Incorrect polar coordinate integration limits, assuming they always span from -pi to pi or 0 to 2*pi without analyzing domain restrictions where r^2 is positive.

Always find where r = 0 and sketch the curve first. Only integrate over the intervals of theta where r is real and defined.

Failing to relate normal vectors to the sine of the angle between lines and planes, incorrectly defaulting to the cosine formula.

Remember that the dot product of the line's direction vector and the plane's normal vector gives sin(theta), not cos(theta). If using cosine, subtract the resulting angle from 90 degrees.

Under-developing mathematical induction proofs by leaving out the base case verification details or omitting the final inductive summary statement.

Explicitly write out LHS and RHS evaluation for the base case (usually n=1) and end with the standardized inductive conclusion statement.

Losing track of negative signs when differentiating and integrating hyperbolic trigonometric functions (e.g. thinking d/dx(cosh x) is -sinh x).

Verify using the formula booklet or convert to exponential forms if unsure. Remember: d/dx(cosh x) = +sinh x and d/dx(sinh x) = +cosh x.

Losing track of multiple physical constants (mass m, damping R, stiffness k) during algebraic manipulations in second-order differential equations.

Keep terms bracketed clearly, use substitutions if necessary, and meticulously trace dimensions to ensure no constants are dropped.

AQA A-Level · 考試技巧

Further Mathematics 7367 考試技巧

Expert guidance and evidence-based strategies for AQA A Level Further Mathematics 7367. Master high-yield chapters (Complex Numbers and Matrices), avoid critical integration and vector pitfalls, and learn how to use your calculator to verify answers systematically.

閱讀時間 4 分鐘更新於: 2026年6月21日

試卷概覽

卷數

總分

200

考試時間

4小時

題型

試卷	時間	分數	題數	比重	題型
Paper 1 (Core Pure)	2小時	100	16	50%	選擇題, 結構題
Paper 2 (Core Pure)	2小時	100	16	50%	選擇題 / Tick Box, 結構題

評級

A*ABCDEU

計算機規定

A scientific or graphical calculator that meets JCQ regulations may be used (some GCSE Mathematics and Science papers are non-calculator). Graphical calculators must be set to exam mode; you must clear any stored programs, notes or data before the exam, and the calculator must not be able to retrieve stored text or formulae.

AO1: AO1: Use and apply standard techniques (50%)
AO2: AO2: Reason, interpret and communicate mathematically (30%)
AO3: AO3: Solve problems within mathematics and in other contexts (20%)

根據歷屆試題與評分準則整理（2022–2023）。

計算機程式

Graph: zeros, intersections & turning points

Graphical calculator / GDC (exam mode)

用途: Plot a function to read its roots (zeros), points of intersection, and maxima/minima.

使用時機: Checking solutions, sketching, or solving where an analytic method is hard.

步驟

Graph the function(s) and use the built-in zero, intersect and maximum/minimum tools.

考試提示: Allowed under JCQ rules, but you must still show your method — an unsupported calculator answer earns no method marks. Clear all stored programs, notes and data (graphical calculators in exam mode) before the exam.

Numerical equation solver

Graphical calculator / GDC (exam mode)

用途: Solve an equation or find a variable numerically when an algebraic route is long or implicit.

使用時機: Iterative or implicit equations, or to confirm an algebraic solution.

步驟

Use the equation/zero solver, entering the equation and a sensible starting estimate.

Numerical integration & differentiation

Graphical calculator / GDC (exam mode)

用途: Evaluate a definite integral \(\int_a^b f(x)\,dx\) or a gradient \(f'(x)\) at a point.

使用時機: Checking calculus answers, or where only a numerical value is needed.

步驟

Use the GDC's numeric integral / derivative function with the limits or the point.

Statistics & probability distributions

Graphical calculator / GDC (exam mode)

用途: 1-var/2-var statistics, linear regression, and cumulative binomial / normal / Poisson probabilities without tables.

使用時機: Statistics questions and hypothesis tests.

步驟

Enter data in the statistics editor, or use the distribution menu (binomial cdf, normal cdf, …).

常見錯誤

1high涉及分數: 4Polar coordinates
Incorrect polar coordinate integration limits, assuming they always span from -pi to pi or 0 to 2*pi without analyzing domain restrictions where r^2 is positive.
如何避免: Always find where r = 0 and sketch the curve first. Only integrate over the intervals of theta where r is real and defined.
2medium涉及分數: 3Further vectors
Failing to relate normal vectors to the sine of the angle between lines and planes, incorrectly defaulting to the cosine formula.
如何避免: Remember that the dot product of the line's direction vector and the plane's normal vector gives sin(theta), not cos(theta). If using cosine, subtract the resulting angle from 90 degrees.
3high涉及分數: 2Proof
Under-developing mathematical induction proofs by leaving out the base case verification details or omitting the final inductive summary statement.
如何避免: Explicitly write out LHS and RHS evaluation for the base case (usually n=1) and end with the standardized inductive conclusion statement.
4medium涉及分數: 2Hyperbolic functions
Losing track of negative signs when differentiating and integrating hyperbolic trigonometric functions (e.g. thinking d/dx(cosh x) is -sinh x).
如何避免: Verify using the formula booklet or convert to exponential forms if unsure. Remember: d/dx(cosh x) = +sinh x and d/dx(sinh x) = +cosh x.
5medium涉及分數: 4Differential equations
Losing track of multiple physical constants (mass m, damping R, stiffness k) during algebraic manipulations in second-order differential equations.
如何避免: Keep terms bracketed clearly, use substitutions if necessary, and meticulously trace dimensions to ensure no constants are dropped.

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