# 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

#### C1

- Algebra and functions
- Coordinate geometry in the (x, y) plane
- Sequences and series
- Differentiation
- Integration

#### C2

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

#### C3

- Algebra and functions
- Trigonometry
- Exponentials and logarithms
- Differentiation
- Numerical methods

#### C4

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

#### FP1

- Series
- Complex numbers
- Numerical solution of equations
- Coordinate systems
- Matrix algebra
- Proof

#### FP2

- Inequalities
- Series
- First order differential equations
- Second order differential equations
- Further complex numbers
- Maclaurin and Taylor series

#### FP3

- Further matrix algebra
- Vectors
- Hyperbolic functions
- Differentiation
- Integration
- Further coordinate systems

#### M1

- Mathematical models in mechanics
- Vectors in mechanics
- Kinematics of a particle moving in a straight line
- Dynamics of a particle moving in a straight line or plane
- Statics of a particle
- Moments

#### M2

- Kinematics of a particle moving in a straight line or plane
- Centres of mass
- Work and energy
- Collisions
- Statics of rigid bodies

#### M3

- Further kinematics
- Elastic strings and springs
- Further dynamics
- Motion in a circle
- Statics of rigid bodies

#### M4

- Relative motion
- Elastic collisions in two dimensions
- Further motion of particles in one dimension
- Stability

#### M5

- Applications of vectors in mechanics
- Variable mass
- Moments of inertia of a rigid body
- Rotation of a rigid body about a fixed smooth axis

#### S1

- Mathematical models in probability and statistics
- Representation and summary of data
- Probability
- Correlation and regression
- Discrete random variables
- Discrete distributions
- The Normal distribution

#### S2

- The Binomial and Poisson distributions
- Continuous random variables
- Continuous distributions
- Samples
- Hypothesis tests

#### S3

- Combinations of random variables
- Sampling
- Estimation
- Confidence intervals and tests
- Goodness of fit and contingency tables
- Regression and correlation

#### S4

- Quality of tests and estimators
- One-sample procedures
- Two-sample procedures

#### D1

- Algorithms
- Algorithms on graphs
- The route inspection problem
- Critical path analysis
- Linear programming
- Matchings

#### D2

- Transportation problems
- Allocation (assignment) problems
- The travelling salesman
- Game theory
- Further linear programming
- Dynamic programming
- Flows in network

Assesment

#### C1

- Non-calculator
- 75 marks
- 1 hour 30 minutes written paper
- 33.3% of total AS

#### C2

- 75 marks
- 1 hour 30 minutes written paper
- 33.3% of total AS

#### Optional Unit

- M1, S1 or D1
- 75 marks
- 1 hour 30 minutes written paper
- 33.3% of total AS

#### C1

- Non-calculator
- 75 marks
- 1 hour 30 minutes written paper
- 16.67% of total A level

#### C2

- 75 marks
- 1 hour 30 minutes written paper
- 16.67% of total A level

#### C3

- 75 marks
- 1 hour 30 minutes written paper
- 16.67% of total A level

#### C4

- 75 marks
- 1 hour 30 minutes written paper
- 16.67% of total A level

#### Optional Units

- M1 and S1, M1 and D1, S1 and D1, S1 and S2, M1 and M2 or D1 and D2
- 75 marks (x2)
- 1 hour 30 minutes written paper (x2)
- 16.67% of total A level (x2)

#### FP1

- 75 marks
- 1 hour 30 minutes written paper
- 33.3% of total AS

#### Optional Units

- Any two excluding C1-C4
- 75 marks (x2)
- 1 hour 30 minutes written paper (x2)
- 33.3% of total AS (x2)

#### FP1

- 75 marks
- 1 hour 30 minutes written paper
- 16.67% of total A level

#### Optional Units

- FP2 or FP3 and any other four excluding C1-C4
- 75 marks (x5)
- 1 hour 30 minutes written paper (x5)
- 16.67% of total A level (x5)