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Mathematics B (MEI) - H640

21個單元

Pure Mathematics: Proof

Proof

Pure Mathematics: Algebra

Algebraic language
Solution of equations
Inequalities
Surds Indices
Proportion
Partial fractions
Rational expressions

Pure Mathematics: Functions

Polynomials
The language of functions
The modulus function
Modelling

Pure Mathematics: Graphs

Sketching curves
Transformations

Pure Mathematics: Coordinate Geometry

The coordinate geometry of straight lines
The coordinate geometry of curves
Parametric equations

Pure Mathematics: Sequences and Series

Binomial expansions
Sequences
Arithmetic series
Geometric series
Modelling

Pure Mathematics: Trigonometry

Basic trigonometry
Trig. functions
Area of triangle; sine and cosine rules
Identities
Equations
Radians
Secant, cosecant and cotangent
Compound angle formulae
Proofs and problems

Pure Mathematics: Exponentials and Logarithms

Exponentials and Logarithms
Exponentials and natural logarithms
Exponential growth and decay

Pure Mathematics: Calculus

Basic differentiation
Differentiation of functions
Applications of differentiation to functions and graphs
Product, quotient and chain rules
Implicit differentiation
Integration as reverse of differentiation
Integration to find area under a curve
Integration by substitution
Integration by parts
Partial fractions
Differential equations

Pure Mathematics: Numerical Methods

Solution of equations
Integration
Problem solving

Pure Mathematics: Vectors

General vectors
Position vectors
Using vectors

Statistics: Sampling

Population and sample
Sampling techniques

Statistics: Data representation and interpretation

Data presentation for single variable
Data presentation
Summary measures

Statistics: Probability

Probability of events in a finite sample space
Probability of two or more events
Conditional probability

Statistics: Probability Distributions

Situations leading to a binomial distribution
Calculations relating to binomial distribution
Mean and expected frequencies for binomial distribution
Discrete probability distributions
Normal distribution
Modelling with probability

Statistics: Statistical Hypothesis Testing

Hypothesis testing for a binomial probability p
Hypothesis testing for a mean using Normal distribution
Informal hypothesis testing for correlation/ association

Mechanics: Models and Quantities

Standard models in mechanics
Units and quantities

Mechanics: Kinematics in 1 Dimension

Motion in 1 dimension
Kinematics graphs
Calculus in kinematics
Constant acceleration formulae
Problem solving
Motion in 2 dimensions
Motion under gravity in 2 dimensions

Mechanics: Forces

Identifying and representing forces
Vector treatment of forces
Frictional force and normal contact force

Mechanics: Newton's Laws of Motion

Newton’s laws for a particle
Connected particles

Mechanics: Rigid Bodies

Rigid bodies in equilibrium

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