CIE International A-Level Maths: Pure Mathematics 1 from Udemy

CIE International A-Level Maths is a course for anyone studying the Cambridge International A-Level Maths:

This course covers all the pure content in Paper 1 (Pure Mathematics 1) of the Cambridge International A-Level Maths Course, covered in the first year of study. It is also a great introduction to pure maths for anyone interested in getting started.

The main sections of the course are:

- Equations and Inequalities – we will look at a wide range of different functions, including quadratic, linear and cubic functions.

- Quadratics - we look at quadratic functions, how to sketch and work with them, solve equations and inequalities and work with the discriminant.

- Functions - we learn about domain, range, inverse and composite functions, as well as graph transformations.

- Straight Line Graphs – we take this topic, familiar from GCSE, and push it to the next level, introducing new ways of using straight line graphs.

- Circles – we learn how to represent circles in the coordinate plane, find tangents to circles and solve intersections with lines.

- Trigonometry – in the two trigonometry chapters we look at how to use trigonometry to solve triangle problems, but also solve trigonometric equations, sketch tri graphs, and prove trigonometric identities.

- Circular Measure - we learn how to work with radians to calculate sector areas, arc lengths and solve trigonometric equations.

- Graphs – we will learn how to sketch and work with graphs, including higher order polynomials, as well as graph transformations.

- Series - we learn about binomial expansion and the choose function, as well as how to work with arithmetic and geometric series.

- Differentiation – in this huge chapter we introduce one of the most powerful and exciting ideas in mathematics. We look at gradients of curves, tangents, stationary points and optimisation problems.

- Integration – here we look at the other side of calculus, and learn how to use integration to find areas under curves.

- Exponentials and Logarithms – we learn about the exponential function, logarithms, the natural log, as well as how to use these ideas to model a range of real-world scenarios.

Please note: This course is intended for people studying the Cambridge International A-Level Maths Syllabus, and not the UK syllabus (covered by Edexcel If you are looking for these, check out my other courses on these.

What you get in this course:

Videos: Watch as I explain each topic, introducing all the key ideas, and then go through a range of different examples, covering all the important ideas in each. In these videos I also point out the most common misconceptions and errors so that you can avoid them.

Quizzes: Each sub-section is followed by a short quiz for you to test your understanding of the content just covered. Most of the questions in the quizzes are taken from real A-Level past papers. Feel free to ask for help if you get stuck on these.

Worksheets: At the end of each chapter I have made a collection of different questions taken from real A-Level past papers for you to put it all together and try for yourself. At the bottom of each worksheet is a full mark-scheme so you can see how you have done.

This course comes with:

· A printable Udemy certificate of completion.

· Support in the Q&A section - ask me if you get stuck.

I really hope you enjoy this course.

Woody

What's inside

Learning objectives

Quadratic equations
Functions
Coordinate geometry
Circular motion

Trigonometry
Series
Differentiation
Integration

Quadratic equations
Functions
Coordinate geometry
Circular motion
Trigonometry
Series
Differentiation
Integration

