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Mathematics A - H240

19個單元

Pure Mathematics: Proof

Pure Mathematics: Algebra and Functions

Simultaneous equations

Quadratic functions

The modulus function

Curve sketching

Graph transformations

Partial fractions

Models in context

Pure Mathematics: Coordinate Geometry in the x–y Plane

Parametric equations of curves

Parametric equations in context

Pure Mathematics: Sequences and Series

Binomial expansion

Arithmetic sequences

Geometric sequences

Pure Mathematics: Trigonometry

sin, cos and tan for all arguments

Sine and cosine rules

Small angle approximations

Graphs of the basic trigonometric functions

Exact values of trigonometric functions

Inverse and reciprocal trigonometric ratios

Trigonometric identities

Further trigonometric identities

Trigonometric equations

Proof involving trigonometric functions

Trigonometric functions in context

Pure Mathematics: Exponentials and Logarithms

Properties of the exponential function

Gradient of ekx

Properties of the logarithm

Laws of logarithms

Equations involving exponentials

Reduction to linear form

Modelling using exponential functions

Pure Mathematics: Differentiation

Differentiation from first principles

Differentiation of standard functions

Tangents, normals, stationary points, increasing and decreasing functions

Techniques of differentiation

Parametric and implicit differentiation

Constructing differential equations

Pure Mathematics: Integration

Fundamental theorem of calculus

Indefinite integrals

Definite integrals and areas

Integration as the limit of a sum

Integration by substitution

Integration by parts

Use of partial fractions in integration

Differential equations with separable variables

Interpreting the solution of a differential equation

Pure Mathematics: Numerical Methods

Sign change methods

Formal iterative methods

Numerical integration

Use numerical methods in context

Pure Mathematics: Vectors

Magnitude and direction of vectors

Basic operations on vectors

Position vectors

Distance between points

Problem solving using vectors

Statistics: Statistical Sampling

Statistical sampling

Statistics: Data Presentation and Interpretation

Single variable data

Measures of average and spread

Calculations of mean and standard deviation

Outliers and cleaning data

Statistics: Probability

Mutually exclusive and independent events

Modelling with probability

Statistics: Statistical Distributions

Discrete probability distributions

The normal distribution

Selecting an appropriate distribution

Statistics: Statistical Hypothesis Testing

The language of hypothesis testing

Hypothesis test for the proportion in a binomial distribution

Hypothesis test for the mean of a normal distribution

Hypothesis test using Pearson’s correlation coefficient

Mechanics: Quantities and Units in Mechanics

Mechanics: Kinematics

Language of kinematics

Graphical representation

Constant acceleration

Non uniform acceleration

Mechanics: Forces and Newton’s Laws

Newton’s first law

Newton’s second law

Newton’s third law

Applications of vectors in a plane

Frictional forces

Mechanics: Moments

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