Mathematics - International - 0607 CIE

Inequalities

Muhtasari

An inequality says that one quantity is less than, or greater than, another, rather than exactly equal. Speed limits, minimum ages, budget ceilings and safe ranges are all inequalities, and they describe the world far more often than tidy equalities do.

In this lesson you will represent inequalities on a number line, then at Extended level construct and solve linear inequalities, solve them with a graphic display calculator, and picture linear inequalities in two variables as regions on a graph. You will also learn to read off the inequalities that define a shaded region.

Malengo

Represent and interpret inequalities, including on a number line.
Construct, solve and interpret linear inequalities. (Extended only)
Solve inequalities using a graphic display calculator. (Extended only)
Represent and interpret linear inequalities in two variables graphically. (Extended only)
List inequalities that define a given region. (Extended only)

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Maelezo ya Somo

Real limits are rarely a single number; they are ranges. You must be at least a certain height for a ride, spend no more than a budget, keep a temperature within safe bounds. Inequalities are how mathematics captures these everyday constraints, and the same ideas underpin optimisation, the art of getting the best result within limits.

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Tathmini ya Somo

Hongera kwa kukamilisha somo la Inequalities. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.

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Solve 3x - 4 < 11. A. x < 5 B. x > 5 C. x < 7 D. x > 7 Answer: A
Solve -2x >= 6. A. x >= 3 B. x <= 3 C. x >= -3 D. x <= -3 Answer: D
On a number line, which circle marks a value that is included, as in x >= 2? A. an open circle B. a filled circle C. an arrow only D. a dashed circle Answer: B
When drawing the region for y < 2x + 1, the boundary line should be: A. solid B. dashed C. dotted and shaded D. omitted Answer: B
Is the origin (0, 0) in the region y < 2x + 1? A. Yes B. No C. Only on the line D. Cannot tell Answer: A

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Vitabu Vinavyopendekezwa

Cambridge IGCSE Mathematics Core and Extended Coursebook

Manukuu: Second edition

Mchapishaji: Cambridge University Press

Mwaka: 2018

ISBN: 978-1-108-43718-9

Maelezo: Endorsed coursebook with full coverage of the 0580/0980 syllabus, worked examples and practice exercises.

Cambridge IGCSE Core and Extended Mathematics

Manukuu: Fifth edition

Mchapishaji: Hodder Education

Mwaka: 2023

ISBN: 978-1-398-37391-4

Maelezo: Endorsed textbook with worked examples and graded questions across Core and Extended content.

Jifunze zaidi kutoka vyanzo huria

Sehemu ya kitabu Solve Linear Inequalities OpenStax · Elementary Algebra
Graph inequalities on the number line

"Elementary Algebra: Solve Linear Inequalities" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/elementary-algebra/pages/2-7-solve-linear-inequalities. Access for free at https://openstax.org/books/elementary-algebra/pages/1-introduction
Sehemu ya kitabu Graphs of Linear Inequalities OpenStax · Elementary Algebra
Verify solutions to an inequality in two variables

"Elementary Algebra: Graphs of Linear Inequalities" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/elementary-algebra/pages/4-7-graphs-of-linear-inequalities. Access for free at https://openstax.org/books/elementary-algebra/pages/1-introduction

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