Maths Extension 1 Year 11 - Module 1 - Lesson 2
Linear & Quadratic Inequalities
Name
Date
Class
1. Lesson focus
Linear and quadratic inequalities. For quadratics, move all terms to one side, find critical roots, then use a sign chart and include endpoints only for non-strict inequalities.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. Solve x²−5x+6≤0.
3. Solve −x²+4x+5>0.
3. Challenge
Solve 2x²−8x+6≥0.
4. Multiple choice
The solution of (x−2)(x−3)<0 is which interval?
A. 2<x<3
B. x<2 or x>3
C. x≤2 or x≥3
D. x>3
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Solve 3x−5>7.
3x>12, so x>4.
2. Solve x²−5x+6≤0.
(x−2)(x−3)≤0; the parabola opens upward, so 2≤x≤3.
3. Solve −x²+4x+5>0.
Roots are −1 and 5; the parabola opens downward, so −1<x<5.
Challenge. Solve 2x²−8x+6≥0.
2(x−1)(x−3)≥0; upward parabola gives x≤1 or x≥3.
Multiple choice. The solution of (x−2)(x−3)<0 is which interval?
Correct answer: A. The product is negative between the two distinct roots; strict inequality excludes both endpoints.
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