A-level Mathematics for Year 13 - Course 2: General Motion, Moments and Equilibrium, The Normal Distribution, Vectors, Differentiation Methods, Integration Methods and Differential Equations

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. 38:T69c, By th

• Use calculus in kinematics for motion in a straight line
• Use differentiation and integration of a vector with respect to time for motion in two dimensions
• Solve projectile motion problems using both calculus/vector methods and constant acceleration formulae
• Use a standard model for friction
• Calculate moments understanding what they mean and how they might be used
• Solve problems involving parallel and nonparallel coplanar forces
• Apply an understanding of moments to statics problems involving rigid bodies
• Use the Normal distribution as a model for continuous data
• Conduct a hypothesis test of the mean using a Normal distribution
• Use a Normal distribution as an approximation of a Binomial distribution
• Add vectors diagrammatically
• Perform the algebraic operations of vector addition and multiplication by scalars
• Apply vector calculations to problems in pure mathematics
• Use methods for differentiating a function of a function, differentiating a product and differentiating a quotient
• Differentiate trigonometric and inverse trigonometric functions
• Use implicit and parametric differentiation
• Identify integrals that can be dealt with “by sight”
• Use a substitution method to integrate a function
• Use partial fractions to integrate rational functions
• Use the method of integration by parts
• Use the method of separating the variable to solve differential equations
• find the family of solutions for a differential equation