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KS2 SATs 2023 Paper 3: reasoning
23 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)
Chen has these digit cards.
Diagram: 4 digit cards in a row: 4, 8, 2, 7.
She uses three of the cards to make a three-digit number.
Each card can be used only once.
Chen puts the 4 in the tens place.Write the lowest three-digit number that Chen could make.
(1 mark)
Question 2 (1 mark)
Tick the number eighty thousand, three hundred and six.
Tick one.
8,306 80,036 80,306 800,306 80,300,006 (1 mark)
Question 3 (1 mark)
Amina draws triangle ABC on a grid as shown.
Diagram: A squared grid 14 squares wide and 7 squares tall, with no numbers. The x-axis runs along the bottom and the y-axis goes up through the middle. Triangle ABC is to the left of the y-axis: A is 5 squares left of the y-axis and 5 squares up; B is 5 squares left of the y-axis and 2 squares up; C is 2 squares left of the y-axis and 2 squares up.
She then reflects the triangle in the y-axis.
Draw the reflected triangle on the grid.
Use a ruler.
(1 mark)
Question 4 (1 mark)
Write the next two numbers in this sequence.
1,780 1,880 1,980
(1 mark)
Question 5 (1 mark)
Circle the two decimals that round to the same whole number.
13.2 14.7 15.9 16.3 17.6
(1 mark)
Question 6 (1 mark)
Write the missing number to make the calculation correct.
1,300,450 = 1,000,000 + boxedphantomXX + 400 + 50
(1 mark)
Question 7 (1 mark)
Here is part of a number square.
The other part of the square has been torn off.
Diagram: Part of a number square 5 columns wide, counting up in halves from left to right along each row. The bottom-left part has been torn off. The numbers still showing are: and 1/2, 1, 1 and 1/2, 2, 2 and 1/2, 3, 3 and 1/2, 4, 4 and 1/2, 5, 6, 6 and 1/2, 7, 7 and 1/2, 9, 9 and 1/2, 10, 12, 12 and 1/2.
What number was in the bottom-left corner of the number square?
(1 mark)
Question 8 (1 mark)
Match each shape to the correct name.
Diagram: 4 polygons, one above another on the left, with 6, 5, 5, 6 sides (top to bottom). On the right, 4 names, top to bottom: irregular pentagon, irregular hexagon, regular hexagon, regular pentagon.
(1 mark)
Question 9 (1 mark)
Jack says,
“I multiplied a whole number by 3
My answer was 32”Explain why Jack is not correct.
(1 mark)
Question 10 (1 mark)
Write the missing square number to make this addition correct.
8² + boxedphantomXX² = 73
(1 mark)
Question 11 (2 marks)
At the start of April, a shop had 15,000 games.
The shop sold:
• 7,918 games in April
• 4,624 games in May.How many games did the shop have left at the end of May?
Show your method
(2 marks)
Question 12 (2 marks)
This is a drawing of a cuboid.
Diagram: A drawing of a cuboid standing on one end: a long thin box 3 times as tall as it is wide, with square ends.
Tick the nets that could make the cuboid.
A
Diagram: Net A: 6 faces: 2 squares and 4 long rectangles.
B
Diagram: Net B: 6 faces: 2 squares and 4 long rectangles.
C
Diagram: Net C: 6 faces: 2 squares and 4 long rectangles.
D
Diagram: Net D: 6 faces: 2 squares and 4 long rectangles.
(2 marks)
Question 13 (1 mark)
Write the missing number to make this calculation correct.
754 × 6 + 754 × 3 = 754 × boxedphantomXX
(1 mark)
Question 14 (2 marks)
Here are five digit cards.
Diagram: 5 digit cards in a row: 1, 2, 3, 4, 5.
(a)
Use two cards to make a fraction equivalent to 25%
(1 mark)
(b)
Use two cards to make a fraction equivalent to 0.4
(1 mark)
Question 15 (2 marks)
Amina went to a concert one evening.
(a)
It took her an hour and twenty minutes to get there from home.
She arrived at ten past seven.At what time did she leave home?
(1 mark)
(b)
The concert started at 7:20 pm.
It finished at 9:05 pm.How long did the concert last, in hours and minutes?
(1 mark)
Question 16 (2 marks)
A box of 24 chocolate eggs has a mass of 870 grams.
The empty box has a mass of 30 grams.
What is the mass of one chocolate egg, in grams?
Show your method
(2 marks)
Question 17 (1 mark)
This rectangle is divided into three parts.
Diagram: A rectangle divided into three parts. Part A, shaded, is on the left. Part B, shaded, is in the middle; its right-hand side is a slanted line from the top edge down to the bottom right corner of the rectangle. Part C, white, is the triangle at the top right. Not to scale.
Part A is 1/2 of the area of the rectangle.
Part B is 1/3 of the area of the rectangle.
What fraction of the area of the rectangle is shaded?
(1 mark)
Question 18 (3 marks)
This table shows the total rainfall and sunshine each year at Heathrow Airport from 2010 to 2015.
Year Rainfall in mm Sunshine in hours 2010 521 1,371 2011 509 1,540 2012 700 1,503 2013 560 1,452 2014 864 1,669 2015 562 1,508 (a)
Use this table to complete the graph.
Use a ruler.
Diagram: A bar chart titled Rainfall at Heathrow Airport: rainfall in mm (0 to 1,000, a line every 200) against the year. 2010: a bar to 521 mm. 2011: a bar to 509 mm. 2012: no bar. 2013: a bar to 560 mm. 2014: a bar to 864 mm. 2015: a bar to 562 mm.
(1 mark)
(b)
Use the table to calculate the mean hours of sunshine for Heathrow Airport from 2013 to 2015.
Show your method
(2 marks)
Question 19 (2 marks)
These are the prices of some vegetables in a shop.
Mushrooms Carrots £3.20 for 1 kg 60p for 1 kg Layla buys 500 grams of mushrooms and 11/4 kg of carrots.
She pays with a £5 note.
How much change does Layla get, in pounds (£)?
Show your method
(2 marks)
Question 20 (2 marks)
The length of this rectangle is 6 cm.
The width is w cm.
Diagram: A rectangle, wider than it is tall. An arrow under it is labelled 6 cm (the length). An arrow up its right-hand side is labelled w cm (the width). Not actual size.
Circle all the methods below that can be used to work out the perimeter of the rectangle.
w × 6 w × 2 + 12 2 × (w + 6) 6 + w + 6 + w (2 marks)
Question 21 (3 marks)
There are 25 classes in a school.
Each class has 34 pupils.
62% of all the pupils play a sport after school.
What number of pupils do not play a sport?
Show your method
(3 marks)
Question 22 (1 mark)
Megan uses these number machines to calculate how many diagonals different shapes have.
Diagram: Number machines, one row for each shape: the number of vertices goes in, is multiplied, then divided, and the number of diagonals comes out. triangle: 3, times 0, divided by 2, gives 0. quadrilateral: 4, times 1, divided by 2, gives 2. pentagon: 5, times 2, divided by 2, gives 5.
Complete the number machine for the octagon.
Diagram: Number machines, one row for each shape: the number of vertices goes in, is multiplied, then divided, and the number of diagonals comes out. octagon: all four boxes are empty.
(1 mark)
Question 23 (2 marks)
Write the missing decimals.
One has been done for you.
a b a/b 1 4 0.25 3 20 5 8 (2 marks)
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.