Paper 1 · Algebra
⏱ Tested in 1 exam question since 2025
Lesson 22 of 23
Algebra 22 – Abstract Inequalities
In this lesson you’ll learn to
- Prove abstract inequalities such as a + b ≥ 2√(ab) by algebraic manipulation
- Clear surds by squaring and fractions by multiplying through
- Move everything to one side and recognise a² ± 2ab + b² as (a ± b)²
- Justify the final line with 'any real number squared is ≥ 0' — reals only
Most recent exam questions
- 2025 Paper 1 Q10(b) — algebraic identification: points where taxicab distance = Euclidean distance
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