This course by Imperial College London is designed to help you develop the skills you need to succeed in your A-level maths exams.
You will investigate key topic areas to gain a deeper understanding of the skills and techniques that you can apply throughout your A-level study. These skills include:
Fluency – selecting and applying correct methods to answer with speed and efficiency
Confidence – critically assessing mathematical methods and investigating ways to apply them
Problem solving – analysing the ‘unfamiliar’ and identifying which skills and techniques you require to answer questions
Constructing mathematical argument – using mathematical tools such as diagrams, graphs, logical deduction, mathematical symbols, mathematical language, construct mathematical argument and present precisely to others
Deep reasoning – analysing and critiquing mathematical techniques, arguments, formulae and proofs to comprehend how they can be applied
Over seven modules, covering general motion in a straight line and two dimensions, projectile motion, a model for friction, moments, equilibrium of rigid bodies, vectors, differentiation methods, integration methods and differential equations, your initial skillset will be extended to give a clear understanding of how background knowledge underpins the A -level course.
You’ll also be encouraged to consider how what you know fits into the wider mathematical world.
Module 1: Calculus in Kinematics and Projectile Motion
Using calculus for kinematics for motion in a straight line:
Using calculus in kinematics for motion extended to 2 dimensions using vectors.
Modelling motion under gravity in a vertical plane using vectors; projectiles.
Composition of functionsInverse functions
Module 2: Friction, Moments and Equilibrium of rigid bodies
Understanding and using the F≤μR model for friction
The coefficient of friction motion of a body on a rough surface limiting friction
Understanding and using moments in simple static contexts.
The equilibrium of rigid bodies involving parallel and nonparallel coplanar forces
Module 3: The Normal Distribution
Understanding and using the Normal distribution as a model
Finding probabilities using the Normal distribution
Conducting statistical hypothesis tests for the mean of a Normal distribution with known, given or assumed variance
Interpreting the results of hypothesis tests in context
Module 4: Vectors
Using vectors in two dimensions and in three dimensions
Adding vectors diagrammatically
Performing the algebraic operations of vector addition and multiplication by scalars
Understanding the geometrical interpretations of vector calculations
Understanding and using position vectors
Calculating the distance between two points represented by position vectors.
Using vectors to solve problems in pure mathematics
Module 5: Differentiation Methods
Differentiation using the product rule, the quotient rule and the chain rule
Differentiation to solve problems involving connected rates of change and inverse functions.
Differentiating simple functions and relations defined implicitly or parametrically
Module 6: Integration Methods
Integrating e^kx, 1/x, sinkx, coskx and related sums, differences and constant multiples
Integration by substitution
Integration using partial fractions that are linear in the denominator
Integration by parts
Module 7: Differential Equations
The analytical solution of simple first order differential equations with separable variables
Finding particular solutions
Sketching members of a family of solution curves
Interpreting the solution of a differential equation in the context of solving a problem
Identifying limitations of the solution to a differential equation
Start your review of A-level Mathematics for Year 13 - Course 2: General Motion, Moments and Equilibrium, The Normal Distribution, Vectors, Differentiation Methods, Integration Methods and Differential Equations