A-level Mathematics for Year 13 - Course 1: Functions, Sequences and Series, and Numerical Methods 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.
The course is most appropriate to the Edexcel, AQA, OCR and OCR(MEI) papers. 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 an introduction to functions and their notation, sequences and series and numerical methods testing 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:

Define a mapping and a function
Define the domain and range for a function
Combine functions to create a composite function
Find the inverse of a function
Define a sequence using an nth term formula and an inductive definition
Define an arithmetic and a geometric sequence
Use sigma notation to define a series
Expand a binomial expression for both a positive integer index and for an index which is not a positive integer
Use radians as a measure of angle
Find arc lengths, areas of sectors and areas of segments on circles where angles are in radians
Use small angle approximations for sine, cosine and tangent functions
Find multiple solutions to trigonometric equations
Use the reciprocal trigonometric functions
Use the inverse trigonometrical functions
Use trigonometrical identities
Derive and use the trapezium rule to find the area under a curve
Approximate the root of an equation using a sign change method
Approximate the root of an equation using the Newton-Raphson method
Approximate the root of an equation by fixed point iteration

What's inside

Learning objectives

Define a mapping and a function
Define the domain and range for a function
Combine functions to create a composite function
Find the inverse of a function
Define a sequence using an nth term formula and an inductive definition
Define an arithmetic and a geometric sequence
Use sigma notation to define a series
Expand a binomial expression for both a positive integer index and for an index which is not a positive integer
Use radians as a measure of angle
Find arc lengths, areas of sectors and areas of segments on circles where angles are in radians

Use small angle approximations for sine, cosine and tangent functions
Find multiple solutions to trigonometric equations
Use the reciprocal trigonometric functions
Use the inverse trigonometrical functions
Use trigonometrical identities
Derive and use the trapezium rule to find the area under a curve
Approximate the root of an equation using a sign change method
Approximate the root of an equation using the newton-raphson method
Approximate the root of an equation by fixed point iteration

Define a mapping and a function
Define the domain and range for a function
Combine functions to create a composite function
Find the inverse of a function
Define a sequence using an nth term formula and an inductive definition
Define an arithmetic and a geometric sequence
Use sigma notation to define a series
Expand a binomial expression for both a positive integer index and for an index which is not a positive integer
Use radians as a measure of angle
Find arc lengths, areas of sectors and areas of segments on circles where angles are in radians
Use small angle approximations for sine, cosine and tangent functions
Find multiple solutions to trigonometric equations
Use the reciprocal trigonometric functions
Use the inverse trigonometrical functions
Use trigonometrical identities
Derive and use the trapezium rule to find the area under a curve
Approximate the root of an equation using a sign change method
Approximate the root of an equation using the newton-raphson method
Approximate the root of an equation by fixed point iteration

Syllabus

Module 1: Algebra and Functions

The difference between a mapping and a function

Function notation

Domain and range of a function

Composition of functions

Inverse functions

Module 2: Sequences and Series 1

How to define a sequence by an nth term rule

How to define a sequence by an inductive rule

Arithmetic sequences

Geometric sequences

The sum of n terms of an arithmetic and a geometric sequence

Series and the sigma notation

Module 3: Sequences and Series 2

The binomial expansion for positive integer n

The general binomial expansion

Properties of sequences

Module 4: Trigonometry 1

Radian measure

Circle calculations

Small angle approximations

Circular functions

Module 5: Trigonometry 2

The reciprocal trigonometric functions

Inverse trigonometric functions

Addition and double angle formulae

Trigonometric identities

Module 6: Numerical Methods 1

An introduction to numerical methods

The trapezium rule

Numerical solution of equations

Module 7: Numerical Methods 2

The Newton-Raphson method

Fixed point iteration

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Examines key mathematical concepts and techniques, supporting fluency, confidence, problem-solving, constructing mathematical argument, and deep reasoning

Provides a solid foundation for A-level math exams, covering core skill areas

Encourages critical thinking and deep understanding of mathematical techniques, formulas, and proofs

Taught by experienced instructors from Imperial College London, known for their expertise in mathematics education

Appropriate for students preparing for Edexcel, AQA, OCR, and OCR(MEI) A-level exams

Reviews summary

Mathematics for year 13

According to students, this course provides assistance to those seeking a mathematics degree. Based on only one review, it is difficult to determine whether the majority of learners found the course to be an overall positive experience.

