Master the Pearson Edexcel International A Level Further Mathematics (YFM01) curriculum with this examiner-backed strategy guide. Learn how to manage the strict 1.2-minute-per-mark pace, avoid fatal algebraic sign slips, secure rigorous proof-by-induction marks, and legally leverage your scientific calculator to verify exact solutions.
閱讀時間 4 分鐘更新於: 2026年6月21日
試卷概覽
卷數
3
總分
225
考試時間
4小時 30分鐘
題型
3
試卷
時間
分數
題數
比重
題型
Further Pure Mathematics F1
1小時 30分鐘
75
10
33.33%
Procedural Summation or Induction, Structured Algebra and Equations, Multi-step Proofs and Coordinates
Further Pure Mathematics F2
1小時 30分鐘
75
8
33.33%
Procedural Inequalities & Complex Numbers, Structured Series & Calculus, Long Multi-step Differential Equations
Further Pure Mathematics F3
1小時 30分鐘
75
7
33.33%
Structured Hyperbolics and Coordinates, Long Multi-step Integration & Vectors
評級
A*ABCDEU
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.
根據歷屆試題與評分準則整理（2023–2026）。
計算機程式
Graph: zeros, intersections & turning points
Graphical calculator / GDC (exam mode)
用途: Plot a function to read its roots (zeros), points of intersection, and maxima/minima.
使用時機: Checking solutions, sketching, or solving where an analytic method is hard.
步驟
Graph the function(s) and use the built-in zero, intersect and maximum/minimum tools.
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.
Numerical equation solver
Graphical calculator / GDC (exam mode)
用途: Solve an equation or find a variable numerically when an algebraic route is long or implicit.
使用時機: Iterative or implicit equations, or to confirm an algebraic solution.
步驟
Use the equation/zero solver, entering the equation and a sensible starting estimate.
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.
Numerical integration & differentiation
Graphical calculator / GDC (exam mode)
用途: Evaluate a definite integral \(\int_a^b f(x)\,dx\) or a gradient \(f'(x)\) at a point.
使用時機: Checking calculus answers, or where only a numerical value is needed.
步驟
Use the GDC's numeric integral / derivative function with the limits or the point.
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 & probability distributions
Graphical calculator / GDC (exam mode)
用途: 1-var/2-var statistics, linear regression, and cumulative binomial / normal / Poisson probabilities without tables.
使用時機: Statistics questions and hypothesis tests.
步驟
Enter data in the statistics editor, or use the distribution menu (binomial cdf, normal cdf, …).
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: 2Matrix algebra integration (Unit FP1: Further Pure Mathematics 1)
Sign slips during the expansion of matrix determinants: \( ad - bc \) calculations often missing parenthesis signs on negative terms.
如何避免: Always write negative coefficients inside parenthesis brackets before simplifying, e.g. \( (a)(d) - (b)(c) \).
2high涉及分數: 3Polar coordinates (Unit FP2: Further Pure Mathematics 2)
Integrating polar coordinate equations without expanding trig functions or dropping the \( \frac{1}{2} \) coefficient.
如何避免: Write out the full integration formula \( \frac{1}{2}\int r^2 d\theta \) explicitly first and use double-angle or power-reduction identities (e.g. \( \sin^2 2\theta = \frac{1}{2}(1 - \cos 4\theta) \)) before attempting integration.
3medium涉及分數: 2Further matrix algebra (Unit FP3: Further Pure Mathematics 3)
Failing to divide by the magnitude of the eigenvectors in orthogonal diagonalisation, leaving non-normalised vectors in matrix P.
如何避免: Normalize each column vector in matrix P by dividing the vector's components by its magnitude \( \sqrt{x^2 + y^2 + z^2} \).
4high涉及分數: 3Inequalities (Unit FP2: Further Pure Mathematics 2)
Algebraic slips when manipulating the common denominator in fractional inequalities, especially when multiplying by squared denominators.
如何避免: Do not expand the numerator immediately. Keep the terms factorised to spot common brackets that can be simplified easily.
5high涉及分數: 1Proof (Unit FP1: Further Pure Mathematics 1)
Incomplete mathematical induction statements: failing to link the \( n=1 \) and the final inductive step conclusion cleanly.
如何避免: State the full closing logic: 'If true for \( n=k \), then shown true for \( n=k+1 \). Since it is true for \( n=1 \), the statement is true for all positive integers \( n \) by mathematical induction.'