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Mathematics A - H230

19個單元

Pure Mathematics: Proof

Proof
Algebra and Functions
Coordinate Geometry in the x-y Plane
Sequences and Series
Trigonometry
Exponentials and Logarithms
Differentiation
Integration
Vectors

Pure Mathematics: Algebra and Functions

Indices
Surds
Simultaneous equations
Quadratic functions
Inequalities
Polynomials
Curve sketching
Functions
Graph transformations

Statistics

Statistical Sampling
Data Presentation and Interpretation
Probability
Statistical Distributions
Statistical Hypothesis Testing

Pure Mathematics: Coordinate Geometry in the x-y Plane

Straight lines
Circles

Mechanics

Quantities and Units in Mechanics
Kinematics
Forces and Newton’s Laws

Pure Mathematics: Sequences and Series

Binomial expansion

Pure Mathematics: Trigonometry

sin, cos and tan for all arguments
Sine and cosine rules
Graphs of the basic trigonometric functions
Exact values of trigonometric functions
Trigonometric identities
Trigonometric equations

Pure Mathematics: Exponentials and Logarithms

Properties of the exponential function
Gradient of e^(kx)
Properties of the logarithm
Laws of logarithms
Equations involving exponentials
Reduction to linear form
Modelling using exponential functions

Pure Mathematics: Differentiation

Gradients
Differentiation from first principles
Differentiation of standard functions
Tangents, normals, stationary points, increasing and decreasing functions

Pure Mathematics: Integration

Fundamental theorem of calculus
Indefinite integrals
Definite integrals and areas

Pure Mathematics: Vectors

Vectors
Magnitude and direction of vectors
Basic operations on vectors
Distance between points
Problem solving using vectors

Statistics: Statistical Sampling

Statistical sampling

Statistics: Data Presentation and Interpretation

Single variable data
Bivariate data
Measures of average and spread
Calculations of mean and standard deviation
Outliers and cleaning data

Statistics: Probability

Mutually exclusive and independent events
Probability

Statistics: Statistical Distributions

Discrete probability distributions

Statistics: Statistical Hypothesis Testing

The language of hypothesis testing
Hypothesis test for the proportion in a binomial distribution

Mechanics: Quantities and Units in Mechanics

SI units

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
Weight
Newton’s third law
Frictional forces

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