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 1: Functions, Sequences and Series, and Numerical Methods with these activities:

Review module prerequisites

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Ensure you have a strong grasp of the core concepts covered in previous math courses to succeed in this A-Level course.

Browse courses on Sequences and Series

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Review notes and textbooks from previous math courses.
Complete practice problems to refresh your memory.

Review Pre-calculus trigonometry

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Revisit the foundational concepts of trigonometry to ensure you understand and can apply them in this course

Browse courses on Trigonometry

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Review the definitions of sine, cosine, and tangent
Practice finding the values of trigonometric ratios using the unit circle
Solve basic trigonometric equations

Review 'Mathematics for A-Level' by C. Baker

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This book provides a comprehensive review of the mathematical concepts covered in this course.

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Read through the relevant chapters of the book.
Complete the practice problems and exercises in the book.

Seven other activities

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Watch video tutorials and attend online workshops

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These resources can provide additional support and help you understand complex concepts more clearly.

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Search for video tutorials on specific topics you're struggling with.
Attend online workshops offered by the course instructors or other experts.

Join a study group or discussion forum

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Collaborating with peers can enhance your understanding and provide support throughout the course.

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Form a study group with classmates to discuss course material and work on problems together.
Participate in online discussion forums to connect with other students and ask questions.

Practice solving functions

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Reinforce your understanding of functions by solving a variety of practice problems

Browse courses on Functions

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Find the domain and range of functions
Sketch the graphs of functions
Solve equations involving functions

Solve practice problems regularly

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Regular practice will help you master the techniques and improve your problem-solving skills.

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Work through the practice problems provided in the course materials.
Seek out additional practice problems online or in textbooks.

Create concept maps or diagrams

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Visualizing the relationships between concepts can help you retain information and improve your understanding.

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Identify the key concepts in each module.
Create a concept map or diagram that shows how these concepts are connected.

Create a visual representation of a trigonometric identity

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Deepen your understanding of a trigonometric identity by creating a visual representation, such as a diagram or animation

Browse courses on Trigonometric Identities

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Identify the trigonometric identity you want to represent
Choose a visual format that will effectively represent the identity
Create the visual representation
Explain how your visual representation illustrates the identity

Write a summary or explanation of a complex topic

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Explaining concepts to others will deepen your understanding and help you identify areas where you need more clarification.

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Share your summary or explanation with others for feedback.
Choose a complex topic from the course material.
Write a summary or explanation of the topic in your own words.

Career center

Learners who complete A-level Mathematics for Year 13 - Course 1: Functions, Sequences and Series, and Numerical Methods will develop knowledge and skills that may be useful to these careers:

Actuary

Actuaries use mathematical and statistical models to assess risk and uncertainty. The skills you will learn in this course, such as problem-solving, critical thinking, and data analysis, are essential for success in this field. This course will help you develop the strong foundation in mathematics that is required for a career as an Actuary.

See salaries and explore the career path for Actuary

Market Researcher

Market Researchers use their knowledge of mathematics and statistics to collect and analyze data about consumer behavior. The skills you will learn in this course, such as data analysis, problem-solving, and critical thinking, are essential for success in this field. This course will help you develop the strong foundation in mathematics and statistics that is required for a career as a Market Researcher.

See salaries and explore the career path for Market Researcher

Data Analyst

Data Analysts use their knowledge of mathematics and statistics to collect, clean, and analyze data. The skills you will learn in this course, such as data analysis, problem-solving, and critical thinking, are essential for success in this field. This course will help you develop the strong foundation in mathematics and statistics that is required for a career as a Data Analyst.

