An evidence-based exam preparation package for Pearson Edexcel International AS Level Pure Mathematics (XPM01). This guide contains structured revision strategies, exact paper profiles for P1 and P2, high-frequency examiner-reported pitfalls, and legal calculator verification methods to secure top-tier marks.
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: Recall, select and use mathematical facts, concepts and techniques (60%)
AO2: Construct rigorous mathematical arguments and proofs (30%)
AO3: Translate real-world and mathematical problems into processes (10%)
過去問と採点基準にもとづいて作成（2023–2026）。
電卓プログラム
Graph: zeros, intersections & turning points
Graphical calculator / GDC (exam mode)
目的: Plot a function to read its roots (zeros), points of intersection, and maxima/minima.
使う場面: Checking solutions, sketching, or solving where an analytic method is hard.
手順
Graph the function(s) and use the built-in zero, intersect and maximum/minimum tools.
試験での注意: Allowed, but clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
Numerical equation solver
Graphical calculator / GDC (exam mode)
目的: Solve an equation or find a variable numerically when an algebraic route is long or implicit.
使う場面: Iterative or implicit equations, or to confirm an algebraic solution.
手順
Use the equation/zero solver, entering the equation and a sensible starting estimate.
試験での注意: Allowed, but clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
Numerical integration & differentiation
Graphical calculator / GDC (exam mode)
目的: Evaluate a definite integral \(\int_a^b f(x)\,dx\) or a gradient \(f'(x)\) at a point.
使う場面: Checking calculus answers, or where only a numerical value is needed.
手順
Use the GDC's numeric integral / derivative function with the limits or the point.
試験での注意: Allowed, but clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
Statistics & probability distributions
Graphical calculator / GDC (exam mode)
目的: 1-var/2-var statistics, linear regression, and cumulative binomial / normal / Poisson probabilities without tables.
使う場面: Statistics questions and hypothesis tests.
手順
Enter data in the statistics editor, or use the distribution menu (binomial cdf, normal cdf, …).
試験での注意: Allowed, but clear stored programs/data (graphical calculators in exam mode) and show the required working — unsupported calculator answers score no method marks.
よくあるミス
1high影響する配点: 2Binomial expansion (Unit P2)
Omission of brackets around algebraic terms during substitution or binomial expansions, such as writing kx^2 instead of (kx)^2.
回避方法: Always use enclosing parentheses when substituting variables or raising algebraic binomial terms containing coefficients to a power.
2medium影響する配点: 3Coordinate geometry in the (x, y) plane (Unit P1)
Skipping explicit surd division and rationalization steps when solving coordinate geometry equations, leading to M0A0 marks.
回避方法: Show the full intermediate multiplication by the conjugate surd (e.g., multiplying numerator and denominator by the denominator's conjugate) to secure method marks.
3high影響する配点: 3Integration (Unit P1)
Failing to include the constant of integration (+c) in indefinite integration questions before solving for boundary conditions.
回避方法: Write '+ c' immediately on the line where the integration operator is removed, before attempting to substitute coordinates to find its value.
4high影響する配点: 2Algebra and functions (Unit P1)
Relying entirely on calculator solvers to obtain roots of quadratic equations or cubic intersections without writing down factorized forms.
回避方法: Always write down the factorized quadratic form (x - a)(x - b) = 0 or the fully substituted quadratic formula before showing the final roots.
5medium影響する配点: 2Proof (Unit P2)
Using the flawed assumption 4k+1 to define all odd integers in proof by exhaustion or deduction tasks.
回避方法: Ensure all cases are covered. Odd integers must be expressed as 2k+1, or if using modulo 4, both 4k+1 and 4k+3 must be separately evaluated and summarized.
6medium影響する配点: 1Proof (Unit P2)
Failing to write down a concluding summary statement in proof by exhaustion or deduction to link the algebraic result back to the initial assertion.
回避方法: Conclude your proof with a final statement such as: 'Since 8n is a multiple of 8 for all integers n, the original statement is proven.'
7high影響する配点: 2Integration (Unit P2)
Converting intermediate fractions or surds into rounded decimals in integration tasks, causing compounding rounding errors.
回避方法: Perform all intermediate steps using exact fractions, exact surds, or log terms, only rounding at the very final step if explicitly asked.