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Mathematics A - H240

19 sections available

Pure Mathematics: Proof

Proof

Pure Mathematics: Algebra and Functions

Indices
Surds
Simultaneous equations
Quadratic functions
Inequalities
Polynomials
The modulus function
Curve sketching
Functions
Graph transformations
Partial fractions
Models in context

Pure Mathematics: Coordinate Geometry in the x–y Plane

Straight lines
Circles
Parametric equations of curves
Parametric equations in context

Pure Mathematics: Sequences and Series

Binomial expansion
Sequences
Sigma notation
Arithmetic sequences
Geometric sequences
Modelling

Pure Mathematics: Trigonometry

sin, cos and tan for all arguments
Sine and cosine rules
Radians
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

Gradients
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

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
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
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

SI units

Mechanics: Kinematics

Language of kinematics
Graphical representation
Constant acceleration
Non uniform acceleration
Gravity

Mechanics: Forces and Newton’s Laws

Newton’s first law
Newton’s second law
Weight
Newton’s third law
Applications of vectors in a plane
Frictional forces

Mechanics: Moments

Statics

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