OpenRevise GCSE

Maths · Topic 1: Year 10

Number

Counting and problem solving, place value and estimating, prime factors with HCF and LCM, powers and roots, standard form and surds.

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Key terms in this chapter

All 43, gathered from every lesson.

Outcome
One possible result of a choice or experiment.
Systematic list
A list that follows a pattern so no outcome is missed or repeated.
Product rule for counting
If there are \(m\) ways to do one thing and \(n\) ways to do another, there are \(m \times n\) ways to do both. (Higher)
Arrangement
An ordering of items, for example people in a queue.
Restriction
A rule that limits the choices, such as "the number must be even".
Factorial
\(n! = n \times (n-1) \times \dots \times 2 \times 1\). For example, \(4! = 24\).
Place value
The value of a digit, which depends on its position in the number.
Decimal place (d.p.)
A digit after the decimal point.
Significant figure (s.f.)
Any digit of a number starting from the first non-zero digit.
Estimate
An approximate answer found by rounding the numbers first.
Approximately equal to
The symbol \(\approx\), used for an estimate.
Overestimate
An estimate bigger than the exact answer.
Underestimate
An estimate smaller than the exact answer.
Factor
A number that divides exactly into another number.
Multiple
A number in another number's times table.
Prime number
A number with exactly two factors, 1 and itself.
Prime factor decomposition
Writing a number as a product of its prime factors.
Index form
Writing repeated factors as powers, e.g. \(2^3 \times 3^2\).
Highest common factor (HCF)
The largest number that is a factor of two or more numbers.
Lowest common multiple (LCM)
The smallest number that is a multiple of two or more numbers.
Power (index)
The small number that says how many times the base is multiplied by itself.
Base
The number being multiplied, e.g. the 5 in \(5^3\).
Square number
A number made by multiplying a whole number by itself, e.g. \(49 = 7^2\).
Cube number
A number made by multiplying a whole number by itself three times, e.g. \(64 = 4^3\).
Square root
The number that squares to give a number: \(\sqrt{49} = 7\).
Cube root
The number that cubes to give a number: \(\sqrt[3]{64} = 4\).
Index laws
The rules for multiplying, dividing and raising powers of the same base.
Zero index
Any non-zero number to the power 0 equals 1.
Negative index
\(a^{-n} = \dfrac{1}{a^n}\): one over the positive power.
Reciprocal
One divided by a number. The reciprocal of 4 is \(\frac{1}{4}\); of \(\frac{2}{3}\) is \(\frac{3}{2}\).
Fractional index (Higher)
A power that is a fraction: the bottom is a root, the top is a power.
nth root
The number that, raised to the power \(n\), gives the original number.
Standard form
A number written as \(A \times 10^n\), where \(1 \le A < 10\) and \(n\) is an integer.
Power of 10
10 multiplied by itself a number of times, e.g. \(10^3 = 1000\).
Prefix
Letters in front of a unit that stand for a power of 10, e.g. kilo \(= 10^3\).
Ordinary number
A number written out in full, without powers of 10.
Integer
A whole number, positive, negative or zero.
Rational number
A number that can be written as a fraction of two integers.
Irrational number
A number that cannot be written as a fraction; its decimal never ends or repeats.
Surd
A root that is irrational, such as \(\sqrt{2}\) or \(\sqrt{10}\).
Like surds
Multiples of the same surd, such as \(5\sqrt{2}\) and \(3\sqrt{2}\), which can be added and subtracted.
Simplest form
A surd with the largest possible square number taken out, e.g. \(6\sqrt{2}\).
Rationalise the denominator
Rewrite a fraction so there is no surd on the bottom.