KS Learning
Maths Exercises
Maths Exercises
The Maths exercises on this page are for secondary school up to and including year 11. They are provided free of charge by KS Learning for anyone teaching
pupils at home or in school. They may not be used for commericial purposes.
- Factors and Multiples
1) Explain each term.
- multiple
- factor
- common multiple
- common factor
2) List the first 5 multiples of
- 3
- 8
- 7
- 12
3) List three common multiples
- 8 and 10
- 20 and 15
- 2, 5, and 7
- 16, 12, and 20
4) Make a list of
- multiples of 8 between 20 and 50
- multiples of 3 less than 40 that are odd numbers
- even numbers between 10 and 60 that are also multiples of 5
- the multiples of 12 less than 150 whose digits sum to less than 10
5) List the factor pairs of
- 12
- 16
- 30
- 100
6) List three common factors of
- 16 and 22
- 20, 100, and 40
- 88, 132, and 110
- 32, 128, and 256
7) Make a list of
- factors of 144 from 10 to 30
- even numbers that are also factors of 72
- factors of 120 that are also integers
- numbers between 0 and 100 that are factors of 200 and multiples of 5
8) Write
- the first three cube numbers
- the smallest square number that is also a cube number
9) Provide answers
- Define a prime number
- How many even prime numbers are there?
- List the prime numbers between 10 and 50
- Is 149 a prime number? Explain.
10) Write the following numbers as products of their primes
- 18
- 150
- 840
- 264
11) Explain the terms
- LCM
- HCF
12) Find the HCF of the pairs of numbers
- 24 and 16
- 42 and 48
- 120 and 144
- 96 and 72
13) Find the HCF of the groups of numbers
- 24, 42, and 72
- 30, 75, and 100
- 54, 117, and 216
14) Find the LCM of the pairs of numbers
- 48 and 108
- 54 and 72
- 90 and 120
- 100 and 125
15) Determine both the HCF and LCM of the following pairs of numbers
- 84 and 60
- 72 and 108
- 180 and 200
- Percentages
1) Write each percentage (i) as a decimal, and (ii) as a fraction
- 48%
- 15%
- 75%
- 27%
2) Write each fraction (i) as a decimal, and (ii) as a percentage
- \(\frac{4}{20}\)
- \(\frac{12}{18}\)
- \(\frac{10}{35}\)
- \(\frac{11}{15}\)
3) Find
- \(\frac{4}{20}\) of 210kg
- 28% of £295
- 82% of 0.32 ml
- \(1\frac{4}{20}\) of 32m
4) Increase
- £34 by 12%
- 270km by 48%
- 54.5g by 21.5%
- 4m by 135%
5) Decrease
- £29.50 by 22%
- 1kg by 9.75%
- £1.12 by 72%
- 95m by 12.5%
6) A pair of shoes is selling for £54 at George's Emporium.
- They are reduced by £5. What is the percentage decrease?
- George bought them for £18. Find the percentage profit on the original price?
- The shoes eventually sell for £38. What is George's percentage profit?
7) Ami makes 5l of daal at a cost of £7.20 which she sells for £18.50.
- What does it cost to make a litre of daal?
- What Ami's percentage profit?
- She sells 10l at an 8% discount. What does she charge?
- How much profit does she make on the sale of 10l of daal?
8) Anjali sets up a store. Express her profit and loss for each item. Anjali sets up a store. Express her
profit and loss for each item.
- an old black shoe with a hole in it that bought for £5 & sold at £3
- half a chocolate bar that she found under her bed, bought for 85p and sold for 15p
- three old samosas bought for 30p each & sold for a total of £1
9) Hrishita invests £55 and must choose between 3.5% compound interest or 4.2% simple interest. Which is better
if she leaves the investment untouched for
- 2 years
- 8 years
- 15 years
10) The number of crows in Bushy Park is due to fall by 12% per year. In 2020, there were 4000 crows.
- How many will there be in 2021?
- How many will there be in 2030?
- When will there be 1000?
11) Oscar puts £120 in a savings account. He gets 5% for the first 3 years, and the interest rate falls to 3.5%,
both compound interest
- 3 years
- 6 years
- 10 years
- 25 years
12) Alisha puts £120 in a savings account at 5% simple interest at the same time as Oscar. At each interval in
the previous question, who has more money?
13) A watch was increased by 5% to £145. What was its original price?
14) A laptop is reduced by 21% to £428. What was its original price?
15) VAT is added to the price of goods at a rate of 20%. Given the prices of the following items, how much of each
price is VAT?
