Number, indices & surds (Higher)

Edexcel 1MA1 N

GCSE Maths (1MA1) · Higher · exam-style practice, examiner-report intelligence and the tools that drill it.

Verified against Edexcel 1MA1 (2026 spec)

The topic on one screen

Fractional index $a^{m/n}$ : the denominator is the root, the numerator is the power. Do the root FIRST to keep the numbers small.
Negative index means reciprocal: $a^{-n} = \dfrac{1}{a^n}$ . A negative fractional index does both — flip, then root-and-power.
Simplify a surd by pulling out the largest square factor: $\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$ .
Rationalise by multiplying top and bottom by the surd — or by the conjugate for an $(a + b\sqrt{c})$ denominator. The bottom turns rational every time.
Standard form on the non-calculator paper: handle the powers of $10$ separately from the digits, then fix $1 \le A < 10$ at the very end.
Bounds: the upper bound of a rounded value sits halfway to the next unit. For a division the LARGEST result is $\text{UB} \div \text{LB}$ — picking the wrong pair is where the marks go.

Where students actually lose marks

Bounds questions are marked on the correct upper/lower pairing being shown: a right-looking final value built from the wrong bounds combination is not credited.

Edexcel 1MA1 mark-scheme conventions (accuracy & bounds)

A negative or fractional index answered as a whole-number power (e.g. treating $a^{-2}$ as $a^2$ ) is the most common indices slip — the reciprocal step is a mark in itself.

Edexcel 1MA1 Higher — recurring indices error

Surd answers must be fully simplified: leaving $\sqrt{8}$ instead of $2\sqrt{2}$ , or a surd left in the denominator, loses the final accuracy mark even when the working is right.

Edexcel 1MA1 mark-scheme conventions (surd form)

Try it — exam-style

Medium

2 marks

ORIGINAL

Work out the exact value of $27^{-2/3}$ .

Medium

2 marks

ORIGINAL

Simplify fully $\sqrt{75} - \sqrt{12} + \sqrt{3}$ .

Hard

3 marks

ORIGINAL

Rationalise the denominator and simplify $\dfrac{2 + \sqrt{5}}{\sqrt{5} - 1}$ .

Medium

3 marks

ORIGINAL

A rectangle has length 8.4 cm and width 3.5 cm, each measured to the nearest 0.1 cm. Work out the upper bound for the area of the rectangle.

Easy

2 marks

ORIGINAL

Work out $(3 \times 10^5) \times (8 \times 10^{-2})$ . Give your answer in standard form.

Easy

1 mark

ORIGINAL

A cafe meal deal is one main, one side and one drink. There are 4 mains, 3 sides and 5 drinks. How many different meal deals are possible?

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

Get the printable question packfree account

Drill it properly

Standard Form Trainer

Drill the index arithmetic these questions lean on.

Rounding Trainer

Bounds and degrees of accuracy — the marks around every number.

GCSE maths flashcards

Index laws and surd routines, drilled to instant recall.

Stuck on number, indices & surds (higher)?

Indices and surds are pure method — the grade 7-9 student never guesses them. I teach the routines until they're automatic, and your first lesson is free.

Book a free intro call