Master the Pearson Edexcel International GCSE Further Pure Mathematics (4PM1) with our examiner-backed guide. Learn how to manage the 120-minute papers, prevent accuracy loss through proper exact-value working, score maximum marks on 'Show That' proofs, and implement strategic checks using substitution and numerical methods.
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
200
考試時間
4小時
題型
4
試卷
時間
分數
題數
比重
題型
Paper 1 (4PM1/01)
2小時
100
11
50%
Short Answer (Algebra & Series), Medium Structured (Calculus & Coordinate Geometry), Long Applied (Trig & Coordinate Proof)
Paper 2 (4PM1/02)
2小時
100
11
50%
Short Answer (Trig & Inequalities), Medium Structured (Graphs, Logs & Series), Long Applied (Vectors & 3D Geometry)
評級
9876543U
計算機規定
A scientific or graphical calculator is permitted. Graphical calculators must be in exam mode with all stored programs and data cleared before the exam; the calculator must not be able to retrieve stored text or formulae.
AO1: AO1: Demonstrate knowledge and understanding of mathematical techniques (55%)
AO2: AO2: Apply mathematical techniques to solve problems and prove identities (45%)
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 clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
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 clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
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 clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
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 clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
常見錯誤
1high涉及分數: 3Trigonometry
Premature rounding of intermediate surd and trigonometric values in multi-step questions.
如何避免: Store exact intermediate values in calculator variables (A, B, C, D) instead of writing down and working with truncated decimals.
2high涉及分數: 4Trigonometry
Cancelling out trigonometric terms by dividing both sides of an equation (e.g. dividing by sin A) instead of factorising.
如何避免: Collect all terms on one side of the equation and factorise (e.g. sin A(2cos A - 1) = 0) to avoid losing valid roots in the given interval.
3high涉及分數: 5Calculus
Skipping explicit algebraic integration steps and limit substitutions, presenting only the final numerical value computed by a calculator.
如何避免: Always write down the integrated algebraic expression in square brackets, show the substituted upper and lower limits explicitly as a subtraction, and then solve.
4medium涉及分數: 1The quadratic function
Forgetting to write final formulated quadratic equations with '= 0', leaving only a quadratic expression.
如何避免: Double-check that any final quadratic equation requested contains the equality sign and zero (e.g., 3x^2 - 12x - 81 = 0) to secure the final accuracy mark.
5medium涉及分數: 2Logarithmic functions and indices
Failing to check and reject invalid roots in logarithmic equations.
如何避免: Substitute all calculated x-values back into the original logarithmic arguments; if an argument becomes negative or zero, explicitly state that the root is rejected.