- bicycle £120
- shirt £35
- calculator £6.40
- phone £78
- Fractions
1) Write Sam's results as fractions
- 10 out of 20 for English
- 15 out of 25 for Maths
- 18 out of 30 for French
- 8 out of 24 for History
2) Find the value of \( x \) in the equivalent fractions
- \(\frac{x}{5} = \frac{4}{20}\)
- \(\frac{2}{3} = \frac{8}{x}\)
- \(\frac{4}{x} = \frac{12}{18}\)
- \(\frac{2}{7} = \frac{x}{35}\)
3) Write as an improper fraction
- \(2\frac{3}{5}\)
- \(5\frac{1}{4}\)
- \(-1\frac{3}{8}\)
- \(-3\frac{2}{3}\)
4) Write as a mixed fraction
- \(\frac{15}{4}\)
- \(\frac{121}{9}\)
- \(\frac{23}{5}\)
- \(\frac{84}{6}\)
5) Work out the answer
- \(\frac{2}{3} + \frac{1}{4}\)
- \(\frac{5}{6} + \frac{1}{2}\)
- \(\frac{3}{5} + \frac{2}{3}\)
- \(\frac{3}{2} + \frac{2}{5}\)
6) Determine the result
- \(\frac{3}{8} - \frac{1}{4}\)
- \(\frac{5}{6} - \frac{2}{3}\)
- \(\frac{4}{5} - \frac{2}{3}\)
- \(\frac{7}{10} - \frac{2}{5}\)
7) xxx
- \(\frac{3}{8} \times \frac{1}{4}\)
- \(\frac{5}{6} \times \frac{2}{3}\)
- \(\frac{7}{10} \times \frac{2}{5}\)
- \(\frac{8}{9} \times \frac{3}{4}\)
8) xxx
- \(\frac{2}{5} \div \frac{1}{4}\)
- \(\frac{3}{5} \div \frac{2}{3}\)
- \(\frac{1}{2} \div \frac{3}{8}\)
- \(\frac{5}{12} \div \frac{3}{10}\)
9) Convert each decimal to a fraction
- 0.35
- 0.64
- 0.08
- 0.13
10) Convert each fraction to a decimal
- \(\frac{3}{8}\)
- \(\frac{2}{5}\)
- \(\frac{7}{10}\)
- \(\frac{3}{4}\)
11) Convert each fraction to a decimal
- \(\frac{2}{9}\)
- \(\frac{1}{11}\)
- \(\frac{3}{9}\)
- \(\frac{5}{11}\)
12) Write from smallest to largest
- \(0.25, \frac{3}{8}, \frac{2}{9}, 0.3, \frac{5}{10} \)
- \(\frac{5}{8}, 0.5, \frac{4}{7}, 0.55, \frac{4}{6} \)
- \(0.41, 0.4\dot{1}, \frac{3}{7}, \frac{5}{11}, \frac{2}{5} \)
- \( \frac{7}{8}, \frac{8}{9}, 0.9, \frac{6}{7}, \frac{9}{11} \)
- Bidmas
1) Work our
- \(1 - 5 + 4 - 2\)
- \(1 - (5 + 4) - 2\)
- \(1 - 5 + (4 - 2)\)
- \((1 - 5) + 4 - 2\)
- \(1 - (5 + 4 - 2)\)
- \((1 + 5 - 4) - 2\)
2) Determine
- \(4 \times 3 - 5 + 3\)
- \(4 \times (3 - 5) + 3\)
- \((4 \times 3) - 5 + 3\)
- \(4 \times 3 - (5 + 3)\)
- \((4 \times 3 - 5) + 3\)
- \(4 \times 3 - (5 + 3)\)
3) Calculate
- \(8 - (2 + 7) - 5 + 3\)
- \(8 - 2 + 7 - 5 + 3\)
- \((8 - 2 + 7) - 5 + 3\)
- \(8 - (2 + 7) - (5 + 3)\)
- \(8 - (2 + 7 - 5) + 3\)
- \((8 - 2) + 7 - (5 + 3)\)
4) Determine
- \(-(2 + 5 - 7) + 2 - 4\)
- \(-(2 + 5 - (7 + 2)) - 4\)
- \((-2 + 5) - (7 + 2 - 4)\)
- \(-(2 + (5 - (7 + 2 - 4)))\)
- \(-(2 + 5 - ((7 + 2) - 4))\)
- \(-(2 + (5 - 7)) + 2 - 4\)
5) Work out
- \(5 - 7 \times 2 - 6 \div 2\)
- \((5 - 7) \times 2 - 6 \div 2\)
- \(5 - 7 \times (2 - 6) \div 2\)
- \(5 - (7 \times 2 - 6) \div 2\)
- \((5 - 7) \times (2 - 6 ) \div 2\)
- \((5 - 7 \times (2 - 6)) \div 2\)
6) List the following numbers
- the first 5 square numbers
- the first 5 cube numbers
- the prime numbers from 50 to 80
- all the factors of 144
- three multiples of 4 greater than 200
- a number that is a multiple of 6 and has a factor of 5
7) Determine the answer
- \(( ( - 7 ) - ( - 8 ) ) - 6\)
- \(3 + ( ( - 2 ) - ( - 9 ) )\)
- \(6 + ( 1 + ( - 5 ) )\)
