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.
読了時間 4 分更新日: 2026年6月21日
試験の概要
試験数
2
満点
200
制限時間
4時間
出題形式
3
試験
時間
配点
問題数
配点比率
出題形式
Paper 1 (Core Pure)
2時間
100
16
50%
Multiple Choice, Structured Questions
Paper 2 (Core Pure)
2時間
100
16
50%
Multiple Choice / Tick Box, Structured Questions
評価段階
A*ABCDEU
電卓の規定
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%)
過去問と採点基準にもとづいて作成（2022–2023）。
電卓プログラム
Graph: zeros, intersections & turning points
Graphical calculator / GDC (exam mode)
目的: Plot a function to read its roots (zeros), points of intersection, and maxima/minima.
使う場面: Checking solutions, sketching, or solving where an analytic method is hard.
手順
Graph the function(s) and use the built-in zero, intersect and maximum/minimum tools.
試験での注意: 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)
目的: Solve an equation or find a variable numerically when an algebraic route is long or implicit.
使う場面: Iterative or implicit equations, or to confirm an algebraic solution.
手順
Use the equation/zero solver, entering the equation and a sensible starting estimate.
試験での注意: 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 integration & differentiation
Graphical calculator / GDC (exam mode)
目的: Evaluate a definite integral \(\int_a^b f(x)\,dx\) or a gradient \(f'(x)\) at a point.
使う場面: Checking calculus answers, or where only a numerical value is needed.
手順
Use the GDC's numeric integral / derivative function with the limits or the point.
試験での注意: 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.
Statistics & probability distributions
Graphical calculator / GDC (exam mode)
目的: 1-var/2-var statistics, linear regression, and cumulative binomial / normal / Poisson probabilities without tables.
使う場面: Statistics questions and hypothesis tests.
手順
Enter data in the statistics editor, or use the distribution menu (binomial cdf, normal cdf, …).
試験での注意: 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.
よくあるミス
1high影響する配点: 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.
回避方法: Always find where r = 0 and sketch the curve first. Only integrate over the intervals of theta where r is real and defined.
2medium影響する配点: 3Further vectors
Failing to relate normal vectors to the sine of the angle between lines and planes, incorrectly defaulting to the cosine formula.
回避方法: 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影響する配点: 2Proof
Under-developing mathematical induction proofs by leaving out the base case verification details or omitting the final inductive summary statement.
回避方法: Explicitly write out LHS and RHS evaluation for the base case (usually n=1) and end with the standardized inductive conclusion statement.
4medium影響する配点: 2Hyperbolic functions
Losing track of negative signs when differentiating and integrating hyperbolic trigonometric functions (e.g. thinking d/dx(cosh x) is -sinh x).
回避方法: 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影響する配点: 4Differential equations
Losing track of multiple physical constants (mass m, damping R, stiffness k) during algebraic manipulations in second-order differential equations.
回避方法: Keep terms bracketed clearly, use substitutions if necessary, and meticulously trace dimensions to ensure no constants are dropped.