CCEA A2 Further Mathematics: how the 300 marks split across Pure and Applied papers, the limit notation, discriminant checks and toppling conditions that decide marks, and a timed plan for both 135-minute papers.
閱讀時間 5 分鐘更新於: 2026年9月3日
試卷概覽
卷數
2
總分
300
考試時間
4小時 30分鐘
題型
12
試卷
時間
分數
題數
比重
題型
A2 1: Pure Mathematics
2小時 15分鐘
150
11
50%
First-order Differential Equations, Improper Integrals & Inverse Hyperbolics, Polar Coordinates Area Integration, Second-order Non-homogeneous Differential Equations, Hyperbolic Definitions & Algebraic Equations, Summation of Series & Method of Differences, Reduction Formulae & Definite Integrals, Maclaurin Series & Small Angle Approximations, Trigonometric Forms & Proof by Induction, Inverse Hyperbolic Calculus & Bounded Regions, Complex Numbers Roots & de Moivre Trigonometry
A2 2: Applied Mathematics
2小時 15分鐘
150
10
50%
Applied option questions, answer two of four sections under a permitted pairing
評級
A*ABCDE
計算機規定
Calculators are required and permitted throughout both A2 1 and A2 2, there is no non-calculator paper. Computer algebra systems that manipulate algebra symbolically are explicitly banned for this specification, and calculators must not have any retrievable information stored in them, including formulae, notes or programs. A calculator capable of matrix operations to at least order 3 by 3, an iterative or numeric solve function, and summary statistics and standard-distribution probabilities is required for the applied options.
AO1: AO1: use and apply standard techniques, by selecting and correctly carrying out routine procedures and accurately recalling facts, terminology and definitions. (35%)
AO2: AO2: reason, interpret and communicate mathematically, by constructing rigorous mathematical arguments including proofs, making deductions and inferences, assessing the validity of mathematical arguments, explaining reasoning, and using mathematical language and notation correctly. (35%)
AO3: AO3: solve problems within mathematics and in other contexts, by translating problems into mathematical processes, interpreting solutions in their original context, translating situations into mathematical models, using those models, and evaluating outcomes and limitations. (30%)
用途: Compute sample means, standard deviations and t-test or chi-squared statistics directly from data given in the question.
使用時機: The A2 2 Statistics option: two-sample and one-sample t-tests, chi-squared goodness of fit, and confidence intervals.
步驟
Open the statistics menu, enter the sample data or summary values given in the question, select the relevant test from the test menu, and read off the test statistic, then write the formula and substitution on the page so the method marks are visible.
考試提示: This is a live keystroke sequence performed on data printed in the exam, not a stored program. CCEA and JCQ ban any retrievable stored information, formulae or notes.
Memory recall for repeated intermediate values
Casio fx-991EX ClassWiz (or equivalent)
用途: Hold a repeated intermediate value, such as a pooled variance used across two consecutive test statistics, without retyping it.
使用時機: Two-sample t-test questions where the pooled variance or standard error feeds into more than one calculation.
步驟
Calculate the value, press the memory store key and a letter to save it, continue with the rest of the working, then recall it with the same letter when needed again.
考試提示: Clear the memory at the start of the exam and only store values calculated live during the paper, this is not a saved program.
Numeric equation solver as a check
Casio fx-991EX ClassWiz (or equivalent with a numeric solve function)
用途: Confirm a root or critical value already derived algebraically.
使用時機: After solving a differential equation's auxiliary equation or a complex-number root by hand, to catch an arithmetic slip.
步驟
Enter the equation into the solve function, give a starting estimate close to your algebraic answer, and compare the number returned against your own working.
考試提示: Computer algebra systems that solve equations symbolically are banned for this specification. This numeric solver only confirms a number, it does not replace the written method.
常見錯誤
1high涉及分數: 2Pure Mathematics, further calculus
Evaluating an improper integral by substituting the problematic value directly rather than defining an explicit limit first.
如何避免: Write the limit notation, such as the limit as t tends to the boundary value, before evaluating, and show the limit being taken as a separate line.
Confusing critical damping with under-damping when the auxiliary equation's discriminant actually gives equal real roots.
如何避免: Calculate the discriminant explicitly and quote it: zero gives critical damping, negative gives under-damping with complex roots, positive gives over-damping with distinct real roots.
Writing the general solution of a non-homogeneous second-order differential equation as the complementary function alone, omitting the particular integral.
如何避免: State the general solution as complementary function plus particular integral explicitly, and find the particular integral before combining the two.
Dropping the chain rule factor when differentiating a composite hyperbolic function such as arsinh(3x) or tanh(ln root 3x).
如何避免: Identify the inner function first, differentiate it separately, then multiply by the derivative of the outer hyperbolic function.
5high涉及分數: 2Pure Mathematics, proof
Finishing an induction proof with correct algebra but no explicit statement linking the base case and the inductive step to true for all n.
如何避免: Write a specific closing sentence: since it is true for n = 1, and true for n = k implies true for n = k + 1, it is true for all positive integers n.
6medium涉及分數: 3Applied Mathematics, mechanics
Assuming a rigid body topples without checking that the normal reaction at the tipping edge is actually zero.
如何避免: Write the toppling condition explicitly, the normal reaction at the point of contact equals zero, and solve for the toppling angle or position from that equation rather than from intuition.
7medium涉及分數: 3Applied Mathematics, statistics
Calculating a chi-squared test statistic without first pooling expected frequencies below 5, or omitting Yates' continuity correction in a 2 by 2 contingency table.
如何避免: Check every expected frequency before calculating, pool any cell below 5 with a neighbouring category, and apply the continuity correction automatically for any 2 by 2 table.
Treating the Nearest Neighbour algorithm as if it always finds the optimal Hamiltonian route rather than a heuristic that can miss it.
如何避免: State explicitly that Nearest Neighbour gives an upper bound on the optimal tour, not the guaranteed optimum, and compare it with a lower bound method where the question asks for one.