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KS2 SATs 2024 Paper 2: reasoning
27 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 triangle on a grid.
Diagram: A square grid 12 squares across and 6 squares up, with a vertical dashed mirror line 6 squares from the left. A triangle on the right of the mirror line has corners at (8, 2), (11, 2), (10, 4) (squares across and up from the bottom left corner).
Draw the reflection of the triangle in the mirror line.
Use a ruler.
(1 mark)
Question 2 (1 mark)
This table shows the cost of fruit at a school cafeteria.
Fruit Cost for one banana 12p plum 23p apple 32p pear 38p Amir buys two pieces of fruit.
He pays with a £2 coin.
He gets £1.50 change.
Tick the two pieces of fruit that Amir buys.
Tick two.
banana square plum square apple square pear square (1 mark)
Question 3 (1 mark)
Layla plays basketball.
This graph shows how many points she scored in her first 3 games.
Diagram: A bar chart of number of points, with a line at every 2 points from 0 to 12. Game 1: a bar to 7. Game 2: a bar to 5. Game 3: a bar to 10. Game 4: no bar.
After 4 games, Layla had scored a total of 25 points.
Complete the graph.
Use a ruler.
(1 mark)
Question 4 (1 mark)
The numbers in this sequence increase by the same amount each time.
Write the missing numbers.
Diagram: A row of 6 boxes: –11, an empty box, 1, 7, an empty box, 19.
(1 mark)
Question 5 (1 mark)
Write the three missing digits to make this multiplication correct.
beginarraycccc & boxedphantomX & 5 & boxedphantomX \\ × & & & 3 \\ hline & 7 & boxedphantomX & 2 endarray
(1 mark)
Question 6 (1 mark)
Olivia is thinking of a number.
My number
• is greater than 236
• is less than 245
• has a 3 in the tens’ place
• is an even number
What number is Olivia thinking of?
(1 mark)
Question 7 (1 mark)
A box holds 40 packets of envelopes.
Each packet holds 25 envelopes.
How many envelopes does the box hold?
(1 mark)
Question 8 (1 mark)
Write a whole number in each box to make the statements correct.
One has been done for you.
18 rounded to the nearest ten is 20 boxedphantomXX rounded to the nearest thousand is 4,000 boxedphantomXX rounded to the nearest ten thousand is 820,000 (1 mark)
Question 9 (1 mark)
4 ÷ 10 40 ÷ 10 4 ÷ 100 40 ÷ 100 Two of these calculations have the same answer.
Write this answer as a decimal.
(1 mark)
Question 10 (1 mark)
Circle the two prime numbers that have a difference of 2
15 17 19 21 23 25
(1 mark)
Question 11 (1 mark)
This table shows the number of children and adults at a childcare centre.
Complete the table to make it correct.
The first row has been done for you.
Age in years Number of children Number of adults Number of children per adult 1 and under 12 4 3 2 or 3 20 boxedphantomXX 4 4 or 5 boxedphantomXX 3 8 (1 mark)
Question 12 (1 mark)
Shapes W, X, Y and Z cover different fractions of this 10 by 10 square.
Match each shape to the correct fraction.
Diagram: A 10 by 10 square of small squares with four shaded shapes. Shape W is 5 squares across and 5 down, starting 0 squares from the left and 0 from the top. Shape X is 4 squares across and 10 down, starting 6 squares from the left and 0 from the top. Shape Y is 1 squares across and 1 down, starting 0 squares from the left and 6 from the top. Shape Z is 5 squares across and 2 down, starting 0 squares from the left and 8 from the top. The other squares are white.
Diagram: Two columns of boxes. On the left, top to bottom: Shape W, Shape X, Shape Y, Shape Z. On the right, top to bottom: 1/100, 1/4, 2/5, 1/10.
(1 mark)
Question 13 (1 mark)
Match the name of each 3-D shape to its number of vertices.
Diagram: Two columns of boxes. On the left, top to bottom: cube, square-based pyramid, triangular-based prism, octagonal-based pyramid. On the right, top to bottom: 9, 8, 6, 5.
(1 mark)
Question 14 (1 mark)
A class votes for a captain.
Three-quarters of the class vote for Sam.
The remaining 7 pupils vote for Alex.
How many pupils are in the class?
(1 mark)
Question 15 (1 mark)
Write the missing number to make this multiplication correct.
3.207 × 100 = boxedphantomXX × 10
(1 mark)
Question 16 (2 marks)
Here is a number.
9,658,214
Tick the statements that are true.
The digit 5 represents 50,000 square The value of the digit 9 is nine hundred thousands. square The digit 6 represents 6 millions. square The value of the digit 2 is twenty tens. square (2 marks)
Question 17 (2 marks)
Chen buys these four items.
Item Mass Price apples 670 grams £1.50 bread 400 grams £0.70 butter 500 grams — cereal 750 grams £1.45 Chen pays for the four items with a £10 note. The price of the butter is not shown.
She receives £3.85 change.
What is the price of the butter?
Show your method
(2 marks)
Question 18 (1 mark)
Draw an arrow (↑) on the scale below to show 1350 grams.
Diagram: A scale in kilograms from 1 to 2, labelled 1, 1.5 and 2, with a mark at every 0.1 kilograms and a shorter mark halfway between each pair (every 0.05 kilograms).
(1 mark)
Question 19 (2 marks)
A hall has 1,250 seats.
At 7 pm, 880 seats are filled.
At 8 pm, there are 40 empty seats.
How many seats were filled between 7 pm and 8 pm?
Show your method
(2 marks)
Question 20 (2 marks)
Each day, a school has
• break from 10:15 am to 10:30 am
• lunchtime from 12:40 pm to 1:30 pm.
What is the total time the school has for breaks and lunchtime in a 5-day week?
Show your method
(2 marks)
Question 21 (1 mark)
Diagram: Two horizontal lines, AB at the top and GH at the bottom. Two vertical lines join them: CD on the left, from C on AB down to D on GH, and EF on the right, from E on AB down to F on GH. Right angles are marked at C, D, E and F.
Tick all the correct statements.
AB is parallel to CD square GH is parallel to AB square CD is perpendicular to GH square EF is perpendicular to CD square (1 mark)
Question 22 (2 marks)
This table shows the distance that five friends travel to school each day.
Name Distance (km) Amina 1.8 William 2.4 Layla 3.2 Chen 1.6 Dev 4.5 What is the mean distance they travel to school each day?
Show your method
(2 marks)
Question 23 (2 marks)
Mrs Mills has 940 seeds to plant into trays.
She plants 12 seeds in each tray.
The last tray is not full.
What fraction of the last tray is filled?
Show your method
(2 marks)
Question 24 (2 marks)
Here are four numbers.
40 60 64 100
Use each number once to complete these statements.
boxedphantomXX is a square number.
boxedphantomXX is a cube number.
boxedphantomXX is a common multiple of 4 and 5
boxedphantomXX is a common factor of 80 and 120
(2 marks)
Question 25 (2 marks)
Write the missing numbers so that 3 × b – a = 2
a b boxedphantomXX 2 13 boxedphantomXX (2 marks)
Question 26 (1 mark)
Here are 3 translations on a coordinate grid.
Tick the translations that are four units to the left.
from (0, 2) to (4, 2) square from (6, 8) to (2, 8) square from (–3, 5) to (–7, 5) square (1 mark)
Question 27 (1 mark)
Olivia has two jars of beads.
The number of beads in Jar A is double the number of beads in Jar B.
Olivia says, “25% of the number of beads in Jar A is the same as 50% of the number of beads in Jar B.”
Explain why Olivia is correct.
(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.