The ultimate Cambridge International A Level Mathematics (9709) exam preparation package. Grounded in the 2023-2025 examiner reports, this package contains structural paper insights, tactical time-management guidance, highly recurring mark-loss alerts, and verified calculator methods to secure your A*.
閱讀時間 4 分鐘更新於: 2026年6月21日
試卷概覽
卷數
6
總分
350
考試時間
8小時 40分鐘
題型
1
試卷
時間
分數
題數
比重
題型
9709/15
1小時 50分鐘
75
11
30%
Structured
9709/25
1小時 15分鐘
50
8
20%
Structured
9709/35
1小時 50分鐘
75
11
30%
Structured
9709/45
1小時 15分鐘
50
7
20%
Structured
9709/55
1小時 15分鐘
50
7
20%
Structured
9709/65
1小時 15分鐘
50
7
20%
Structured
評級
A*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: AO1: Knowledge and understanding (50%)
AO2: AO2: Application and analysis (50%)
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: 3Quadratics (Pure Mathematics 1)
Writing down only the final roots of a quadratic equation with zero supporting algebraic steps.
如何避免: Show intermediate factorisation, explicit quadratic formula substitution, or completing the square steps. The syllabus explicitly penalises calculator-only quadratic solutions with zero marks.
Omitting the constant of integration (+c) when solving indefinite integrals or differential equations before substituting boundary conditions.
如何避免: Always write '+ c' immediately upon integrating, and solve for it before substituting values or reorganising the function.
3high涉及分數: 4Differentiation (Pure Mathematics 3)
Working in degree mode on the calculator when differentiating, integrating, or applying limits to trigonometric variables.
如何避免: Always switch your calculator to RADIAN mode when performing any calculus operations or when solving trigonometric equations where the interval is specified in radians.
4medium涉及分數: 2The normal distribution (Probability & Statistics 1)
Omitting the continuity correction (+/- 0.5) when using the Normal distribution to approximate discrete distributions (Binomial or Poisson).
如何避免: Apply a continuity correction of +/- 0.5 when transitioning from discrete integer boundaries to continuous standard normal intervals (e.g., P(X < 20) becomes P(Y < 19.5)).
5high涉及分數: 1Trigonometry (Pure Mathematics 1)
Premature rounding of intermediate decimals to 3 significant figures, causing cumulative rounding errors in final answers.
如何避免: Keep intermediate values to at least 4 or 5 significant figures (or use exact fractions/surds) and only round your final answer to 3 significant figures (or 1 decimal place for angles in degrees).