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Paper 1
Inequalities & Regions
Both
Shade the region that satisfies all inequalities.
Key Facts
- Flip inequality when multiplying/dividing by negative.
- Solid line for ≤ or ≥, dashed for < or >.
- Shade the side that satisfies the inequality.
- Intersection of regions satisfies all inequalities.
Topics Covered
Solving Inequalities
What you need to know
- •Solve like equations but keep inequality sign.
- •Flip the inequality when multiplying/dividing by negative.
- •Show solutions on a number line.
Exam Tips
- Use open circle for < or >, closed circle for ≤ or ≥.
Quadratic Inequalities
What you need to know
- •Solve quadratic equation first to find critical values.
- •Sketch parabola to determine regions.
- •Test a value in each region.
Exam Tips
- Sketch the graph to visualize the solution.
Graphical Regions
What you need to know
- •Draw each inequality as a line (solid for ≤/≥, dashed for </>).
- •Shade the required region.
- •Test a point to check shading direction.
Exam Tips
- Label each line clearly.
- Use origin as test point if not on line.
Key Terms
Inequality
Mathematical statement using <, >, ≤, or ≥.
Region
Area on a graph satisfying an inequality.
Critical value
Boundary value where inequality changes.
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Common Exam Questions
Solve 3x - 5 ≥ 10.
2 markseasyPaper 1
Model Answer
3x ≥ 15, so x ≥ 5.
What examiners want to see
- ✓Solve like an equation.
- ✓Keep inequality sign correct.
Solve x^2 - 5x + 6 < 0.
3 marksmediumPaper 1
Model Answer
(x-2)(x-3) < 0, so 2 < x < 3.
What examiners want to see
- ✓Factorize quadratic.
- ✓Identify region between roots.
Shade the region satisfying y > 2x + 1 and y ≤ 5.
3 marksmediumPaper 1
Model Answer
Draw dashed line y = 2x + 1 and solid line y = 5. Shade above first, below second.
What examiners want to see
- ✓Draw both lines correctly.
- ✓Shade intersection.
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