Alevel Mathematics for Year 13  Course 2: General Motion, Moments and Equilibrium, The Normal Distribution, Vectors, Differentiation Methods, Integration Methods and Differential Equations
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Overview
This course by Imperial College London is designed to help you develop the skills you need to succeed in your Alevel maths exams.
You will investigate key topic areas to gain a deeper understanding of the skills and techniques that you can apply throughout your Alevel 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.
Syllabus
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
Taught by
Philip Ramsden and Phil Chaffe
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