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Summary OCR MEI Mathematics: Year 1 (AS) Pure - Inequalities Cheat Sheet $0.00

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Summary OCR MEI Mathematics: Year 1 (AS) Pure - Inequalities Cheat Sheet

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This document briefly summarises the 'Inequalities' topic of the Year 1 (AS) Pure section of the OCR MEI Mathematics A Level Course.

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  • January 22, 2021
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  • 2020/2021
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By: tsmith3553 • 1 year ago

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Inequalities
Symbols
● < → less than
● > → greater than
● ≤ → less than or equal to
● ≥ → greater than or equal to
● Number line inequalities - filled-in circle means ‘or equal to’
● Graphical inequalities - solid line means ‘or equal to’


Linear Inequalities
● Involves only x terms and constants
● Solve linear inequalities as you would solve an algebraic equation ​for the
most part
● However if you multiply or divide each side by a negative number the
inequality symbol ​must​ be reversed
● Check solutions by picking a number and plugging it into the inequality to
see if it satisfies your solution

Example
S olve 1 − x ≥ 2x − 5
1 − x ≥ 2x − 5
1 ≥ 3x − 5
6 ≥ 3x
x ≤2


Quadratic Inequalities
● Quadratic inequalities solved by factorising quadratic expression
● The numbers in the brackets tell you the boundaries of the solutions
● To decide which inequality signs to use, visualise graph

Example
S olve 3 − 5x ≤ 2x2
3 − 5x − 2x2 ≤ 0
2x2 + 5x − 3 ≥ 0
(2x − 1)(x + 3) ≥ 0
x ≥ 21 or x ≤ −3

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