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KS2 SATs 2022 Paper 3: reasoning
21 questions · 35 marks. Every question from the paper, recreated, with the official mark scheme, an annotated worked solution and a shadow question (the same skill with new numbers). Open the paper in the Ultimate Exam Question Finder to present it, print it or build a set.
Question 1 (1 mark)
Here is a drawing of a hexagonal prism.
Diagram: A drawing of a hexagonal prism lying on its side, with one hexagon end at the front left and its length going back to the upper right.
How many faces does the prism have?
(1 mark)
Question 2 (1 mark)
Here are six number cards.
Diagram: 6 number cards in a row: 3, 4, 5, 6, 7, 8.
Use all six cards to complete the three multiplications below.
24 = boxedphantomX × boxedphantomX
28 = boxedphantomX × boxedphantomX
30 = boxedphantomX × boxedphantomX
(1 mark)
Question 3 (2 marks)
Olivia buys a banana, an apple and a bag of nuts.
banana apple bag of nuts 30p 45p 60p She pays with three 50p coins.
What is her change, in pence?
Show your method
(2 marks)
Question 4 (2 marks)
Draw four lines to match each fraction to its equivalent decimal.
Diagram: Four fraction boxes on the left, top to bottom: 1/2, 3/10, 3/4, 3/100. Six decimal boxes on the right, top to bottom: 0.3, 0.5, 0.8, 0.03, 0.25, 0.75.
(2 marks)
Question 5 (2 marks)
Some children vote for their favourite ice-cream flavour.
Ice-cream flavour Number of children vanilla 87 chocolate 154 strawberry ? mint 38 Total 402 How many children vote for strawberry?
Show your method
(2 marks)
Question 6 (2 marks)
This chart shows the range of temperatures each day during one week
from Monday to Friday.Diagram: A chart with a temperature scale in °C along the bottom from –8 to 8 (numbered every 2, a line at every degree). One bar for each day, top to bottom, goes from that day’s lowest to its highest temperature: Monday –4 to 1, Tuesday –7 to 0, Wednesday –5 to 3, Thursday –1 to 6, Friday –7 to 4.
(a)
What was the lowest temperature, in °C?
(1 mark)
(b)
What was the difference between the highest and lowest temperatures on Wednesday, in °C?
(1 mark)
Question 7 (2 marks)
One Saturday afternoon, a total of 234,869 people attended three rugby matches.
• 80,978 people attended match 1
• 72,319 people attended match 2How many people attended match 3?
Show your method
(2 marks)
Question 8 (2 marks)
boxed7,546
Round this number:
to the nearest 1,000 to the nearest 100 to the nearest 10 (2 marks)
Question 9 (1 mark)
Complete the calculation.
1,000 × 416 = 10 × boxedphantomXX
(1 mark)
Question 10 (2 marks)
Adam buys 4 pens and a ruler and pays £4.75 altogether.
Jack buys 2 pens and pays £1.98 altogether.
How much does a ruler cost?
Show your method
(2 marks)
Question 11 (1 mark)
Ally chooses a whole number.
When she multiplies her number by 4, the answer is less than 100
When she multiplies her number by 5, the answer is greater than 100
Write a number that Ally could have started with.
(1 mark)
Question 12 (2 marks)
William says the rule for this diagram.
“Find the difference between the numbers in the circles.
Double this to make the number in the square.”Diagram: Two circles side by side with a square above, between them. The left circle shows 5, the right circle 20 and the square 30.
Use the same rule to write the missing numbers below.
(a)
Diagram: The left circle shows 32 and the right circle 100. The square is empty.
(1 mark)
(b)
Diagram: The left circle shows 110 and the square 400. The right circle is empty.
(1 mark)
Question 13 (1 mark)
Write the missing fraction to make this addition correct.
2/3 + boxedphantomXX = 5/6
(1 mark)
Question 14 (1 mark)
Jack hires a hall for a party.
This formula is used to work out the total cost.
Total cost = £15 booking fee + £12.50 per hour
What is the total cost of hiring the hall from 6 pm until 11 pm, in pounds (£)?
(1 mark)
Question 15 (2 marks)
Stefan stands in the centre of this square.
Diagram: A square with a point marked at each corner and at the middle of each side, labelled clockwise from the middle of the left side: A (left), B (top left corner), C (top), D (top right corner), E (right), F (bottom right corner), G (bottom), H (bottom left corner). Arrows go from the centre of the square to each of the eight points. Not actual size.
(a)
Stefan is facing towards F.
He turns anti-clockwise to face D.What angle does Stefan turn through, in degrees?
(1 mark)
(b)
Stefan is now facing towards D.
He turns 3 right angles clockwise.Write the letter he faces after the turn.
(1 mark)
Question 16 (2 marks)
Part of this 10 × 10 grid is shaded.
Diagram: A 10 by 10 square grid. 4 whole columns are shaded: columns 1, 5, 8, 10 from the left.
Tick the fractions that represent the shaded part of the grid.
1/4 2/5 4/10 6/10 40/100 (2 marks)
Question 17 (2 marks)
Kim makes a cuboid model using straws.
Diagram: A cuboid made of straws, one straw along each of its 12 edges. The edge along the bottom at the front is labelled length, the upright edge at the front left is labelled height, and the edge going back at the bottom right is labelled width.
She uses straws that are 7.5 cm long for the height.
She uses straws that are 11 cm long for the length.
She uses straws that are 8.5 cm long for the width.What is the total length of all the straws in her model, in centimetres?
Show your method
(2 marks)
Question 18 (2 marks)
The full price of a T-shirt is £15
The price is reduced by 30%.
What is the reduced price, in pounds (£)?
Show your method
(2 marks)
Question 19 (1 mark)
Jack says,
“When you square a prime number, the answer has only two factors.”
Explain why Jack is not correct.
(1 mark)
Question 20 (3 marks)
This table shows how many people finished the New York Marathon in each of the first four decades it was held.
Decade Total number of people who finished 1st decade 24,863 2nd decade 170,932 3rd decade 282,420 4th decade 350,824 What is the mean number of people who finished the marathon per decade? Round your answer to the nearest hundred.
Show your method
(3 marks)
Question 21 (1 mark)
These two rectangles are identical.
The length of each rectangle is three times its width.
Diagram: An x-axis and a y-axis with two identical shaded rectangles. One stands upright to the left of the y-axis, its right side on the y-axis; its top left corner is labelled (–2, 8). The other lies to the right of the y-axis, its left side on the y-axis; its bottom left corner is labelled (0, 1) and its top right corner is labelled P. Not to scale.
What are the coordinates of point P?
(1 mark)
Questions Crown copyright (Standards and Testing Agency), recreated by Mr Barton Maths for teaching. Each question is credited to its board, series, paper and number.