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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