AQA · A-Level · 数学

1 Deduction, contradiction and counterexamples · ⁨演绎法、反证法和反例⁩ 2 Complete cases and counterexamples 3 Irrational roots and infinitely many primes

1 Indices, surds and standard form · ⁨指数、根式与标准形式⁩ 2 Quadratics and inequalities 3 Domains, inverses and composition · ⁨定义域、反函数与复合函数⁩ 4 Polynomial division, remainders and factors 5 Algebraic fractions and excluded values 6 Partial fractions with distinct linear factors 7 Repeated linear factors in partial fractions 8 Linear and quadratic simultaneous equations 9 Rational indices and real domains 10 Surds and conjugate denominators 11 Completing the square and quadratic structure 12 Equations quadratic in another expression 13 Inequalities, fractions and solution sets 14 Regions between linear and quadratic boundaries 15 Modulus graphs and piecewise solutions 16 Reciprocal graphs and asymptotes 17 Inverse graphs and restricted branches 18 Composite functions and intermediate domains 19 Combined graph transformations and order 20 Fitting and refining a function model 21 Polynomial sketches, repeated roots and signs

1 Coordinate geometry and tangents 2 Parametric curves, domains and direction 3 Parametric modelling in motion and design 4 General-form lines and contextual models 5 Shifted circles, chords and tangents

1 Sequences, series and recurrence 2 Binomial expansion and valid approximations 3 Factorials, combinations and binomial coefficients 4 Increasing, decreasing and periodic recurrences 5 Sigma notation, indices and changed limits 6 Arithmetic series and inverse problems 7 Geometric sums, alternating ratios and convergence 8 Repeated-deposit sequence models and timing

1 Right triangles and non-right triangles · ⁨直角三角形与非直角三角形⁩ 2 Radians, identities and trigonometric equations 3 Radian measure, arcs, sectors and segments 4 Small-angle approximations and their limits 5 All-angle definitions, exact values and periodic graphs 6 Reciprocal trigonometric functions and excluded angles 7 Inverse trigonometric branches and principal values 8 Reciprocal identities and one-sided proof chains 9 Compound-angle formulae and geometric proofs 10 Double-angle identities, quadrant signs and squared forms 11 Auxiliary-angle forms, ranges and interval solutions 12 Quadratic trigonometric equations and complete root sets 13 Multiple-angle equations and transformed intervals 14 Trigonometric components and motion models 15 Sine rule, cosine rule and triangle area 16 The ambiguous sine-rule case and valid triangle counts 17 Key-point sketches and transformed tangent domains

1 Exponentials, logarithms and modelling · ⁨指数函数、对数与建模⁩ 2 Exponential graphs and logarithmic inverses 3 Logarithm laws, negative powers and equation domains 4 Logarithmic graphs for power and exponential fits 5 Proportional rates, half-life and model limits

1 Derivatives and stationary points · ⁨导数与驻点⁩ 2 Chain, product, quotient and implicit differentiation · ⁨链式法则、乘积法则、商法则和隐函数求导⁩ 3 Secants, limits and first-principles power derivatives 4 First-principles sine and cosine derivatives 5 Gradient graphs, concavity and inflection tests 6 Rational-power derivatives and valid domains 7 Exponential, logarithmic and trigonometric derivatives 8 Product and quotient rules with retained exclusions 9 Chain rules for nested functions and restricted inputs 10 Inverse derivatives at corresponding points 11 Connected rates, geometry and time units 12 Implicit first derivatives and tangent domains 13 Parametric first derivatives and vertical tangents 14 Tangent and normal equations and gradient conditions 15 Optimisation with constraints, boundaries and rejected roots 16 Constructing differential equations from rate laws

1 Integrals, area and accumulation · ⁨积分、面积与累积量⁩ 2 Substitution, parts and partial fractions 3 Differential equations and numerical solutions · ⁨微分方程与数值解法⁩ 4 The Fundamental Theorem and accumulated change 5 Integration as the limit of rectangle sums 6 Elementary antiderivatives, coefficients and domains

1 Root finding and numerical integration · ⁨求根与数值积分。⁩

1 Vectors and transformation geometry · ⁨向量与变换几何⁩ 2 Reflections, rotations and enlargements · ⁨反射、旋转和位似变换。⁩

1 Sampling and a large data set · ⁨抽样与大规模数据集⁩

1 Data summaries, histograms and interpretation 2 Regression, financial models and residuals · ⁨回归、财务模型与残差⁩

1 Probability, trees and conditional reasoning

1 Binomial, normal and Poisson models · ⁨二项分布、正态分布与泊松分布模型⁩

1 Hypothesis testing and contextual conclusions

1 Accuracy, bounds and compound measures · ⁨精度、界限与复合测量⁩ 2 Kinematics and Newton's laws

1 Kinematics and Newton's laws 2 Integrals, area and accumulation · ⁨积分、面积与累积量⁩

1 Kinematics and Newton's laws

1 Moments, equilibrium and centres of mass · ⁨力矩、平衡与重心⁩