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

Develop your thinking skills, fluency and confidence to aim for an A* in A-level maths and prepare for undergraduate STEM degrees.

A-level Mathematics for Year 13 - Course 2: General Motion, Moments and Equilibrium, The Normal Distribution, Vectors, Differentiation Methods, Integration Methods and Differential Equations
7 weeks
2–4 hours per week
Progress at your own speed
Optional upgrade available

There is one session available:

6,994 already enrolled! After a course session ends, it will be archivedOpens in a new tab.
Starts Nov 29

About this course

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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.

At a glance

  • Institution: ImperialX
  • Subject: Math
  • Level: Intermediate
  • Prerequisites:
  • Language: English
  • Video Transcript: English
  • Associated skills: Normal Distribution, Differential Equations

What you'll learn

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By the end of this course, you'll be able to:

  • 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

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, sin⁡kx, cos⁡kx 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

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