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KS2 SATs 2018 Paper 2: 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)
Here is a shape on a grid.
Complete the design so that it is symmetrical about the mirror line.
Use a ruler.
Diagram: A squared grid, 12 squares across and 8 squares up, with a dashed vertical mirror line down the middle (6 squares from the left edge). A shaded shape on the right of the mirror line has corners at (6, 6), (9, 6), (8, 5), (8, 2), (6, 4) (squares across and up from the bottom left corner of the grid).
(1 mark)
Question 2 (1 mark)
Stefan completes this calculation.
beginarrayr boxed9 boxed5 \\ – boxed6 boxed7 \\ hline boxed2 boxed8 endarray
Write an addition calculation he could use to check his answer.
beginarrayr boxedphantomX boxedphantomX \\ + boxedphantomX boxedphantomX \\ hline boxedphantomX boxedphantomX endarray
(1 mark)
Question 3 (1 mark)
On the line below, mark the point that is 6.7 centimetres from A.
Diagram: A straight line about 12.4 cm long, with point A marked by a short line across it, 1.9 cm from its left end.
(1 mark)
Question 4 (1 mark)
These diagrams show three equivalent fractions.
Diagram: Three equal rectangles with equals signs between them. Each is split into 4 equal rows, with the top 3 rows shaded. The first rectangle has 1 column, the second 3 columns and the third 6 columns of equal parts.
Write the missing values.
3/4 = dfrac9boxedphantomXX = dfracboxedphantomXX24
(1 mark)
Question 5 (2 marks)
Here are the temperatures in four cities at midnight and at midday.
City Temperature at midnight Temperature at midday Paris –4°C –2°C Oslo –13°C –7°C Rome 3°C 10°C Warsaw –6°C 2°C (a)
At midnight, how many degrees colder was Paris than Rome?
(1 mark)
(b)
Which city was 6 degrees colder at midnight than at midday?
(1 mark)
Question 6 (1 mark)
The numbers in this sequence decrease by the same amount each time.
303,604 302,604 301,604 300,604 …
What is the next number in the sequence?
(1 mark)
Question 7 (1 mark)
Tick the two numbers that are equivalent to 1/4
Tick two.
0.25 square 0.75 square 25/100 square 0.5 square 2/5 square (1 mark)
Question 8 (2 marks)
Ken buys 3 large boxes and 2 small boxes of chocolates.
Each large box has 48 chocolates. Each small box has 24 chocolates.
How many chocolates did Ken buy altogether?
Show your method
(2 marks)
Question 9 (1 mark)
The list below shows the years in which the Cricket World Cup was held since 1992:
1992, 1996, 1999, 2003, 2007, 2011, 2015
Adam says,
“The Cricket World Cup has been held every four years since 1992.”
Adam is not correct.
Explain how you know.
(1 mark)
Question 10 (2 marks)
boxed > boxed = boxed <
Write the correct symbol in each box to make the statements correct.
11 × 12 boxedphantomXX 15 × 10 90 ÷ 30 boxedphantomXX 60 ÷ 20 120 ÷ 4 boxedphantomXX 160 ÷ 8 30 × 8 boxedphantomXX 100 × 10 (2 marks)
Question 11 (2 marks)
Here is a drawing of a 3-D shape.
Diagram: A 3-D shape like a square-based pyramid with its top cut off: a large square base, a smaller square top parallel to it, and four sloping faces joining them. Hidden edges are dashed.
Complete the table.
Number of faces Number of vertices Number of edges (2 marks)
Question 12 (1 mark)
Here is a shape on a grid.
The shape is translated so that point A moves to (7, 8).
Draw the shape in its new position.
Use a ruler.
Diagram: A coordinate grid, x from 0 to 10 and y from 0 to 10. A shaded shape has corners (1, 0), (1, 5), (3, 5), (3, 0), (2, 2). Point A, at (3, 5), is one of its corners.
(1 mark)
Question 13 (1 mark)
Circle the improper fraction that is equivalent to 67/8
67/8 48/8 62/8 55/8 76/8
(1 mark)
Question 14 (1 mark)
6/5 3/5 3/4
Write these fractions in order, starting with the smallest.
(1 mark)
Question 15 (2 marks)
A box contains trays of melons.
There are 15 melons in a tray.
There are 3 trays in a box.
A supermarket sells 40 boxes of melons.
How many melons does the supermarket sell?
Show your method
(2 marks)
Question 16 (2 marks)
Adam wants to use a mental method to calculate 182 – 97
He starts from 182
Here are some methods that Adam could use.
Tick the methods that are correct.
add 3 then subtract 90 square subtract 100 then add 3 square subtract 7 then subtract 90 square subtract 3 then subtract 100 square (2 marks)
Question 17 (3 marks)
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?
Show your method
(3 marks)
Question 18 (2 marks)
Last year, Jacob went to four concerts.
Three of his tickets cost £5 each.
The other ticket cost £7
What was the mean cost of the tickets?
Show your method
(2 marks)
Question 19 (1 mark)
Layla wants to estimate the answer to this calculation.
39/10 – 21/8 + 14/5
Tick the calculation below that is the best estimate.
Tick one.
3 – 2 + 2 square 4 – 2 + 1 square 4 – 2 + 2 square 3 – 2 + 1 square (1 mark)
Question 20 (2 marks)
The length of an alligator can be estimated by:
• measuring the distance from its eyes to its nose
• then multiplying that distance by 12What is the difference in the estimated lengths of these two alligators?
Diagram: The two alligators’ eyes-to-nose distances: 17.5 cm for the first alligator and 15 cm for the second. Not to scale.
Show your method
(2 marks)
Question 21 (2 marks)
Amina is making designs with two different shapes.
She gives each shape a value.
Total value is 147
Diagram: A design made of 2 hexagons and 3 grey sectors (fan shapes), each sector with its point on a corner of a hexagon.
Total value is 111
Diagram: A design made of 1 hexagon and 3 grey sectors (fan shapes), each sector with its point on a corner of a hexagon.
Calculate the value of each shape.
(a)
Diagram: A hexagon, an equals sign and an empty box.
(1 mark)
(b)
Diagram: A grey sector, an equals sign and an empty box.
(1 mark)
Question 22 (1 mark)
This is the net of a cube.
Diagram: The net of a cube: six squares. Rows from the top: 1 square, 1 square, 3 squares, 1 square. A double arrow down the left side, from the top of the net to the bottom, is labelled 20 cm. Not actual size.
What is the volume of the cube?
(1 mark)
Question 23 (2 marks)
The length of a day on Earth is 24 hours.
The length of a day on Mercury is 582/3 times the length of a day on Earth.
What is the length of a day on Mercury, in hours?
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.