A-Level Maths: Pure (Year 1 / AS) from Udemy

A-Level Maths: Pure (Year 1 / AS) is a course for anyone studying A-Level Maths:

This course covers all the pure content in A-Level AS maths, usually covered in the first year of study (Year 12). The course is suitable for all major exam boards, including Edexcel 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.

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

- Polynomial Division – we learn new and powerful algebraic techniques that allow us to divide, factorise and solve higher order polynomials.

- Proof – we learn a range of different techniques for proving mathematical claims.

- Binomial expansion – here we learn a new algebraic technique for expanding brackets raise to large powers.

- 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.

- Vectors – we extend GCSE vector ideas to much more complex problems, including vector proofs.

- 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.

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 30 day money-back guarantee.

· 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

Solving equations - linear, quadratic, cubic, trigonometric and more!
Solving inequalities - linear and quadratic
Circle equations and geometry
Binomial expansion
Graphs - polynomials, reciprocals and trigonometric
Trigonometry - equations, identities, graphs and proofs
Calculus - differentiation and integration

Stationary points and applications of differentiation
Exponentials logarithms - solving equations, modelling and graphs
Polynomial division
Proof
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Solving equations - linear, quadratic, cubic, trigonometric and more!
Solving inequalities - linear and quadratic
Circle equations and geometry
Binomial expansion
Graphs - polynomials, reciprocals and trigonometric
Trigonometry - equations, identities, graphs and proofs
Calculus - differentiation and integration
Stationary points and applications of differentiation
Exponentials logarithms - solving equations, modelling and graphs
Polynomial division
Proof
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Show less

Syllabus

Introduction

Solving quadratic equations, find turning points by completing the square, use the discriminant and use quadratics to model real-world situations.

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Covers all the pure content typically found in the first year of A-Level AS maths, making it a comprehensive resource for exam preparation

Includes quizzes with questions taken from real A-Level past papers, offering valuable practice and familiarity with the exam format

Provides worksheets with questions from real A-Level past papers and full mark schemes, enabling students to assess their progress effectively

Introduces core concepts like differentiation and integration, which are fundamental to calculus and have wide applications in various fields

Explores topics such as binomial expansion and polynomial division, which are essential for developing strong algebraic skills

Suitable for all major exam boards, including Edexcel, providing flexibility for students following different curricula

Reviews summary

Clear explanations and exam practice

According to learners, this course is a highly effective resource for A-Level Pure Maths (Year 1 / AS). Many highlight the clarity of the explanations provided by the instructor, Woody, noting how he breaks down complex concepts simply. A significant strength consistently mentioned is the inclusion of practice questions taken from real past papers in both the quizzes and worksheets, which students found invaluable for exam preparation. While the course covers the key topics of the Year 1/AS syllabus comprehensively, a few reviewers felt the pace could be fast in certain sections or that some topics lacked depth, occasionally requiring supplementary resources. Overall, the feedback indicates it's a strong aid for reinforcing classroom learning or self-study.

Instructor provides responsive support.

"Q&A support is responsive."

"The Q&A was helpful when I got stuck."

Covers all key Year 1/AS topics.

"A solid introduction to A-Level Pure Maths Year 1 topics. Covers all the key areas..."

"Covers the curriculum well."

"Perfect for reinforcing classroom learning or self-studying."

Includes exam-relevant questions.

"The practice questions taken from past papers were invaluable."

"The inclusion of past paper questions in quizzes and worksheets is a massive plus."

"Worksheets are challenging and exam-relevant."

"The quizzes and worksheets are helpful practice..."

Instructor explains concepts clearly.

"The explanations were incredibly clear, especially the calculus sections which I struggled with in school."

"The instructor breaks everything down into manageable chunks."

"Woody is fantastic at explaining complex ideas simply. Highly, highly recommended..."

"Woody explains everything clearly and logically."

Pace can be fast; some topics need depth.

"Some explanations felt a bit rushed, particularly the section on graph transformations."

"Had to supplement with other resources to fully grasp some concepts."

"Found some of the video explanations quite basic and lacking depth for certain topics."

"Maybe not for complete beginners struggling with the GCSE foundations."

