GCSE Maths Number questions by topic

Use the number line and written methods for this question.

1. (a)Write −3, −7, 2, −1 in ascending order.[1]
2. (b)Work out −4 + 9 − 6.[1]
3. (c)Work out 2⅓ + 1½, giving your answer as a mixed number.[2]

A shop sells 3.42 m of ribbon per box. Ribbon comes in 6-box packs.

1. (a)Work out the total metres of ribbon in a pack.[2]
2. (b)A student answers “205.2 m”. Use an estimate to explain why this cannot be right.[2]

Here are two numbers: 60 and 45.

1. (a)Express 60 as a product of prime factors.[2]
2. (b)Express 45 as a product of prime factors.[1]
3. (c)Hence write down the highest common factor of 60 and 45.[1]
4. (d)Hence write down the lowest common multiple of 60 and 45.[1]

A café menu is being planned.

1. (a)The café offers 3 soups and 5 sandwiches. Work out the number of different soup-and-sandwich lunches.[1]
2. (b)A 4-digit PIN uses the digits 0 to 9, and digits may be repeated. Work out the number of possible PINs.[2]
3. (c)Write down one assumption you made in part (b).[1]

A family visits a theme park. Adult tickets cost £34.75 each and child tickets cost £23.80 each.

1. (a)Work out the total cost of tickets for 2 adults and 3 children.[3]
2. (b)The family pays with exactly £150. Work out the change they should receive.[1]

A jogger plans to run 28 km in one week.

1. (a)On Saturday she runs 3⁄7 of the 28 km. Work out how far she runs on Saturday.[2]
2. (b)She runs the distance that is left in four equal runs on Sunday to Wednesday. Work out how far each of those runs is.[2]

Work out the following.

1. (a)Work out (2 + 3)² − 4 × 3².[3]
2. (b)Write down the reciprocal of 1¼, giving your answer as a fraction in its simplest form.[2]

Here are two numbers: 504 and 120.

1. (a)Express 504 as a product of prime factors in index form.[3]
2. (b)Given that 120 = 2³ × 3 × 5, find the highest common factor of 504 and 120.[2]

This question is about squares and roots.

1. (a)Work out √81 + ∛125.[2]
2. (b)A square has area 72 cm². Show that the length of one side is between 8 cm and 9 cm.[3]

Inequalities, reciprocals and conversions.

1. (a)Insert <, > or = in each box: ⅜ ☐ 0.375 and ⅔ ☐ 0.67[2]
2. (b)An integer x satisfies −2 ≤ x < 3. List all the possible values of x.[2]

A number is written as 2³ × 5².

1. (a)Work out the number.[2]
2. (b)Explain why 2³ × 5² is not a square number.[2]

A school issues passcodes made from two letters followed by three digits.

1. (a)Each letter is chosen from A to D, and letters may repeat. Work out the number of possible two-letter starts.[1]
2. (b)Each digit is chosen from 0 to 9, the first digit cannot be 0, and no digit may be repeated within a code. Work out the number of possible three-digit ends.[2]
3. (c)Work out the total number of possible passcodes.[2]

A factory prints registration labels of the form LLDD: two letters chosen from A to F, then two digits chosen from 1 to 9.

1. (a)Letters may repeat. Work out the number of possible two-letter starts.[1]
2. (b)Digits may not repeat. Work out the number of possible two-digit ends.[2]
3. (c)Work out the total number of different labels.[3]

Two alarm bells ring at noon. One rings every 12 minutes; the other rings every 18 minutes.

1. (a)Express 12 and 18 as products of prime factors.[2]
2. (b)Find the lowest common multiple of 12 and 18.[2]
3. (c)Write down the time when the two bells next ring together.[1]
4. (d)Write down the highest common factor of 12 and 18.[1]

Do not use a calculator for this question. (Higher)

1. (a)Show that ∛100 is between 4 and 5.[2]
2. (b)Estimate ∛100 to one decimal place, showing the cubes you check.[3]
3. (c)State whether your estimate is an over-estimate or an under-estimate, giving a reason.[1]

Here are two numbers: 420 and 168.

1. (a)Express 420 as a product of prime factors in index form.[2]
2. (b)Express 168 as a product of prime factors in index form.[2]
3. (c)Find the highest common factor of 420 and 168.[1]
4. (d)Find the lowest common multiple of 420 and 168.[2]

This question is about estimating a square root. Do not use a calculator. (Higher)

1. (a)Show that √110 is between 10 and 11.[2]
2. (b)By testing tenths, find an estimate of √110 to one decimal place.[2]
3. (c)State whether your estimate is an over-estimate or an under-estimate, giving a reason.[1]

A lighthouse beacon flashes every 45 seconds. A second beacon flashes every 60 seconds, and a third flashes every 75 seconds. All three have just flashed together.

1. (a)Give the prime factorisations of both 45 and 60.[2]
2. (b)State the HCF of 45 and 60.[1]
3. (c)Find the time, in minutes, until all three beacons next flash together.[3]