Number Toolkit (Edexcel IGCSE Maths A (Modular))

A factor of a number is a positive integer that divides exactly into the number.

A multiple of a number is a positive integer that can be made by multiplying the number by another integer.

A prime number is a positive integer which has exactly two factors, itself and 1.

False.

1 is not a prime number, as it only has one factor.

2 is the only even prime number.

The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

The first twelve square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.

The first five cube numbers are: 1, 8, 27, 64, 125.

True.

Any positive integer has an infinite number of multiples.

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.

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!

A currency is a system of money in general use in a particular country or region.

False.

You should usually round answers involving money to two decimal places.

However, you may sometimes be asked to round answers to the nearest integer.

True.

Large monetary amounts, such as the cost of a car, are usually rounded to the nearest whole number.

False.

Monetary values given in more than two decimal places should be used in the working.

They should only be rounded for the final answer.

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.

True.

is the same as .

For example, is the same as .

It is okay to swap them round.

False.

is not the same as .

For example, is not the same as .

The first gives but the second gives .

False.

The correct answer is: if then .

That is because means (the stays on the top of the fraction).

You could write as .

Then bring the 9 and 15 together, giving .

You know that so the number above becomes .

Multiplying by ten each time adds an extra zero, so the answer is .

False.

is the same as .

This is also the same as .

Alternatively, you can use fractions to see this: .

The correct answer is .

.

You multiply the top and bottom of the fraction by 10 to remove the decimal.

These two fractions are identical, so you can continue working on the second one.