Pearson Edexcel · International A-Level

数学

Papers, samples and curriculum documents for this course. · ⁨本课程的文件、样卷和课程大纲。⁩

Qualification code · ⁨资格代码⁩: XMA01 / YMA01

Recent past papers · ⁨近期真题⁩

104 paper and mark-scheme pairs · ⁨真题与评分标准对⁩

Browse papers and mark schemes · ⁨浏览文件和评分标准⁩ →

Course units and learning goals · ⁨课程单元与学习目标⁩

These lessons teach selected course objectives. Check the remaining coverage gaps; the material is not a complete preparation programme. · ⁨这些课程教授选定的教学目标。请检查剩余的覆盖缺口；本材料并非完整的备考方案。⁩

Lessons · ⁨课程⁩ →Vocabulary practice · ⁨词汇练习⁩ →

P1 · Pure Mathematics 1

Indices, surds and standard form: The power to which a base is raised.
Quadratics and inequalities: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
Coordinate geometry and tangents: The change in y divided by the corresponding change in x.
Right triangles and non-right triangles: The side opposite the right angle in a right-angled triangle.
Radians, identities and trigonometric equations: The angle subtended by an arc whose length equals the radius.
Derivatives and stationary points: The instantaneous rate of change, also the gradient of a tangent.
Integrals, area and accumulation: A function whose derivative equals the given integrand.

index: The power to which a base is raised.
discriminant: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
gradient: The change in y divided by the corresponding change in x.
hypotenuse: The side opposite the right angle in a right-angled triangle.
radian: The angle subtended by an arc whose length equals the radius.
derivative: The instantaneous rate of change, also the gradient of a tangent.
antiderivative: A function whose derivative equals the given integrand.

P2 · Pure Mathematics 2

Deduction, contradiction and induction: A single valid case that disproves a universal claim.
Quadratics and inequalities: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
Coordinate geometry and tangents: The change in y divided by the corresponding change in x.
Sequences, series and recurrence: The constant multiplier between consecutive terms of a geometric sequence.
Binomial expansion and valid approximations: The number of ways to choose a specified number of objects from a set.
Exponentials, logarithms and modelling: The time for a decaying quantity to fall to half its initial value.
Radians, identities and trigonometric equations: The angle subtended by an arc whose length equals the radius.
Derivatives and stationary points: The instantaneous rate of change, also the gradient of a tangent.
Integrals, area and accumulation: A function whose derivative equals the given integrand.
Root finding and numerical integration: A repeated update in which each new approximation is calculated from the previous one.

counterexample: A single valid case that disproves a universal claim.
discriminant: The quantity b²-4ac that determines the real roots of ax²+bx+c=0.
gradient: The change in y divided by the corresponding change in x.
common ratio: The constant multiplier between consecutive terms of a geometric sequence.
binomial coefficient: The number of ways to choose a specified number of objects from a set.
half-life: The time for a decaying quantity to fall to half its initial value.
radian: The angle subtended by an arc whose length equals the radius.
derivative: The instantaneous rate of change, also the gradient of a tangent.
antiderivative: A function whose derivative equals the given integrand.
iteration: A repeated update in which each new approximation is calculated from the previous one.

P3 · Pure Mathematics 3

Domains, inverses and composition: The set of allowed inputs to a function.
Radians, identities and trigonometric equations: The angle subtended by an arc whose length equals the radius.
Exponentials, logarithms and modelling: The time for a decaying quantity to fall to half its initial value.
Chain, product, quotient and implicit differentiation: The rule that multiplies the outer derivative by the inner derivative for a composite function.
Integrals, area and accumulation: A function whose derivative equals the given integrand.
Root finding and numerical integration: A repeated update in which each new approximation is calculated from the previous one.

domain: The set of allowed inputs to a function.
radian: The angle subtended by an arc whose length equals the radius.
half-life: The time for a decaying quantity to fall to half its initial value.
chain rule: The rule that multiplies the outer derivative by the inner derivative for a composite function.
antiderivative: A function whose derivative equals the given integrand.
iteration: A repeated update in which each new approximation is calculated from the previous one.

P4 · Pure Mathematics 4

Deduction, contradiction and induction: A single valid case that disproves a universal claim.
Equations, identities and rearrangement: An equality that holds for every allowed value of its variable.
Binomial expansion and valid approximations: The number of ways to choose a specified number of objects from a set.
Conics, parametric curves and tangent reasoning: A representation in which coordinates are expressed using a common parameter.
Chain, product, quotient and implicit differentiation: The rule that multiplies the outer derivative by the inner derivative for a composite function.
Substitution, parts and partial fractions: An integration method based on the derivative of a product.
Differential equations and numerical solutions: A specified value that selects a particular solution from a family.
Spatial vectors, lines and angles: A nonzero vector giving the direction of a line.

counterexample: A single valid case that disproves a universal claim.
identity: An equality that holds for every allowed value of its variable.
binomial coefficient: The number of ways to choose a specified number of objects from a set.
parametric equation: A representation in which coordinates are expressed using a common parameter.
chain rule: The rule that multiplies the outer derivative by the inner derivative for a composite function.
integration by parts: An integration method based on the derivative of a product.
initial condition: A specified value that selects a particular solution from a family.
direction vector: A nonzero vector giving the direction of a line.