See salaries and explore the career path for Data Analyst

Financial Analyst

Financial Analysts use their knowledge of mathematics and statistics to analyze financial data and make investment recommendations. The skills you will learn in this course, such as problem-solving, critical thinking, and data analysis, are essential for success in this field. This course will help you develop the strong foundation in mathematics and statistics that is required for a career as a Financial Analyst.

See salaries and explore the career path for Financial Analyst

Risk Analyst

Risk Analysts use their knowledge of mathematics and statistics to assess and manage risk. The skills you will learn in this course, such as problem-solving, critical thinking, and data analysis, are essential for success in this field. This course will help you develop the strong foundation in mathematics and statistics that is required for a career as a Risk Analyst.

See salaries and explore the career path for Risk Analyst

Quantitative Analyst

Quantitative Analysts use their knowledge of mathematics and statistics to develop and implement mathematical models for financial analysis. The skills you will learn in this course, such as problem-solving, critical thinking, and data analysis, are essential for success in this field. This course will help you develop the strong foundation in mathematics and statistics that is required for a career as a Quantitative Analyst.

See salaries and explore the career path for Quantitative Analyst

Operations Research Analyst

Operations Research Analysts use their knowledge of mathematics and statistics to solve problems in business and industry. The skills you will learn in this course, such as problem-solving, critical thinking, and data analysis, are essential for success in this field. This course will help you develop the strong foundation in mathematics and statistics that is required for a career as an Operations Research Analyst.

See salaries and explore the career path for Operations Research Analyst

Statistician

Statisticians use their knowledge of mathematics and statistics to collect, analyze, and interpret data. The skills you will learn in this course, such as data analysis, problem-solving, and critical thinking, are essential for success in this field. This course will help you develop the strong foundation in mathematics and statistics that is required for a career as a Statistician.

See salaries and explore the career path for Statistician

Investment Banker

Investment Bankers use their knowledge of mathematics and finance to help companies raise capital and make investment decisions. The skills you will learn in this course, such as problem-solving, critical thinking, and data analysis, are essential for success in this field. This course will help you develop the strong foundation in mathematics and statistics that is required for a career as an Investment Banker.

See salaries and explore the career path for Investment Banker

Teacher

Teachers use their knowledge of mathematics to teach students about the subject. The skills you will learn in this course, such as problem-solving, critical thinking, and communication, are essential for success in this field. This course will help you develop the strong foundation in mathematics that is required for a career as a Teacher.

See salaries and explore the career path for Teacher

Loan Officer

Loan Officers use their knowledge of mathematics and finance to help clients get loans. The skills you will learn in this course, such as problem-solving, critical thinking, and communication, are essential for success in this field. This course will help you develop the strong foundation in mathematics and finance that is required for a career as a Loan Officer.

See salaries and explore the career path for Loan Officer

Financial Planner

Financial Planners use their knowledge of mathematics and finance to help clients plan for their financial future. The skills you will learn in this course, such as problem-solving, critical thinking, and communication, are essential for success in this field. This course will help you develop the strong foundation in mathematics and finance that is required for a career as a Financial Planner.

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Economist

Economists use their knowledge of mathematics and economics to analyze economic data and make policy recommendations. The skills you will learn in this course, such as problem-solving, critical thinking, and data analysis, are essential for success in this field. This course will help you develop the strong foundation in mathematics and economics that is required for a career as an Economist.

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Insurance Agent

Insurance Agents use their knowledge of mathematics and insurance to help clients assess and manage their risk. The skills you will learn in this course, such as problem-solving, critical thinking, and communication, are essential for success in this field. This course will help you develop the strong foundation in mathematics and insurance that is required for a career as an Insurance Agent.

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Management Consultant

Management Consultants use their knowledge of mathematics and business to help companies improve their operations. The skills you will learn in this course, such as problem-solving, critical thinking, and communication, are essential for success in this field. This course will help you develop the strong foundation in mathematics and business that is required for a career as a Management Consultant.

See salaries and explore the career path for Management Consultant