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KS2 SATs 2017 Paper 3: reasoning
24 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)
Write the missing number to make this division correct.
75 ÷ boxedphantomXX = 7.5
(1 mark)
Question 2 (1 mark)
A group of friends earns £80 by washing cars.
They share the money equally.
They get £16 each.
How many friends are in the group?
(1 mark)
Question 3 (1 mark)
Chen uses these digit cards.
Diagram: 3 digit cards in a row: 5, 6, 9.
She makes a 2-digit number and a 1-digit number.
She multiplies them together.
Her answer is a multiple of 10What could Chen’s multiplication be?
boxedphantomXboxedphantomX × boxedphantomX
(1 mark)
Question 4 (2 marks)
This graph shows the temperature in °C from 2 am to 3 pm on
a cold day.Diagram: A line graph of the temperature in °C (–6 to 8, a grid line every degree) against the time of day, every hour from 2 am to 7 pm. The readings, joined by straight lines, are: 2 am –3°C, 3 am –5°C, 4 am –4°C, 5 am –4°C, 6 am –2°C, 7 am 0°C, 8 am 3°C, 9 am 4°C, 10 am 5°C, 11 am 6°C, 12 pm 6°C, 1 pm 7°C, 2 pm 4°C, 3 pm 2°C. The line stops at 3 pm.
(a)
How many degrees warmer was it at 3 pm than at 3 am?
(1 mark)
(b)
At 6 pm the temperature was 4 degrees lower than at 3 pm.
What was the temperature at 6 pm, in °C?
(1 mark)
Question 5 (1 mark)
The children at Farmfield School are collecting money for charity.
Their target is to collect £360
So far they have collected £57.73
How much more money do they need to reach their target, in pounds (£)?
(1 mark)
Question 6 (1 mark)
William wants to travel to Paris by train.
He needs to arrive in Paris by 5:30 pm.
Circle the latest time that William can leave London.
Leaves London Arrives Paris 12:01 15:22 12:25 15:56 13:31 16:53 14:01 17:26 14:31 17:53 15:31 18:53 16:01 19:20 (1 mark)
Question 7 (1 mark)
Here is a triangle drawn on a coordinate grid.
Diagram: A coordinate grid, x and y from –6 to 6. A triangle has corners at (–5, –1), (–5, –4), (–2, –4).
The triangle is translated 7 right and 5 up.
Draw the triangle in its new position.
(1 mark)
Question 8 (2 marks)
Write three factors of 30 that are not factors of 15
(2 marks)
Question 9 (1 mark)
Here is the morning timetable for Chen’s class this week.
Time 9:00 am–10:30 am 10:30 am–11:00 am 11:00 am–12:00 pm Mon Maths Break English Tue English Break Maths Wed Maths Break Science Thu English Break Maths Fri Maths Break English What is the total number of hours for English on this timetable?
(1 mark)
Question 10 (1 mark)
A bottle contains 568 millilitres of milk.
Jack pours out half a litre.
How much milk is left?
(1 mark)
Question 11 (1 mark)
A bicycle wheel has a diameter of 64 cm.
What is the radius of the bicycle wheel, in centimetres?
(1 mark)
Question 12 (1 mark)
white balloons red balloons 24 in a bag 12 in a bag Adam buys 6 bags of white balloons.
Chen buys 3 bags of red balloons.Adam says,
‘I have four times as many balloons as Chen.’
Explain why Adam is correct.
(1 mark)
Question 13 (1 mark)
Circle the pentagon with exactly four acute angles.
Shape A
Diagram: Shape A: a regular pentagon.
Shape B
Diagram: Shape B: a pentagon shaped like a house: a square with a pointed roof, the two bottom corners marked as right angles.
Shape C
Diagram: Shape C: a pentagon shaped like the letter M: a flat bottom, two sloping sides going up to two points, and a V cut in the top between them.
Shape D
Diagram: Shape D: a hexagon shaped like a bow: straight sides on the left and right, and a V cut into the middle of the top and of the bottom.
Shape E
Diagram: Shape E: a regular hexagon.
(1 mark)
Question 14 (2 marks)
3 pineapples cost the same as 2 mangoes.
One mango costs £1.35
How much does one pineapple cost, in pounds (£)?
Show your method
(2 marks)
Question 15 (1 mark)
Look at the letters below.
Circle the letter below that has both parallel and perpendicular lines.
A C E L Z
(1 mark)
Question 16 (2 marks)
There are 2,400 leaflets in a box.
William and Ally take 450 leaflets each.
Adam and Chen share the rest of the leaflets equally.
How many leaflets does Adam get?
Show your method
(2 marks)
Question 17 (2 marks)
In each box, circle the number that is greater.
11/2 1.2 11/4 1.3 15/100 1.4 13/5 1.5 (2 marks)
Question 18 (1 mark)
A square number and a prime number have a total of 22
What are the two numbers?
undersetsquare numberboxedphantomXX + undersetprime numberboxedphantomXX = 22
(1 mark)
Question 19 (2 marks)
Dev thinks of a whole number.
He multiplies it by 4
He rounds his answer to the nearest 10
The result is 50Write all the possible numbers that Dev could have started with.
(2 marks)
Question 20 (3 marks)
A square tile measures 20 cm by 20 cm.
A rectangular tile is 3 cm longer and 2 cm narrower
than the square tile.What is the difference in area between the two tiles, in cm²?
Show your method
(3 marks)
Question 21 (2 marks)
The numbers in this sequence increase by the same amount each time.
Write the missing numbers.
Diagram: A row of 5 boxes: an empty box, 1, 1 and 5 over 8, 2 and 1 over 4, an empty box.
(a)
The first box:
(1 mark)
(b)
The last box:
(1 mark)
Question 22 (2 marks)
In this diagram, the shaded rectangles are all of equal width (w).
Diagram: Two rows of rectangles, the rows the same width. Top row: a shaded rectangle of width w, then a rectangle 34 cm wide. Bottom row: a rectangle 18 cm wide, a shaded rectangle of width w, a rectangle 9 cm wide and a shaded rectangle of width w. Not to scale.
Calculate the width (w) of one shaded rectangle, in centimetres.
Show your method
(2 marks)
Question 23 (1 mark)
Here is a pattern of number pairs.
a b 1 9 2 19 3 29 4 39 Complete the rule for the number pattern.
b = boxedphantomXX × a – boxedphantomXX
(1 mark)
Question 24 (2 marks)
Cube A and cuboid B have the same volume.
Diagram: Cube A, with an edge of 6 cm marked along the bottom. Cuboid B, longer and flatter: its height is marked 4 cm, its depth 6 cm, and its length is marked with a question mark. Not to scale.
Calculate the missing length on cuboid B, in centimetres.
Show your method
(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.