Paper 1 · Algebra
⏱ Tested in 5 exam questions since 2024
Lesson 6 of 23
Algebra 6 – Inequalities
In this lesson you’ll learn to
- Solve quadratic inequalities by factorising, then sketching the parabola
- Read the answer region from the sketch: ≤ 0 inside the roots, ≥ 0 outside
- Multiply by −1 and flip the sign when the x² coefficient is negative
- Match strict vs non-strict inequalities to including the boundary roots
Formula used
Roots of the quadratic equation
x = (-b ± √(b² − 4ac)) / 2a
On page 20 of the log tables — read it off, don’t memorise.Most recent exam questions
- 2025 Paper 1 Q1(a) — modulus inequality
- 2025 Paper 1 Q1(b) — modulus inequality — Paul's universal rule from Algebra 15: always square
- 2025 Paper 1 Q7(a)(v) — solving a quadratic inequality (or equation) modelled as a contextual stage count
- 2025 Paper 1 Q8(e)(ii) — solving a derivative-equals-zero condition involving a surd; squaring to clear the squar…
- 2024 Paper 1 Q10(b) — quadratic inequality; finding boundary roots via the −b formula, then using a sign analy…
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