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

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.

What you'll learn

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

What's inside

Learning objectives

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

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

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, 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

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Builds a foundation for students as preparation for their A levels in mathematics

Encourages problem-solving skills

Emphasizes mathematical reasoning and argumentation

Provides a comprehensive study of key mathematical concepts and techniques for A-level exams

Taught by experienced instructors from Imperial College London, ensuring a high level of academic rigor

Focuses on developing core skills in mathematics, such as fluency, confidence, problem solving, and mathematical argument

Save this course

Save A-level Mathematics for Year 13 - Course 2: General Motion, Moments and Equilibrium, The Normal Distribution, Vectors, Differentiation Methods, Integration Methods and Differential Equations to your list so you can find it easily later:

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in A-level Mathematics for Year 13 - Course 2: General Motion, Moments and Equilibrium, The Normal Distribution, Vectors, Differentiation Methods, Integration Methods and Differential Equations with these activities:

Course Notes and Resource Compilation

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Organize and compile notes, assignments, and other relevant resources to enhance understanding and retention.

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Review and sort through course materials.
Create a structured system for organizing notes and resources.
Identify gaps in knowledge and seek additional resources to fill them.

Mathematical Methods for Physics and Engineering

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Review a foundational textbook to strengthen understanding of mathematical concepts used in physics and engineering.

View Mathematical Methods for Physics and... on Amazon

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Read through the relevant chapters.
Work through practice problems at the end of each chapter.
Identify areas where further clarification is needed.

Vector Calculations in Physics

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Follow video tutorials and practice vector calculations in the context of physics to improve comprehension.

Browse courses on Vectors

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Find tutorials on vector addition, subtraction, and scalar multiplication.
Watch the tutorials and take notes on the key concepts.
Solve practice problems involving vector operations in physics.
Apply vector calculations to real-world physics scenarios.

Four other activities

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Calculus Problem-Solving Group

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Join a study group to work through calculus problems collectively, promoting collaboration and deeper understanding.

Browse courses on Calculus

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Find peers who are enrolled in the same calculus course.
Meet regularly to discuss challenging problems.
Explain solutions and alternative approaches to each other.
Identify areas where further support is required.

Motion Problems

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Solve motion problems using fundamental calculus techniques to strengthen kinematics skills and solidify understanding.

Browse courses on Projectile Motion

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Review the concepts of position, velocity, and acceleration.
Set up the equations of motion using calculus.
Solve practice problems involving motion in a straight line.
Solve practice problems involving projectile motion.
Analyze the results and identify patterns.

Motion Simulation Visualization

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Create a visual representation of motion using vectors and calculus concepts to enhance understanding of motion.

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Choose a programming language or software for creating simulations.
Develop algorithms for simulating motion in two dimensions.
Implement the algorithms to create a visual representation of motion.
Analyze the simulation results and compare them to theoretical predictions.

Contribute to OpenFOAM

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Contribute to the open-source CFD software OpenFOAM to gain hands-on experience in numerical modeling and programming.

Browse courses on Computational Fluid Dynamics

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Familiarize yourself with OpenFOAM documentation and tutorials.
Identify an area where you can contribute, such as bug fixing or feature development.
Collaborate with the OpenFOAM community to implement your changes.
Test and validate your contributions.

Career center

Learners who complete A-level Mathematics for Year 13 - Course 2: General Motion, Moments and Equilibrium, The Normal Distribution, Vectors, Differentiation Methods, Integration Methods and Differential Equations will develop knowledge and skills that may be useful to these careers:

Mathematician

A Mathematician studies the properties of numbers, shapes, and patterns. This course provides a strong foundation in calculus, which is essential for success in this field. Additionally, the course covers topics such as algebra, geometry, and topology, which are also important for mathematicians.

See salaries and explore the career path for Mathematician

Data Scientist

A Data Scientist uses mathematical and statistical techniques to analyze data and extract insights. This course provides a strong foundation in calculus, statistics, and probability, which are essential for success in this field. Additionally, the course covers topics such as machine learning and data mining, which are also important for data scientists.

See salaries and explore the career path for Data Scientist

Actuary

An Actuary uses mathematical and statistical techniques to assess risk and uncertainty. This course provides a strong foundation in calculus, statistics, and probability, which are essential for success in this field.

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Physicist

A Physicist studies the laws of nature and the physical world. This course provides a strong foundation in calculus, which is essential for success in this field. Additionally, the course covers topics such as mechanics, electromagnetism, and quantum mechanics, which are also important for physicists.

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Engineer

An Engineer designs, develops, and maintains machines and structures. This course provides a strong foundation in calculus, which is essential for success in this field. Additionally, the course covers topics such as statics, dynamics, and thermodynamics, which are also important for engineers.

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Statistician

A Statistician uses mathematical and statistical techniques to collect, analyze, and interpret data. This course provides a strong foundation in calculus, statistics, and probability, which are essential for success in this field.

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Quantitative Analyst

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Biostatistician

A Biostatistician uses mathematical and statistical techniques to analyze biological data. This course provides a strong foundation in calculus, statistics, and probability, which are essential for success in this field. Additionally, the course covers topics such as bioinformatics and clinical trials, which are also important for biostatisticians.

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Operations Research Analyst

An Operations Research Analyst uses a variety of mathematical techniques to solve business problems. These techniques include calculus, statistics, and optimization. This course provides a strong foundation in calculus, which is essential for success in this field. Additionally, the course covers topics such as vectors and differential equations, which are also used in operations research.

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Epidemiologist

An Epidemiologist studies the distribution and determinants of health-related states and events in populations. This course provides a strong foundation in calculus, statistics, and probability, which are essential for success in this field. Additionally, the course covers topics such as public health and epidemiology, which are also important for epidemiologists.

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Computer Programmer

A Computer Programmer writes and tests code that instructs computers to perform specific tasks. This course provides a strong foundation in mathematics, which is essential for success in this field. Additionally, the course covers topics such as computer science and programming, which are also important for computer programmers.

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Financial Analyst

A Financial Analyst uses mathematical and statistical techniques to analyze financial data and make investment recommendations. This course provides a strong foundation in calculus, statistics, and probability, which are essential for success in this field.

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Software Engineer

A Software Engineer designs, develops, and maintains software applications. This course provides a strong foundation in mathematics, which is essential for success in this field. Additionally, the course covers topics such as computer science and programming, which are also important for software engineers.

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Economist

An Economist studies the production, distribution, and consumption of goods and services. This course provides a strong foundation in calculus, which is used to analyze economic data and models. Additionally, the course covers topics such as microeconomics and macroeconomics, which are also important for economists.

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Teacher

A Teacher develops and delivers lesson plans, assesses student progress, and provides feedback to students. This course provides a strong foundation in mathematics, which is essential for success in this field. Additionally, the course covers topics such as pedagogy and classroom management, which are also important for teachers.

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