# MATHEMATICS AT WESTMINSTER TUTORS

“One of the best sixth forms in London”

## Mathematics – A Level & AS Level Tuition

Mathematics is a very popular subject at Westminster Tutors with a high success rate. Mathematicians seek out patterns to formulate new conjectures, the truth or falsity of which they resolve by mathematical proof. Both pure mathematics, that is mathematics for its own sake, and applied mathematics, such as statistics and mechanics, are taught, and students are able to choose the topics that suit and interest them. Mathematics is crucial in numerous fields, such as natural science, engineering, medicine, finance and the social sciences.

## Course outline

### AS Level Mathematics

**Paper 1: Pure Mathematics**

- Proof
- Algebra and functions
- Coordinate geometry in the (x, y) plane
- Sequences and series
- Trigonometry
- Exponentials and logarithms
- Differentiation
- Integration
- Vectors

**Paper 2: Statistics and Mechanics**

Statistics

- Statistical sampling
- Data presentation and interpretation
- Probability
- Statistical distributions
- Statistical hypothesis testing

Mechanics

- Quantities and units in mechanics
- Kinematics
- Forces and Newton’s laws

### A Level Mathematics

**Pure Mathematics**

- Proof
- Algebra and functions
- Coordinate geometry in the (x, y) plane
- Sequences and series
- Trigonometry
- Exponentials and logarithms
- Differentiation
- Integration
- Numerical methods
- Vectors

**Statistics and Mechanics**

Statistics

- Statistical sampling
- Data presentation and interpretation
- Probability
- Statistical distributions
- Statistical hypothesis testing

Mechanics

- Quantities and units in mechanics
- Kinematics
- Forces and Newton’s laws
- Moments

### AS Level Further Mathematics

**Paper 1: Core Pure Mathematics**

- Proof
- Complex numbers
- Matrices
- Further algebra and functions
- Further calculus
- Further vectors

**Paper 2: Further Mathematics Options**

Further Pure Mathematics 1

- Further trigonometry
- Coordinate systems
- Further vectors
- Numerical methods
- Inequalities

Further Pure Mathematics 2

- Groups
- Further matrix algebra
- Further complex numbers
- Number theory
- Further sequences and series

Further Statistics 1

- Discrete probability distributions
- Poisson & binomial distributions
- Chi squared tests

Further Statistics 2

- Linear regression
- Continuous probability distributions
- Correlation

Further Mechanics 1

- Momentum and impulse
- Work, energy and power
- Elastic collisions in one dimension

Further Mechanics 2

- Motion in a circle
- Centres of mass of plane figures
- Further kinematics

Decision Mathematics 1

- Algorithms and graph theory
- Algorithms on graphs
- Algorithms on graphs II
- Critical path analysis
- Linear programming

Decision Mathematics 2

- Allocation (assignment) problems
- Flows in networks
- Game theory
- Recurrence relations

### A Level Further Mathematics

**Core Pure Mathematics**

- Proof
- Complex numbers
- Matrices
- Further algebra and functions
- Further calculus
- Further vectors
- Polar coordinates
- Hyperbolic functions
- Differential equations

**Further Mathematics Options**

Further Pure Mathematics 1

- Further trigonometry
- Further calculus
- Further differential equations
- Coordinate systems
- Further vectors
- Further numerical methods
- Inequalities

Further Pure Mathematics 2

- Groups
- Further calculus
- Further matrix algebra
- Further complex numbers
- Number theory
- Further sequences and series

Further Statistics 1

- Discrete probability distributions
- Poisson & binomial distributions
- Geometric and negative binomial distributions
- Hypothesis testing
- Central Limit Theorem
- Chi Squared Tests
- Probability generating functions
- Quality of tests

Further Statistics 2

- Linear regression
- Continuous probability distributions
- Correlation
- Combination of random variables
- Estimation, confidence intervals and tests using a normal distribution
- Other Hypothesis Tests and confidence intervals
- Confidence intervals and tests using the
*t*– distribution

Further Mechanics 1

- Momentum and impulse
- Work, energy and power
- Elastic strings and springs and elastic energy
- Elastic collisions in one dimension
- Elastic collisions in two dimensions

Further Mechanics 2

- Motion in a circle
- Centres of mass of plane figures
- Further centres of mass
- Further dynamics
- Further kinematics

Decision Mathematics 1

- Algorithms and graph theory
- Algorithms on graphs
- Algorithms on graphs II
- Critical path analysis
- Linear programming

Decision Mathematics 2

- Transportation problems
- Allocation (assignment) problems
- Flows in networks
- Dynamic programming
- Game theory
- Recurrence relations
- Decision analysis

## Assesment

#### AS Level Mathematics

**Paper 1**

- 100 marks
- 2 hours written paper
- 62.5% of total AS level

**Paper 2**

- 60 marks
- 1 hour 15 minutes written paper
- 37.5% of total AS level

#### A Level Mathematics

**Paper 1**

- Assessment of any topics from the Pure Mathematics content
- 100 marks
- 2 hours written paper
- 33.3% of total A level

**Paper 2**

- Assessment of any topics from the Pure Mathematics content
- 100 marks
- 2 hours written paper
- 33.3% of total A level

**Paper 3**

- Assessment of topics from the Statistics and Mechanics content
- 100 marks
- 2 hours written paper
- 33.3% of total A level

#### AS Level Further Mathematics

**Paper 1**

- 80 marks
- 1 hour 40 minutes written paper
- 50% of total AS level

**Paper 2**

- Assessment of content from
**two**of the options - 80 marks
- 1 hour 40 minutes written paper
- 50% of total AS level

#### A Level Further Mathematics

**Paper 1**

- Assessment of any topics from the Core Pure Mathematics content
- 75 marks
- 1 hour 30 minutes written paper
- 25% of total A level

**Paper 2**

- Assessment of any topics from the Core Pure Mathematics content
- 75 marks
- 1 hour 30 minutes written paper
- 25% of total A level

**Paper 3**

- Assessment of content from
**one**of the Further Mathematics options - 75 marks
- 1 hour 30 minutes written paper
- 25% of total A level

**Paper 4**

- Assessment of content from
**one**of the Further Mathematics options - 75 marks
- 1 hour 30 minutes written paper
- 25% of total A level

## Specification

**top colleges in London**we believe our results speak for themselves.

## Tutors

BSc (Imperial), MA (King’s), MPhil (King’s)

Anthony Korte

MA (Oxford), MSc (UCL), PhD (Imperial)

John Kinoulty

BSc (Exeter), MSc (Trinity College Dublin)