Quest Arena · Free Worksheet 02

Maths — Number, Fractions & Word Problems

Years 5–6 · Mixed style · 10 questions · suggested time 30 minutes

How to use this sheet. Show your working. A correct answer with no working scores fewer marks in most 11+ schemes than an attempted answer with clear method. Use the back of the sheet if you need space.

Questions

  1. A small theatre has 28 rows of seats. There are 17 seats in each row. How many seats are there in total?

  2. A pizza is cut into 12 equal slices. Hassan eats 1⁄4 of the pizza. Mei eats 1⁄3. How many slices are left?

  3. A school trip costs £270 in total. The cost is shared between teachers and pupils in the ratio 1 : 8. How much do the pupils pay altogether?

  4. A train leaves Euston at 09:47 and arrives in Manchester at 12:13. How long does the journey take, in hours and minutes?

  5. This L-shaped flowerbed is made from rectangles. What is the total area in square metres?

    8 m 3 m 4 m 4 m 5 m

  6. Continue this sequence and find the next two terms:  2, 6, 12, 20, 30, ___ , ___

  7. In a class of 30 children, 18 walk to school. What percentage of the class walks to school?

  8. Lina has £20. She buys 3 notebooks at £2.45 each and one pen at £1.30. How much change does she get?

  9. Round 47,683 to the nearest thousand, then to the nearest hundred.

  10. A water tank holds 240 litres when full. It is currently 5⁄8 full. A leaking tap is losing 4 litres per hour. After how many hours will the tank be empty?

Answer Key & Marking Notes

  1. 476. 28 × 17. Award 1 for partial method (e.g. 28 × 10 + 28 × 7).
  2. 5 slices. Hassan = 3 slices, Mei = 4 slices, eaten = 7, left = 5.
  3. £240. 9 parts total → £30 per part → 8 × £30.
  4. 2 hours 26 minutes. 09:47 → 10:00 = 13 min; 10:00 → 12:00 = 2 h; 12:00 → 12:13 = 13 min; total 2 h 26 min.
  5. 24 m². Split into two rectangles: 8×2 + 4×4 = 16 + 8 = 24 (or 8×5 − 4×3 = 40 − 16). Accept either method.
  6. 42, 56. Differences are 4, 6, 8, 10, 12, 14 — add 12 then 14.
  7. 60%. 18 ÷ 30 = 0.6.
  8. £11.35. 3 × 2.45 = 7.35; 7.35 + 1.30 = 8.65; 20 − 8.65 = 11.35.
  9. 48,000 and 47,700.
  10. 37.5 hours. 5⁄8 × 240 = 150 litres; 150 ÷ 4 = 37.5 hours. Award 1 for finding 150 litres, 1 for correct division.

Total: 12 marks (questions 5 and 10 worth 2 each). Children scoring 9+ are comfortably on track for grammar-school maths.

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