Equations And Inequalities
Overview
Working out a break-even point, finding where two delivery charge plans cost the same, or deciding which range of values keeps a design within safety limits: all of these are equations or inequalities in disguise. Solving them accurately, and knowing which method fits which situation, is one of the most tested skills across the whole 4MB1 paper.
This topic covers solving equations of degree 1, 2 and 3 in one unknown, pairs of simultaneous equations (including a linear equation paired with a quadratic), and linear and quadratic inequalities, represented on a number line and, for two variables, as a region.
Objectives
- Solve equations of 1st, 2nd and 3rd degree containing one unknown quantity, including quadratics by factorisation, graph, completing the square or formula
- Solve linear simultaneous equations in two unknowns
- Solve simultaneous equations in two unknowns where one equation is linear and the other is quadratic
- Solve linear inequalities and represent solutions on the number line and in two-dimensional space
- Solve quadratic inequalities in one unknown and represent the solution set on a number line
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 And Inequalities. Now that youve explored the key concepts and ideas, its 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.
- Which method always works for solving any quadratic equation, even when it does not factorise? A) Trial and improvement only B) The quadratic formula C) Collecting like terms D) Cross-multiplication Answer: B
- Solve x + 3 > 9. A) x > 6 B) x > 12 C) x < 6 D) x < 12 Answer: A
- What happens to an inequality sign when both sides are divided by a negative number? A) Nothing changes B) It reverses direction C) It becomes an equals sign D) It becomes strict Answer: B
- The roots of x^2 - 5x + 6 = 0 are 2 and 3. What is the solution to x^2 - 5x + 6 < 0? A) x < 2 or x > 3 B) 2 < x < 3 C) x < 2 D) x > 3 Answer: B
- To solve simultaneous equations where one is linear and one is quadratic, which method is used? A) Elimination only B) Substitution C) Completing the square on both D) Adding the equations directly Answer: B
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Recommended Books
Further learning from open sources
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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
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Textbook section
Systems of Linear Equations: Two Variables
Solve systems of equations by graphing.
"Algebra and Trigonometry: Systems of Linear Equations: Two Variables" 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/11-1-systems-of-linear-equations-two-variables. 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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