KS2 Mathematics Paper 3: reasoning

1. Write the number four hundred and two thousand and seventeen in digits. [1]

2. 7,000 × 6 = [1]

3. Look at the isosceles triangle.

Work out the missing angle. [1]

4. Complete: 3.08 × 10 = [1]

5. A table: Year 5 28 pupils, Year 6 32 pupils. How many more in Year 6? [1]

6. Find 1/5 of 3/4 of 100. [2]

7. Look at the shaded rectangle. Each square is 1 cm.

Work out the area. [1]

8. Show your method. A runner completes 5 laps of 400 m. How many kilometres is that? [2]

9. Look at the diagram.

Work out the size of angle a. [1]

10. Write 45% as a fraction in simplest form. [1]

11. The temperature is −4°C and rises by 9°. New temperature? [1]

12. A sequence: 3, 10, 17, 24 … What is the term-to-term rule? [1]

13. Show your method. Three parcels weigh 1.2 kg, 850 g and 1.05 kg. Total mass in kilograms. [2]

14. Look at the grid.

Reflect the point (3, 2) in the x-axis. Write the new coordinates. [1]

15. A school starts at 08:50. Break is 20 minutes at 10:30. How long is the first session? [1]

16. 4x = 36. What is x? [1]

17. A bottle holds 750 ml. How many bottles make 3 litres? [2]

18. Which shape has parallel sides but is not a rectangle? Tick one: kite / parallelogram / circle / scalene triangle. [1]

19. Show your method. A bike costs £240. It is reduced by 1/5. Sale price? [2]

20. Look at the line graph.

What was the average growth per week? [2]

21. Write one factor of 48 that is also a square number (not 1). [1]

22. A pentagon interior angles sum to 540°. Four angles are 100°, 110°, 120° and 90°. Work out the fifth. [2]

23. A map scale is 1 cm to 3 km. Two towns are 4.5 cm apart on the map. Real distance? [2]