Equations
Overview
An equation is a statement that two things are equal, and solving one means finding the value (or values) that make it true. From a single linear equation to a pair of simultaneous equations, the skill of keeping an equation balanced is one of the most powerful in mathematics.
In this lesson you will construct and solve linear equations, solve a pair of simultaneous linear equations, and change the subject of a formula. (At Extended these skills extend to fractional, simultaneous non-linear and quadratic equations.)
Objectives
- Construct simple expressions, equations and formulas.
- Solve linear equations in one unknown.
- Solve simultaneous linear equations in two unknowns.
- Change the subject of simple formulas.
- Construct expressions, equations and formulas. (Extended only)
- Solve fractional equations with numerical and linear algebraic denominators. (Extended only)
- Solve simultaneous equations, involving one linear and one non-linear. (Extended only)
- Solve quadratic equations by factorisation, completing the square and by use of the quadratic formula. (Extended only)
- Change the subject of formulas. (Extended only)
Audio Lesson
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Mind map
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Flashcards
Quick recall practice on the facts this topic is tested on.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Equations. Now that you've explored the key concepts and ideas, it's time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- Solve 3x + 5 = 20. A. x = 3 B. x = 5 C. x = 8 D. x = 15 Answer: B
- Solve 2(x - 3) = 10. A. x = 2 B. x = 5 C. x = 8 D. x = 11 Answer: C
- Solve the simultaneous equations x + y = 7 and x - y = 1. What is x? A. 3 B. 4 C. 6 D. 8 Answer: B
- Make a the subject of v = u + at. A. a = v - u - t B. a = (v - u)/t C. a = v - u/t D. a = (u - v)/t Answer: B
- Solve 5x - 4 = 11. A. x = 1.4 B. x = 3 C. x = 7 D. x = 15 Answer: B
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Recommended Books
Further learning from open sources
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Textbook section
Linear Equations in One Variable
Solve equations in one variable algebraically.
"Algebra and Trigonometry: Linear Equations in One Variable" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/2-2-linear-equations-in-one-variable. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
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Textbook section
Quadratic Equations
Solve quadratic equations by factoring.
"Algebra and Trigonometry: Quadratic Equations" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/2-5-quadratic-equations. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
Published by other organisations under open licences, credited as they ask. Links open their websites.
Practice Mock Questions
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