- \(( - 3 ) - (1 - ( - 2 ))\)
- \(( ( - 6 ) - 4 ) - ( - 8 )\)
- \(( 3 - ( - 3 ) ) - 5\)
- \(( - 7 ) - ( ( - 1 ) + 7 )\)
- \(( - 4 ) - ( ( - 7 ) + ( - 8 ) )\)
8 Work out the result
- \((-2) \times (3 + -5)\)
- \((-2) \times (3) + -5\)
- \(-(2 \times 3) + -5\)
- \(-(2 \times 3 + - 5)\)
- \((-3 - - 5 \times (-4))\)
- \(-3 - (- 5 \times -4)\)
- \((-3 - -5) \times (-4)\)
- \(-3 - 5 \times -4\)
9) Find the result
- \(-20 \div 5 + 2\)
- \(2 - 4 \div (-3 - 1)\)
- \(3 + -4 \div 16\)
- \(-(3 \times -2 \div 3 + -5)\)
- \(-2(-3 - -5) \div -4\)
- \(-2 \div -2 \div -2 + 6\)
- \(-(-2 + 7) \div (-3 \times -2)\)
- \(6 - (10 \div - 5) \times -2\)
10) Find the missing number
- \(-2 + \) \( = 5 + 2\)
- \(-2 + \) \( = -5\)
- \(- 3 + \) \( = 0\)
- \(-( 3 - \) \( ) = 4\)
- \(4 \times \) \( = -12\)
- \(-8 = 3 + \)
- \(-3 + -4 = \) \( + 5\)
- \(2 \times-3 = 1 - \)
- \( \times -2 = 10\)
- Number Types
1) Given the following set of numbers
{ \( 12, \frac{2}{3}, 11, -4, 0, 9, -\frac{2}{5}, -6, 8, 3, 17 \)},
select all that are:
- integers
- fractions
- even numbers
- odd numbers
- natural numbers
- real numbers
- surds
2) Define with at least two examples
- even numbers
- natural numbers
- integers
- odd numbers
- real numbers
- prime numbers
- surds
- counting numbers
- square numbers
- composite numbers
3) Mark on a number line from -6 to +6
- all even numbers with an X
- three consecutive natural numbers with an S
- two odd numbers that add up to 8 with an M
- the position of a half with a Y
- three numbers that are not even with a W
- three real numbers with a Z that are not whole numbers
- all the prime numbers with a P
- a square number with Q
4) Write using maths symbols
- six is greater than five
- eight is equal to two times four
- six is greater than or equal to two
- x is between three and five
- seven is not equal to one
- pi is approximately equal to 3.14
- the sum of three and four is lessthan the product of three and four
5) List the following numbers
- all the odd numbers between 6 and 15
- eight real numbers between 9 and 10
- five even numbers greater than twenty
- the next 5 natural numbers that follow right after 11
- the first 10 positive prime numbers
- all even prime numbers
- 4 surds
- all the integers from -5 to +5
- five consecutive natural numbers between 100 and 110
- all the square numbers from 4 to 60
- a number that is both a square and a cube number
6) Use a number line to illustrate
- \(2 \le x \lt 6\) for real numbers
- \(x \ge -3\) for integers
- \(x = -5, -2, 1, 2, 3\)
- \(-3 \le x \le 2\) for real numbers
- \(x \gt 5\) and \(x \lt 2\) for integers
7) Sort in ascending order
- 2, 13, 8, 25, 21, 3
- -5, 11, -8, 7, -6, -3
- -321, 241, -54, 333, -21, 231
8) Sort in descending order
- \(23, \frac{1}{4}, 3, -8, 1\frac{2}{3}, 12\)
- \(-51, 9, -\frac{8}{9}, 17, -2, \frac{2}{3}\)
- \(-32, 2241, -854, 3433, -2311, 227\)
9) Use a calculator to find
- \( 17^2\)
- \(\sqrt[3]{729} \)
- \(23^4\)
- \(\sqrt{324}\)
- \(\sqrt[5]{16807} \)
- \((-3)^7 \)
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