Master the Cambridge International AS Level Mathematics (9709) exam with these expert-vetted examiner strategies, covering time management, critical command words, calculator iteration techniques, and how to avoid mark-losing traps in Pure Mathematics 1 and 2.
閱讀時間 4 分鐘更新於: 2026年6月21日
試卷概覽
卷數
2
總分
125
考試時間
3小時 5分鐘
題型
4
試卷
時間
分數
題數
比重
題型
Paper 1 Pure Mathematics 1 (9709/1)
1小時 50分鐘
75
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Paper 2 Pure Mathematics 2 (9709/2)
1小時 15分鐘
50
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評級
ABCDEU
計算機規定
A silent scientific calculator is required where the syllabus permits one. It must NOT be graphical, programmable, or capable of symbolic algebra (CAS), and it must contain no stored programs or notes.
AO1: Knowledge and understanding (60%)
AO2: Application and relation (40%)
根據歷屆試題與評分準則整理（2023–2025）。
計算機程式
Table mode for roots & turning points
Scientific calculator (e.g. Casio fx-991 series)
用途: Tabulate \(y\) across a range of \(x\) to locate sign changes (roots) and approximate maxima/minima.
使用時機: Solving or sketching a function when you want to find where its graph crosses or turns.
步驟
Enter the function in TABLE mode, set the start, end and step, then read where the sign of \(y\) changes or where it peaks.
考試提示: Allowed, but the calculator must be silent, non-graphical, non-programmable and free of stored content; always show the working the mark scheme requires.
Statistics mode (mean, SD & regression)
Scientific calculator (e.g. Casio fx-991 series)
用途: Read the mean \(\bar{x}\) and standard deviation directly, and the gradient/intercept (and \(r\)) of a linear regression for bivariate data.
使用時機: Any data-handling, statistics, or required-practical analysis question.
步驟
Enter the data in STAT mode (1-VAR or A+BX), then recall \(\bar{x}\), \(\sigma\) or the regression coefficients.
考試提示: Allowed, but the calculator must be silent, non-graphical, non-programmable and free of stored content; always show the working the mark scheme requires.
Carry exact values with Ans & memory
Scientific calculator (e.g. Casio fx-991 series)
用途: Keep full-precision intermediate values to avoid rounding errors.
使用時機: Multi-step calculations where premature rounding loses the final accuracy mark.
步驟
Use Ans, STO/RCL or the M+ memory to reuse the unrounded result of each step; round only the final answer.
考試提示: Allowed, but the calculator must be silent, non-graphical, non-programmable and free of stored content; always show the working the mark scheme requires.
Equation solver — to CHECK your working
Scientific calculator (e.g. Casio fx-991 series)
用途: Use the built-in EQN/SOLVE mode to verify roots of quadratics or simultaneous equations you have already solved by algebra.
使用時機: As a check only, after solving by hand.
步驟
Enter the coefficients in EQN mode (or use SOLVE) and confirm they match your worked solution.
考試提示: Allowed, but the calculator must be silent, non-graphical, non-programmable and free of stored content; always show the working the mark scheme requires.
常見錯誤
1high涉及分數: 2Integration (Pure Mathematics 1)
Failing to show explicit limit substitutions in definite integration, depending purely on calculator outputs.
如何避免: Always write out the integrated function in square brackets, show the explicit substitution of the upper and lower limits, and then write down your calculated final value.
2high涉及分數: 2Trigonometry (Pure Mathematics 1)
Dividing both sides of trigonometric equations by active functions (e.g. dividing by sin theta or tan theta) which eliminates valid solution families.
如何避免: Always move all terms to one side of the equation and factorise the expression to find all valid solution sets.
Using Degree mode on calculators instead of Radian mode for calculus and advanced trigonometry calculations.
如何避免: Always check your calculator's screen for 'R' (Radian) mode before working on differentiation, integration, parametric equations, or circular measures.
4high涉及分數: 1Series (Pure Mathematics 1)
Premature rounding of intermediate values (e.g., progressional ratios, sector radii, or coefficients) to 3 significant figures instead of keeping at least 4 significant figures, resulting in inaccurate final answers.
如何避免: Keep intermediate values written to 4 or 5 significant figures (or store them as variables in your calculator's memory), and round to 3 significant figures only in the final answer step.
5medium涉及分數: 2Functions (Pure Mathematics 1)
Omitting the negative roots when resolving equations derived from squared expressions, such as functions manipulation or quadratic trigonometric equations.
如何避免: When clearing squares (e.g., taking the square root of both sides), always state and evaluate both the positive and negative roots (e.g., ±) unless a specific domain restriction forbids it.