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.
阅读时间 4 分钟更新于: 2026年6月21日
试卷概览
卷数
2
总分
200
考试时间
4小时
题型
4
试卷
时间
分数
题数
比重
题型
Paper 1 (4PM1/01)
2小时
100
11
50%
Short Answer (Algebra & Series), Medium Structured (Calculus & Coordinate Geometry), Long Applied (Trig & Coordinate Proof)
Paper 2 (4PM1/02)
2小时
100
11
50%
Short Answer (Trig & Inequalities), Medium Structured (Graphs, Logs & Series), Long Applied (Vectors & 3D Geometry)
评级
9876543U
计算器规定
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%)
根据历届试题与评分标准整理（2023–2025）。
计算器程序
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.
使用时机: Solving or sketching a function when you want to find where its graph crosses or turns.
步骤
Enter the function in TABLE mode, set the start, end and step, then read where the sign of \(y\) changes or where it peaks.
考试提示: 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.
使用时机: Any data-handling, statistics, or required-practical analysis question.
步骤
Enter the data in STAT mode (1-VAR or A+BX), then recall \(\bar{x}\), \(\sigma\) or the regression coefficients.
考试提示: 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.
使用时机: Multi-step calculations where premature rounding loses the final accuracy mark.
步骤
Use Ans, STO/RCL or the M+ memory to reuse the unrounded result of each step; round only the final answer.
考试提示: 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.
使用时机: As a check only, after solving by hand.
步骤
Enter the coefficients in EQN mode (or use SOLVE) and confirm they match your worked solution.
考试提示: Allowed, but clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
常见错误
1high涉及分数: 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涉及分数: 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涉及分数: 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涉及分数: 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涉及分数: 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.