Number Toolkit (Cambridge (CIE) IGCSE Maths)

A natural number is a positive integer.

They are often referred to as counting numbers.
Zero is not a natural number.

True.

The result of any number multiplied by its reciprocal will be equal to 1.

E.g.

A rational number is a number that can be written as a fraction, , where both and are integer (whole number) values.

False.

is not a rational number, it is irrational.

It cannot be written as a fraction where both the numerator and denominator are integer (whole number) values.

False.

2.456456456... is a recurring decimal so is not an irrational number.

It can be written as the fraction .

False.

When multiplying two negative numbers, the result is a positive value.

When multiplying a positive and a negative, the result is a negative value.

True.

Subtracting a negative number is the same as adding a positive number.

True.

When finding a square of a negative number, the result is positive.

This is because you are multiplying a negative by a negative, which results in a positive.

When finding the cube of a negative number, you are multiplying a negative by a negative, by a negative so the final result is a negative.

False.

Although subtracting a negative number is equivalent to adding a positive number, the final result will only be positive if the number you are adding it to is large enough.

For example, the calculation but the calculation .

False.

but .

It is always important to put brackets around negative values when you are substituting them into calculations!

An exponent is a power or order used in mathematical expressions to represent repeated multiplication of a base number.

E.g. In the expression , the 5 is the exponent.

The symbol ≈ means approximately equal to.

False.

The equals sign (=) is used to show that two expressions are equal, while the identical sign (≡) is used to show that two expressions are identical.

An inequality is a statement that compares two quantities in terms of their size using symbols such as >, <, ≥, or ≤.

True.

The symbol ± is used to represent two distinct (different) answers, often in quadratic equations.

is the positive square root.

It represents the positive result when you find perform the opposite (inverse) operation of squaring a number.

is the negative square root.

The letters in BIDMAS/BODMAS represent: Brackets, Indices, Division, Multiplication, Addition, Subtraction.

BIDMAS/BODMAS is an acronym that stands for the order of operations in mathematics.

True.

When using BIDMAS/BODMAS on a calculation that only involves addition and subtraction, the calculation should be performed from left to right.

E.g.

False.

When using BIDMAS/BODMAS on a calculation that only involves multiplication and division, the calculation should be performed from left to right.

E.g.

The word sum implies that you need to add numbers together.

Subtraction is the mathematical operation of finding the difference between two numbers by taking one number away from another.

True.

The word share implies that you need to divide numbers.

The word product is often used to imply that you need to multiply two numbers together.

A division can be treated like a fraction where common factors from both the numerator and denominator can be found and cancelled.

E.g. can be written as

You can then cancel it to its simplest form by finding common factors,

Use estimation to rounding the numbers to integer values, perform the simpler calculation and compare the estimated value with your actual value.

Turn the division into a fraction, e.g.

Multiply the values by a multiple of 10 to change them to integers,
e.g.

Simplify the fraction (complete the easier calculation), e.g.

Convert the answer by 'undoing' the initial changes, e.g.