M1 · Mechanics 1

Kinematics and Newton's laws: The vector sum of all external forces acting on the modelled object.
Vectors and transformation geometry: The vector sum representing the combined displacement or force.
Moments, equilibrium and centres of mass: Force multiplied by the perpendicular distance from its line of action to a pivot.
Inclined planes, friction and connected particles: The maximum static friction before slipping, equal to μ times the normal reaction in the model.

resultant force: The vector sum of all external forces acting on the modelled object.
resultant: The vector sum representing the combined displacement or force.
moment · ⁨时刻⁩: Force multiplied by the perpendicular distance from its line of action to a pivot.
limiting friction: The maximum static friction before slipping, equal to μ times the normal reaction in the model.

M2 · Mechanics 2

Kinematics and Newton's laws: The vector sum of all external forces acting on the modelled object.
Moments, equilibrium and centres of mass: Force multiplied by the perpendicular distance from its line of action to a pivot.
Work, energy, power and collisions: The ratio of relative separation speed to relative approach speed along the line of impact.
Projectile motion and variable acceleration: A particle moving under gravity after launch in a model that neglects air resistance.

resultant force: The vector sum of all external forces acting on the modelled object.
moment · ⁨时刻⁩: Force multiplied by the perpendicular distance from its line of action to a pivot.
coefficient of restitution: The ratio of relative separation speed to relative approach speed along the line of impact.
projectile: A particle moving under gravity after launch in a model that neglects air resistance.

S1 · Statistics 1

Data summaries, histograms and interpretation: Frequency divided by class width, used as histogram height.
Probability, trees and conditional reasoning: The probability of an event after restricting the sample space to a stated condition.
Regression, financial models and residuals: The observed value minus the value predicted by a fitted model.
Binomial, normal and Poisson models: The probability-weighted mean of a random variable.

frequency density · ⁨频率密度⁩: Frequency divided by class width, used as histogram height.
conditional probability: The probability of an event after restricting the sample space to a stated condition.
residual: The observed value minus the value predicted by a fitted model.
expected value: The probability-weighted mean of a random variable.

S2 · Statistics 2

Binomial, normal and Poisson models: The probability-weighted mean of a random variable.
Sampling and a large data set: The list or population definition from which a sample is selected.
Hypothesis testing and contextual conclusions: The chosen probability threshold for rejecting a null hypothesis.
Continuous distributions and density functions: A nonnegative function whose integral over an interval gives its probability.

expected value: The probability-weighted mean of a random variable.
sampling frame: The list or population definition from which a sample is selected.
significance level: The chosen probability threshold for rejecting a null hypothesis.
probability density: A nonnegative function whose integral over an interval gives its probability.

D1 · Decision Mathematics 1

Algorithms, networks and linear programming: A connected cycle-free network joining every vertex with the smallest possible total edge weight.
Critical paths and scheduling: The time an activity can be delayed without delaying completion under the network model.
Sorting, packing and network algorithms: A finite set of ordered instructions that solves a defined class of problems.

minimum spanning tree: A connected cycle-free network joining every vertex with the smallest possible total edge weight.
float · ⁨浮动⁩: The time an activity can be delayed without delaying completion under the network model.
algorithm: A finite set of ordered instructions that solves a defined class of problems.

Preparing for this qualification · ⁨备考指南⁩

Each examined unit is 90 minutes and 75 marks; calculators must not provide symbolic algebra, differentiation, integration or stored retrievable formulae.
Use the IAL Mathematical Formulae and Statistical Tables booklet, not the UK GCE booklet. A unit may require preceding-unit formulae.
D1 has no archived paper pairs in this collection. Original D1 teaching does not fill that bank gap.
IAS: P1,P2 and one of M1,S1,D1. IAL: P1–P4 and exactly one pair: M1+S1, M1+D1, M1+M2, S1+D1 or S1+S2.

Teaching coverage still needed · ⁨仍需教学覆盖内容⁩

Official question-bank boundaries, scheme alignment and all objective-level teaching coverage require the recorded review; no practice registry promotion.
The authored diagnostic assessments are not full-length qualification mocks.

Specifications and sample documents · ⁨课程大纲和样件文件⁩

Course materials · ⁨课程资料⁩

Course preparation · ⁨课程准备⁩

Documents are available. Board-specific notes, assessments and interactive past-paper practice are not yet available for every course. · ⁨文档已提供。并非所有课程都具备考试局特定的注释、测评及交互式历年真题练习。⁩

Lessons · ⁨课程⁩ →