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 Maths: Pure (Year 1 / AS) with these activities:

Review GCSE Algebra

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Strengthen your foundational algebra skills before diving into A-Level Maths. A solid understanding of GCSE algebra will make grasping more advanced concepts easier.

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Review key concepts like factorizing and solving equations.
Practice with GCSE algebra past papers.

Read 'A-Level Maths for Dummies'

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Gain a broader understanding of A-Level Maths concepts. This book offers a more accessible explanation of complex topics.

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

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Read the chapters relevant to the course syllabus.
Work through the example problems in the book.

Practice Trigonometric Identities

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Master trigonometric identities through repetitive practice. This will improve your problem-solving speed and accuracy in trigonometry-related questions.

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Find a collection of trigonometric identity problems.
Solve problems repeatedly until proficient.

Four other activities

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Show all seven activities

Create a Trigonometry Cheat Sheet

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Consolidate your understanding of trigonometry by creating a cheat sheet. This will help you memorize important formulas and relationships.

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Gather all relevant trigonometric formulas and identities.
Organize the information in a clear and concise manner.
Include diagrams and examples for better understanding.

Model Real-World Scenarios with Calculus

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Apply calculus concepts to model real-world scenarios. This will deepen your understanding of differentiation and integration.

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Identify a real-world scenario that can be modeled using calculus.
Develop a mathematical model using differentiation or integration.
Analyze the model and interpret the results.

Read 'Challenging Problems in Algebra'

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Enhance your problem-solving skills with challenging algebra problems. This book provides a deeper understanding of algebraic concepts.

View Challenging Problems in Algebra (Dover Books on... on Amazon

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Select problems related to the course syllabus.
Attempt to solve the problems independently.
Review the solutions and learn from your mistakes.

Tutor a GCSE Maths Student

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Reinforce your understanding of fundamental concepts by tutoring a GCSE Maths student. Teaching others is a great way to solidify your own knowledge.

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Find a GCSE Maths student who needs help.
Review the relevant GCSE Maths topics.
Explain the concepts clearly and answer questions.

Career center

Learners who complete A-Level Maths: Pure (Year 1 / AS) will develop knowledge and skills that may be useful to these careers:

Actuary

An actuary assesses and manages financial risks, primarily for insurance companies and pension funds. Actuaries use statistical models and mathematical techniques to predict future events and their financial impact. The quantitative skills and mathematical knowledge gained from this course will be useful to build a strong analytical foundation. Actuarial science relies heavily on probability, statistics, and calculus, all of which require a solid understanding of basic equations and functions, as covered in this course.

See salaries and explore the career path for Actuary

Data Scientist

A data scientist analyzes and interprets complex data to help organizations make better decisions. This career role involves using statistical methods, machine learning algorithms, and data visualization techniques to extract insights and trends. The modeling and problem-solving skills emphasized in this course help build a strong foundation for data analysis. The topics covered on functions and graphs may be useful when visualizing and interpreting data. Strong quantitative skills are invaluable for a Data Scientist.

See salaries and explore the career path for Data Scientist

Market Research Analyst

A market research analyst studies consumer behavior and market trends to advise companies on product development, marketing strategies, and pricing. Market research analysis requires strong quantitative skills for analyzing survey data, conducting statistical tests, and creating predictive models. The equation solving, graphing and data analysis skills provided by this course help build a strong foundation for interpreting market data and making informed recommendations. The analytical skills promoted by this course are essential for a market research analyst.

See salaries and explore the career path for Market Research Analyst

Statistician

A statistician collects, analyzes, and interprets data to draw conclusions and make predictions. Statisticians apply statistical methods and mathematical principles to solve problems in various fields such as healthcare, finance, and marketing. This course may be useful because it provides a foundation in mathematical reasoning and problem-solving, which are essential for statistical analysis. A statistician benefits from the skills learned regarding equations, graphs and functions. The course is a great starting point for a career in data science.

See salaries and explore the career path for Statistician

Financial Analyst

A financial analyst provides guidance to businesses and individuals making investment decisions. A financial analyst assesses financial data, market trends, and economic conditions to make forecasts and recommendations. This course may be useful because the analytical and problem-solving skills honed using these mathematical concepts help in financial modeling and forecasting. The equation solving covered by this course helps build a foundation for quantitative finance. Facility with complex numbers can be useful when performing calculations involving risk and return.

