statistics

Mathematics 7356 試験対策

試験の概要

電卓プログラム

Graph: zeros, intersections & turning points

Numerical equation solver

Numerical integration & differentiation

Statistics & probability distributions

よくあるミス

コツを高得点につなげよう