Master the AQA AS Further Mathematics (7366) Paper 1 with high-yield strategies for matrix proof, algebraic manipulation, polar coordinate bounds, and exact complex number arguments.
閱讀時間 4 分鐘更新於: 2026年6月21日
試卷概覽
卷數
1
總分
80
考試時間
1小時 30分鐘
題型
3
試卷
時間
分數
題數
比重
題型
Paper 1: Core Pure Mathematics
1小時 30分鐘
80
28
100%
選擇題, Short Written Response, Extended Written Response
評級
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 (60%)
AO2: AO2: Reason, interpret and communicate mathematically (20%)
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.
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 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.
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.
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, …).
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.
常見錯誤
1high涉及分數: 2Proof
Failing to state the base case explicitly or not completing the concluding logical statement in a proof by induction.
如何避免: Explicitly substitute n=1 into both sides of the equation to show they are equal, state the induction assumption clearly, and conclude with the standard multi-line inductive logic sentence.
2medium涉及分數: 3Hyperbolic functions
Incorrectly assuming that if u = sinh x, then the sum of the roots of a quadratic in u equals the sum of the angles x1 + x2 directly.
如何避免: Solve for the roots of the quadratic in u first, and then apply the inverse hyperbolic sine (arsinh) transformation individually to each root before summing.
3high涉及分數: 3Further algebra and functions
Failing to relate 'only one asymptote' to the discriminant of the quadratic denominator of a rational function being strictly negative.
如何避免: Set the discriminant (b^2 - 4ac) of the quadratic denominator strictly less than zero to ensure there are no real roots, meaning no additional vertical asymptotes.
4high涉及分數: 2Complex numbers
Choosing the principal arctangent value (e.g., -pi/3) as the argument of a complex number without verifying its real and imaginary signs on an Argand diagram.
如何避免: Always sketch the complex number on an Argand diagram first. If it lies in the second quadrant, add pi to the negative calculator angle to find the correct argument.
5medium涉及分數: 4Further algebra and functions
Using calculus to find non-intersection of curves when the question explicitly commands 'Without using calculus'.
如何避免: Form a single algebraic equation by equating the two functions, clear any fractions to form a quadratic, and show that its discriminant is strictly negative.
6medium涉及分數: 2Matrices
Assuming matrix multiplication is commutative (e.g., expanding A(I + B) as I + BA or AB + I) during proofs.
如何避免: Always maintain the precise order of terms when expanding or multiplying matrices: A(I + B) = A + AB.