Try real KS2 maths SATs questions — they’re harder than they look

Amir makes a necklace with blue and red beads. For every 5 blue beads there are 3 red beads. There are 30 blue beads in the necklace. What is the total number of beads in the necklace?

1. The 5 blue beads were scaled up to 30 — find that scale factor, apply it to the 3 red beads, then add blue and red together.
2. 30 ÷ 5 = 6 — Blue beads scaled from 5 to 30 in the ratio, so find what that was multiplied by.
3. 3 × 6 = 18 — Apply the same scale factor to the red beads’ ratio number.
4. 30 + 18 = 48 — Add the blue and red beads together for the total.

Answer: 48

Kirsty mixes blue paint and yellow paint. 25 of her mixture is blue paint. She uses 3.5 litres of blue paint. How many litres of yellow paint does Kirsty use?

1. Blue paint is 25 of the mixture, and yellow is the rest — 35. Finding the value of ONE part lets you work out any number of parts.
2. Two parts (25) make 3.5 litres, so one part (15) is 3.5 ÷ 2 = 1.75 — Blue paint is 2 equal parts (2/5) worth 3.5 litres together, so halve that to find the value of just one part.
3. Yellow is the other 3 parts (35), so 3 × 1.75 = 5.25 — Yellow is the remaining 3 parts (3/5) of the mixture, so multiply the value of one part by 3.

Answer: 5.25 (litres)

35% of the 680 pupils at a school have a pet dog. 159 of the pupils who have a pet dog are boys. How many of the pupils who have a pet dog are girls?

1. There are two steps here. First find how many pupils have a pet dog, which is 35% of 680. Then those dog owners are boys and girls together, so take the boys away to leave the girls.
2. Start with 10% of 680, one tenth, so 680 ÷ 10 = 68 — 10% (one tenth) of the 680 pupils is the building block for working out 35%.
3. 30% is three lots of 10%, so 3 × 68 = 204 — 30% is three of those 10% chunks, so multiply 68 by 3.
4. 5% is half of 10%, so 68 ÷ 2 = 34 — 5% is exactly half of the 10% you already found.
5. 35% is 30% plus 5%, so 204 + 34 = 238 — 35% is the 30% and 5% pieces added together, giving the total number of pupils who have a dog.
6. Those 238 pupils are all the dog owners — 159 are boys, and the rest are girls.
7. Take the boys away from the dog owners, so 238 − 159 = 79 — 159 of the 238 dog owners are boys, so subtracting them leaves just the girls.

Answer: 79

There are 28 pupils in a class. The teacher has 8 litres of orange juice. She pours 225 millilitres of orange juice for every pupil. How much orange juice is left over?

1. Convert the 8 litres to millilitres first, so every amount is in the same unit, then subtract what was poured out.
2. 8 × 1,000 = 8000 — Convert the 8 litres to millilitres so it's in the same unit as the amount poured.
3. 28 × 225 = 6300 — Multiply the 225ml per pupil by all 28 pupils to find the total poured out.
4. 8,000 − 6,300 = 1700 — Subtract what was poured from the total to find what's left.

Answer: 1700 (millilitres (ml))

A band holds a concert for charity. The tickets cost £27 each. They sell 635 tickets. They pay £3,180 to use the hall. They give one-third of the remaining amount to charity. How much money does the band give to charity?

1. Work out how much the tickets raised, subtract the hall cost, then take one-third of what’s left.
2. 27 × 635 = 17145 — The band sells 635 tickets at £27 each, so multiply to find the total raised.
3. 17,145 − 3,180 = 13965 — Subtract the £3,180 hall hire cost from the ticket revenue to see what's left.
4. 13,965 ÷ 3 = 4655 — Charity gets one-third of what's left, so divide the remaining amount by 3.

Answer: 4655 (pounds (£))