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KS2 SATs 2019 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)
In this grid, there are four multiplications.
Write the three missing numbers.
Diagram: A grid of four multiplications. Across the top row: 4 × 8 = a box. Across the middle row: 3 × a box = 21. Down the first column: 4 × 3 = a box. Down the middle column: 8 × the middle box = 56. The other cells are grey.
(1 mark)
Question 2 (1 mark)
What number is 1,000 less than 9,072?
(1 mark)
Question 3 (1 mark)
Order the numbers starting with the largest.
Match each number with its order.Diagram: On the left, four numbers in boxes, top to bottom: 1,009,909, 1,023,065, 1,009,099, 1,230,650. On the right, four boxes, top to bottom: 1st (largest), 2nd, 3rd, 4th (smallest).
(1 mark)
Question 4 (1 mark)
Here is a shaded shape on a square grid.
Diagram: A square grid 14 squares across and 9 up, with a vertical dashed mirror line 7 squares from the left. A shaded shape on the right of the mirror line has corners at (9, 7), (11, 7), (11, 2), (8, 2), (10, 4) (squares across and up from the bottom left corner of the grid).
Reflect the shape in the mirror line.
Use a ruler.
(1 mark)
Question 5 (2 marks)
The numbers in this sequence increase by 45 each time.
Write the missing numbers.
Diagram: A sequence of 6 numbers: an empty box, 155, 200, 245, an empty box, an empty box.
(2 marks)
Question 6 (1 mark)
Write the missing number to make this division correct.
0.3 ÷ boxedphantomXX = 0.03
(1 mark)
Question 7 (1 mark)
Jack pours some dark paint into a container.
Diagram: A container with a scale in litres up the inside: labels 3, 4, 5, with a long mark at each whole litre, a medium mark halfway between them and a short mark halfway between those. Dark paint fills the bottom of the container; only the marks above the paint are shown, and the lowest one is a short mark.
In litres, how much paint is in the container?
(1 mark)
Question 8 (2 marks)
In this sequence, the rule to get the next number is
Multiply by 2, and then add 3
Write the missing numbers.
Diagram: A row of 4 boxes: an empty box, 25, 53, an empty box.
(a)
The missing number in the first box.
(1 mark)
(b)
The missing number in the last box.
(1 mark)
Question 9 (2 marks)
Jack chose a number.
He multiplied the number by 7
Then he added 85
His answer was 953
What number did Jack choose?
Show your method
(2 marks)
Question 10 (1 mark)
A theme park sells tickets online.
Each ticket costs £24
There is a £3 charge for buying tickets.
Which of these shows how to calculate the total cost, in pounds?
Tick one.
number of tickets × 3 + 24 square number of tickets × 24 + 3 square number of tickets + 3 × 24 square number of tickets + 24 × 3 square (1 mark)
Question 11 (2 marks)
Amina is shopping.
She says,
“I would like to buy one-quarter of a kilogram of cheese.”
(a)
Write one-quarter on the scales as a decimal, in kilograms.
(1 mark)
(b)
The cheese costs £1.35
Amina pays with a £2 coin.
How much change should Amina get?
(1 mark)
Question 12 (1 mark)
Here are three symbols.
< > =
Write one symbol in each box to make the statements correct.
7/10 boxedphantomXX 0.07
23/1000 boxedphantomXX 0.23
(1 mark)
Question 13 (2 marks)
Here is a sketch of a triangle.
It is not drawn to scale.
Diagram: A sketch of a right-angled triangle, not to scale. The bottom side is 8 cm, arrowed underneath. The angle at the left-hand end of it is marked 35° and the angle at the right-hand end is a right angle.
Draw the full-size triangle accurately below.
Use an angle measurer (protractor) and a ruler.
One line has been drawn for you.
Diagram: A straight line 8 cm long, arrowed underneath and labelled 8 cm.
(2 marks)
Question 14 (2 marks)
Complete the table.
Round 39,476 to the nearest 10,000 boxedphantomXX to the nearest 1,000 boxedphantomXX to the nearest 100 boxedphantomXX (2 marks)
Question 15 (1 mark)
Amina asked 60 children to choose their favourite flavour of jelly.
These were her results.
Flavour Number of
childrenRaspberry 12 Lemon 8 Orange 15 Blackcurrant 25 Total 60 What percentage of the 60 children chose orange?
(1 mark)
Question 16 (1 mark)
Write the missing number.
6 + 2 × 2 – boxedphantomXX = 6
(1 mark)
Question 17 (2 marks)
These two shapes have the same perimeter.
regular hexagon
Diagram: A shaded regular hexagon.
square
Diagram: A shaded square.
Not actual size
The length of each side of the hexagon is 8 centimetres.
Calculate the area of the square.
Show your method
(2 marks)
Question 18 (1 mark)
Circle the prime number.
95 89 87
Explain how you know the other numbers are not prime.
(1 mark)
Question 19 (2 marks)
A machine pours 250 millilitres of juice every 4 seconds.
How many litres of juice does the machine pour every minute?
Show your method
(2 marks)
Question 20 (2 marks)
Tick the fractions that are equal to 20%.
1/20 square 20/40 square 1/5 square 3/15 square 2/100 square (2 marks)
Question 21 (1 mark)
Adam has this rectangular piece of card. It is marked with grid lines.
Diagram: A rectangle of card marked with grid lines, 7 squares across and 5 squares up.
Adam makes two straight cuts along the grid lines.
The two cuts divide the rectangle into 3 shapes:
• 2 squares of different size, and
• 1 rectangle.Using the grid lines, draw two lines that show where Adam could have made his cuts.
Use a ruler.
(1 mark)
Question 22 (3 marks)
This graph shows the maximum temperature for five days.
Diagram: A graph of the maximum temperature (°C, from 0 to 14 with a line every 2) for each day. A cross for each day, with its temperature written beside it: Mon 8.1, Tue 9.3, Wed 11.9, Thu 11.8, Fri 12.4.
(a)
For what fraction of the five days was the maximum temperature below 10 °C?
(1 mark)
(b)
What was the mean maximum temperature, to one decimal place?
Show your method
(2 marks)
Question 23 (2 marks)
Amina made this cuboid using centimetre cubes.
Diagram: A cuboid made of centimetre cubes, 6 cubes long, 4 cubes tall and 3 cubes deep, with the cube edges drawn on the front, top and side. The edges are marked 6 cm (along the bottom), 4 cm (up the side) and 3 cm (going back). Not actual size.
Stefan makes a cuboid that is 5 cm longer, 5 cm taller and 5 cm wider than Amina’s cuboid.
What is the difference between the number of cubes in Amina’s and Stefan’s cuboids?
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.