See salaries and explore the career path for Financial Analyst

Aerospace Engineer

An aerospace engineer designs, develops, and tests aircraft, spacecraft, and related systems. Aerospace engineering requires a strong understanding of physics, mathematics, and engineering principles. This course may be useful because the study of advanced mathematical concepts helps build a foundation for modeling and analyzing complex systems. Problems in aerodynamics and orbital mechanics often involve calculus and differential equations, topics for which this course provides helpful context.

See salaries and explore the career path for Aerospace Engineer

Software Engineer

A software engineer designs, develops, and tests software applications and systems. Software engineers apply mathematical principles and computer science techniques to create efficient and reliable code. The proof and mathematical reasoning skills developed in this course may be useful when writing and debugging complex algorithms. Understanding of functions, graphs, and transformations are applicable in graphical user interface development and data visualization. The problem-solving inherent in the course prepares one for the challenges of Software Engineering.

See salaries and explore the career path for Software Engineer

Economist

An economist studies the production, distribution, and consumption of goods and services. Economists analyze economic data, develop models, and forecast trends to inform policy decisions. This course may be useful because economic modeling relies on mathematical and statistical techniques. Understanding of functions, graphs, and optimization is particularly applicable in economic analysis. An economist benefits from the analytical skills sharpened by this course.

See salaries and explore the career path for Economist

Structural Engineer

A structural engineer designs and analyzes the structural integrity of buildings, bridges, and other infrastructure. Structural engineering requires a strong understanding of mechanics, materials, and mathematical modeling. This course may be useful because the study of advanced mathematical concepts helps build a foundation for analyzing forces and stresses. A structural engineer applies mathematical skills to ensure structures are safe and stable.

See salaries and explore the career path for Structural Engineer

Investment Banker

An investment banker assists companies with raising capital through the issuance of stocks and bonds. Investment banking requires a deep understanding of financial markets, valuation techniques, and risk management. This course may be useful because the quantitative skills and mathematical reasoning skills developed through its completion are essential for financial modeling and analysis. Investment banking necessitates strong analytical abilities, which this course may build.

See salaries and explore the career path for Investment Banker

Game Developer

A game developer creates video games for various platforms, overseeing aspects from design to programming. Game development requires mathematical understanding, especially in areas like linear algebra and calculus for simulating physics and creating realistic environments. This course may be useful because the study of functions and graphs helps with understanding coordinate systems and transformations in game design. The skills practiced in this course help one to develop the logical reasoning needed for simulating complex game mechanics.

See salaries and explore the career path for Game Developer

Management Consultant

A management consultant advises organizations on how to improve their performance and efficiency. Management consultants analyze business problems, develop solutions, and implement changes. This course may be useful because the analytical and problem-solving skills honed through the study of these mathematical concepts translate well to business strategy and decision-making. This course, which teaches complex ideas, should prepare one for the challenges of a Management Consultant.

See salaries and explore the career path for Management Consultant

Researcher

A researcher conducts systematic investigations to discover new knowledge or validate existing theories. Research roles often require a master's degree or a doctorate. This course may be useful because the problem-solving skills gained through this mathematical focus help one in designing experiments, analyzing data, and drawing conclusions. A researcher in quantitative fields will find the mathematical foundations in this course beneficial for their work.

See salaries and explore the career path for Researcher

Demographer

A demographer studies population trends, including birth rates, death rates, migration patterns, and age structures. Demographers use statistical methods and mathematical models to forecast population growth and analyze its impact on society. This course may be useful because the study of mathematical concepts provides a solid foundation for understanding and applying demographic models. A demographer will appreciate the course for its lessons on functions and graphs.

See salaries and explore the career path for Demographer

Teacher

A teacher educates students in a variety of subjects, fostering their intellectual and personal growth. This role requires an advanced degree. While this course is specifically aimed at higher-level mathematics, the experience of mastering it should help inform teaching strategies at lower levels. A teacher could use this knowledge to create engaging lessons and real-world examples for their students. A teacher may appreciate the course's structure and teaching methods for insights into effective instruction.

See salaries and explore the career path for Teacher

A-Level Maths

Pure (Year 1 / AS)

What's inside

Learning objectives

Syllabus

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Reviews summary

Clear explanations and exam practice

Activities

Career center

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