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Playbook

Surds and Indices

82 q · 22% HARD · falling from 4.6 to 3.0 a paper. Equations with surds are 71% HARD; fractions, exponential equations and square roots of surds are almost free.

Questions in the bank
82
q/paper (21 papers)
3.90
Tagged HARD
22%
Subtopics
8

Strand: Selective

When you’ll see it

Powers, roots and surds to simplify or compare, or an equation in exponents.

How this chapter is tested

82 questions, falling from 4.6 a paper to 3.0. Equations with surds are 71% HARD; fractions, exponential equations and square roots of surds are almost free.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Laws of indices

    aᵐ × aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1.

  • Exponential equations

    Write both sides to the same base and equate the powers.

  • Rationalising

    Multiply by the conjugate: 1/(√a + √b) = (√a − √b)/(a − b).

  • Square roots of surds

    √(a + 2√b) = √x + √y where x + y = a and xy = b.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Adding surds

    √2 + √3 is not √5.

  • Comparing surds

    Raise to a common power before comparing cube and square roots.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each subtopic. Read the notes once, then drill subtopic by subtopic below.

Surds and Indices notes

Drill every Surds and Indices question

82 questions from the bank, across 8 subtopics.

Drill the 82 questions

Drill one subtopic at a time

The 8 subtopics, in teaching order.

Related playbooks

Often paired with this one — the technique or the trap overlaps. Drill these next.