Inequalities

Where this fits in the syllabus

Grade 11 · Term 3

Key points to revise

Revise Inequalities fast with concise, exam-ready key points

About O/L Mathematics: O/L Mathematics covers number systems, algebra, geometry, trigonometry, and statistics across Grade 10 and 11.

• Addition and Subtraction Rule: Adding or subtracting the same number from both sides of an inequality does not change the direction of the inequality
• Multiplication and Division by a Positive Number: Multiplying or dividing both sides by a positive number does not change the direction
• Multiplication and Division by a Negative Number: Multiplying or dividing both sides by a negative number reverses the direction of the inequality
• Solving Linear Inequalities: Isolate the variable using the above rules. Example: 2x - 3 > 5 => 2x > 8 => x > 4
• Solving Quadratic Inequalities:

Must know

• Read the question carefully: Note whether the inequality is strict (<, >) or non-strict (<=, >=). This affects whether endpoints are included
• For linear inequalities, treat them like linear equations first, but remember the sign reversal rule. Always check your final answer by substituting a value from the solution set back into the original inequality
• For quadratic inequalities, always factor first if possible. If factoring is difficult, use the quadratic formula to find the roots accurately. Then draw a quick number line and test one point from each interval
• Use the sign of the leading coefficient to shortcut interval testing: For a quadratic with two distinct roots, if a > 0, the expression is positive outside the roots and negative between them. If a < 0, it is the opposite. This can save time, but be careful with the direction of the inequality

Source: Idasara knowledge pack — english/OL_11/mathematics v16, short_notes: Lesson 20 - Inequalities

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