Syllabus

Introduction

Quadratics

Factorising to Solve a Quadratic

Factorising to Solve a Quadratic - Quiz

The Quadratic Formula

The Quadratic Formula - Quiz

Calculator Use to Solve Quadratics

Calculator Use to Solve Quadratics - Quiz

Completing the Square to Solve Quadratics

Completing the Square to Solve Quadratics - Quiz

Completing the Square to Find the Turning Point of a Quadratic - Part 1

Completing the Square to Find the Turning Point of a Quadratic - Part 1 - Quiz

Completing the Square to Find the Turning Point of a Quadratic - Part 2

Completing the Square to Find the Turning Point of a Quadratic - Part 2 - Quiz

Quadratic Graphs - Part 1

Quadratic Graphs - Part 2

Quadratic Graphs - Quiz

Proof of the Quadratic Formula

The Discriminant - Introduction

The Discriminant - Introduction - Quiz

Applications of the Discriminant

Applications of the Discriminant - Quiz

Quadratic Simultaneous Equations - Part 1

Quadratic Simultaneous Equations - Part 1 - Quiz

Quadratic Simultaneous Equations - Part 2

Linear Inequalities and Set Notation

Linear Inequalities and Set Notation - Quiz

Quadratic Inequalities - Part 1

Quadratic Inequalities - Part 1 - Quiz

Quadratic Inequalities - Part 2

Quadratic Inequalities - Part 2 - Quiz

Quadratic Inequalities - Part 3

Quadratic Inequalities - Part 3 - Quiz

Disguised Quadratics - Part 1

Disguised Quadratics - Part 1 - Quiz

Disguised Quadratics - Part 2

Disguised Quadratics - Part 2 - Quiz

Modelling with Quadratics - Part 1

Modelling with Quadratics - Part 2

Modelling with Quadratics - Quiz

Quadratics - Past Paper Questions Pack

Functions

Mappings

Mappings - Quiz

Domain and Range

Domain and Range - Quiz

Composite Functions

Composite Functions - Quiz

Inverse Functions

Inverse Functions - Quiz

Translations - Part 1

Translations - Part 1 - Quiz

Translations - Part 2

Translations - Part 2 - Quiz

Stretches - Part 1

Stretches - Part 1 - Quiz

Stretches - Part 2

Stretches - Part 2 - Quiz

Reflections

Reflections - Quiz

The Prison Method

Applications of Transformations

Functions - Past Paper Question Pack

Coordinate Geometry - Straight Lines

y = mx + c

Gradients

Gradients - Quiz

The Equation of a Straight Line

Straight Line Problem Solving

Straight Line Problem Solving - Quiz

Parallel Lines

Parallel Lines - Quiz

Perpendicular Lines

Perpendicular Lines - Quiz

Perpendicular Bisectors

Perpendicular Bisectors - Quiz

Length Problems

Length Problems - Quiz

Area Problems

Area Problems - Quiz

Modelling with Straight Lines

Modelling with Straight Lines - Quiz

Straight Lines - Past Paper Question Pack

Coordinate Geometry - Circles

Circles - Introduction

Circles - Introduction - Quiz

The Equation of a Circle

The Equation of a Circle - quiz

Calculating the Centre and Radius of a Circle

Calculating the Centre and Radius of a Circle - quiz

Problem Solving with Circles

Problem Solving with Circles - quiz

Intersecting Lines and Circles - Part 1

Intersecting Lines and Circles - Part 2

Intersecting Lines and Circles - quiz

Tangents to Circles

Tangents to Circles Examples - Part 1

Tangents to Circles Examples - Part 2

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 CIE International A-Level Maths: Pure Mathematics 1 with these activities:

Review GCSE Maths Concepts

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Reinforce foundational maths concepts from GCSE level to ensure a solid base for the more advanced A-Level material. This will help you grasp new concepts more easily and avoid common pitfalls.

Browse courses on Quadratic Equations

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Review key topics like algebra, geometry, and trigonometry.
Work through practice problems from GCSE past papers.
Identify and address any areas of weakness.

Review: A-Level Maths for Dummies

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Supplement your learning with a comprehensive guide to A-Level Maths. This book offers alternative explanations and examples to reinforce your understanding of the course material.

View AS/A Level Maths for AQA - Mechanics 2: Student... on Amazon

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Read the chapters related to the topics covered in the course.
Work through the examples and practice problems in the book.
Compare the book's explanations with the course's explanations.

Practice Quadratic Equation Solving

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Sharpen your skills in solving quadratic equations using various methods. This will improve your speed and accuracy when tackling related problems in the course.

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Solve quadratic equations by factorizing.
Solve quadratic equations using the quadratic formula.
Solve quadratic equations by completing the square.
Solve disguised quadratic equations.

