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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.
Overview
Syllabus
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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
