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LearnAQA8300First teaching 2015Papers 1–3 · Higher tierNumber

Papers 1–3 · Module

Number

5 subtopics≈ 150 min in total

Start the module: Types of number, factors and multiples Open graphing calculator

Types of number, factors and multiples
Every whole number is built from primes, like a molecule from atoms. Writing numbers as products of primes makes highest common factors and lowest common multiples quick. Along the way you meet the families of numbers: integers, squares, cubes, rational and irrational numbers.
≈ 30 min
Fractions and decimals
To add or subtract fractions, give them a common denominator. To multiply, multiply tops and bottoms; to divide, flip the second fraction and multiply. Every fraction is a terminating or recurring decimal, and every recurring decimal can be turned back into a fraction.
≈ 30 min
Indices and standard form
Multiply powers of the same base by adding indices, divide by subtracting, and raise a power to a power by multiplying. $a^0=1$ , $a^{-n}=\dfrac1{a^n}$ , and $a^{\frac1n}$ is the $n$ th root. Standard form $A\times10^n$ ( $1\le A<10$ ) writes huge and tiny numbers compactly.
≈ 30 min
Surds
A surd is a root that can't be simplified to a whole number, like $\sqrt2$ . Keep surds exact: pull out square factors ( $\sqrt{48}=4\sqrt3$ ), collect like surds, and remove surds from denominators by multiplying top and bottom by the right surd or by the conjugate.
≈ 30 min
Estimation and limits of accuracy
Round to significant figures or decimal places, and estimate answers by rounding every number to $1$ s.f. A measurement rounded to the nearest unit could really be up to half a unit either side: those are its bounds. For calculations, choose the bounds that make the answer biggest or smallest.
≈ 30 min