Four other activities

Expand to see all activities and additional details

Show all seven activities

Create a Trigonometric Identity Cheat Sheet

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Compile a cheat sheet of trigonometric identities for quick reference. This will help you memorize and apply these identities more effectively when solving trigonometric problems.

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List all the trigonometric identities covered in the course.
Organize the identities by category (e.g., Pythagorean, reciprocal, quotient).
Include examples of how to use each identity.

Create a Formula Sheet and Worked Examples Compilation

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Consolidate your learning by creating a comprehensive formula sheet and a collection of worked examples. This will serve as a valuable reference tool for future problem-solving.

Show steps

Gather all the formulas and key concepts from each section of the course.
Organize the formulas and concepts into a logical structure.
Include worked examples for each formula and concept.
Review and refine the compilation regularly.

Model Real-World Scenarios with Functions

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Apply your knowledge of functions to model real-world scenarios. This will deepen your understanding of functions and their applications.

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Choose a real-world scenario that can be modeled with a function.
Define the variables and parameters of the function.
Write the equation of the function.
Analyze the behavior of the function.

Review: Advanced Problems in Core Mathematics

Show steps

Challenge yourself with advanced problems to deepen your understanding of core mathematical concepts. This book will help you develop problem-solving skills and prepare for more complex applications.

View Advanced Problems in Mathematics on Amazon

Show steps

Attempt the problems related to the topics covered in the course.
Review the solutions and explanations provided in the book.
Identify and address any areas where you struggled.

Career center

Learners who complete CIE International A-Level Maths: Pure Mathematics 1 will develop knowledge and skills that may be useful to these careers:

Actuary

An Actuary assesses and manages financial risks, particularly in the insurance and pension industries. This career typically requires advanced degrees and specialized actuarial exams. The mathematical concepts covered in the A-Level Pure Mathematics course are essential building blocks for actuarial science. The course's treatment of series, probability (implied in the context of A-Level mathematics), and functions helps build a foundation for actuarial models. A strong understanding of these mathematical concepts is crucial for success as an Actuary.

See salaries and explore the career path for Actuary

Statistician

A Statistician collects, analyzes, and interprets data to draw conclusions and make predictions. This profession often requires at least a master's degree. This course on A-Level Pure Mathematics may provide a strong foundation for statistical analysis. Topics such as functions, graphs, and equations are essential for understanding statistical models and data distributions. The work done in trigonometry may be useful for spatial statistics, should the Statistician wish to work in this subfield. The course may be helpful for success in this area.

See salaries and explore the career path for Statistician

Financial Analyst

A Financial Analyst evaluates financial data, provides investment recommendations, and manages financial risk. The analytical skills and mathematical proficiency developed in this course on A-Level Pure Mathematics are directly applicable to financial modeling and analysis. Topics like series, which are used to calculate present and future values, and functions, which can model financial relationships, are helpful. The understanding of equations and inequalities may support a career as a Financial Analyst.

See salaries and explore the career path for Financial Analyst

Data Scientist

A Data Scientist analyzes complex data sets to extract meaningful insights and inform decision-making. This role requires a strong foundation in mathematical concepts, and this course on A-Level Pure Mathematics provides knowledge to understand the mathematical underpinnings of many data science algorithms. Topics covered, such as functions, coordinate geometry, and series, are essential for understanding data distributions and relationships. This course may help build a foundation for the mathematical skills necessary for success as a Data Scientist.

See salaries and explore the career path for Data Scientist

Economist

An Economist studies the production, distribution, and consumption of goods and services. This career typically requires advanced study. Mathematical modeling is a core component of economic analysis, and this A-Level Pure Mathematics course may help prepare you for this area. The course covers functions, graphs, and calculus, which are tools for building and analyzing economic models. Those wanting to be an Economist may find the course helpful.

See salaries and explore the career path for Economist

Game Developer

A Game Developer creates video games for computers and consoles. Game development requires a strong technical skill set and a knack for creativity. A strong foundation in mathematics is invaluable in this role. The coordinate geometry, trigonometry, and calculus concepts covered in this course are essential for game physics, graphics rendering, and artificial intelligence. This course provides math skills necessary for a career as a Game Developer.

See salaries and explore the career path for Game Developer

Civil Engineer

A Civil Engineer designs, constructs, and maintains infrastructure projects such as roads, bridges, and buildings. This field demands a strong understanding of mathematical principles. This course on A-Level Pure Mathematics may help build a foundation for the calculations and modeling involved in structural analysis and design. Topics like coordinate geometry, trigonometry, and calculus are applied in various civil engineering applications. The work in circle geometry may be useful to Civil Engineers.

See salaries and explore the career path for Civil Engineer

Teacher

A Teacher provides instruction to students of varying ages in a school, tutoring center, or learning environment. This A-Level Pure Mathematics course may help a future instructor strengthen their understanding of functions, graphs, and calculus, and teach students effectively. Furthermore, a Teacher will also be able to assist those students who need extra help in understanding mathematical concepts. This course helps provide the required tools for success in the classroom.

See salaries and explore the career path for Teacher

Software Engineer

A Software Engineer designs, develops, and tests software applications. While this role is heavily programming-focused, a solid mathematical foundation is useful for algorithm design and optimization. The topics covered in this A-Level Pure Mathematics course, such as functions, graphs, and series, may help build a foundation for understanding computational complexity and algorithm efficiency. This course may be useful for those considering a career as a Software Engineer.

See salaries and explore the career path for Software Engineer

Mathematics Professor

A Mathematics Professor teaches mathematics courses at the college or university level and conducts research. This role typically requires a doctoral degree. This course on A-Level Pure Mathematics may solidify core concepts and introduce more advanced topics. The content related to quadratics, functions, coordinate geometry, trigonometry, series, differentiation, and integration may be a valuable starting point for someone who wants to be a Mathematics Professor.

See salaries and explore the career path for Mathematics Professor

Market Research Analyst

A Market Research Analyst studies consumer behavior and market trends to advise companies on product development and marketing strategies. This A-Level Pure Mathematics course provides skills in data analysis and interpretation. The course's examination of functions and graphs may offer a foundation for analyzing market data and identifying trends. The Market Research Analyst may find this course helpful.

See salaries and explore the career path for Market Research Analyst

Researcher

A Researcher is involved in the systematic investigation into a topic of interest. They seek to discover or revise facts, theories, and applications. This course on A-Level Pure Mathematics may help a future researcher deepen their familiarity around the core subjects. This may be a valuable starting point for someone who wants to perform Research.

See salaries and explore the career path for Researcher

Biostatistician

A Biostatistician applies statistical methods to solve problems in biology, medicine, and public health. This career typically requires advanced study in biostatistics or a related field. The course's treatment of functions, graphs, and calculus may help those who want to enter this field. This course may be useful for those considering a career as a Biostatistician.

See salaries and explore the career path for Biostatistician

Financial Planner

A Financial Planner assists clients in setting and achieving financial goals, such as retirement planning, investment management, and estate planning. A strong mathematical background is useful for calculating investment returns, projecting future financial scenarios, and developing personalized financial plans. This A-Level Pure Mathematics course may help with the analytical and problem-solving skills necessary for a career as a Financial Planner.

See salaries and explore the career path for Financial Planner

Meteorologist

A Meteorologist studies the atmosphere and weather patterns to forecast weather conditions. These professionals typically need a bachelor's degree in meteorology or a related field such as atmospheric science. Mathematical models play a key role in weather forecasting, and this course may help build a foundation for understanding these models. This course may be useful for those considering a career as a Meteorologist.

See salaries and explore the career path for Meteorologist

CIE International A-Level Maths

Pure Mathematics 1

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