Independent School Entrance (ISEB Pre-Test and 11+ CEM style) · Mathematics

Geometry, measures, data and probability

40 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 40 questions

  1. A 12 cm by 9 cm rectangle has a 5 cm by 4 cm rectangle cut out of one corner, leaving an L-shape. What is the area of the L-shape?
  2. A circular pond has a circumference of 31.4 m. Taking π as 3.14, what is its area?
  3. In triangle ABC, angle B is three times angle A, and angle C is 20° more than angle A. What is the size of angle B?
  4. Each exterior angle of a regular polygon is 24°. What is the size of each interior angle?
  5. A fish tank measures 60 cm by 30 cm by 40 cm. It is filled to three quarters of its height. How many litres of water does it hold?
  6. A bag holds 4 red, 5 blue and 3 green counters. Two counters are taken out one after the other without replacement. What is the probability that both are red?
  7. Two fair six-sided dice are rolled and the scores are added. What is the probability that the total is 8?
  8. Five whole numbers have a mean of 6, a median of 5, a mode of 4 and a range of 6. What is the largest of the five numbers?
  9. In 20 football matches a team scored 0 goals in 5 matches, 1 goal in 8 matches, 2 goals in 4 matches, 3 goals in 2 matches and 4 goals in 1 match. What was the mean number of goals per match?
  10. A square of area 144 cm² is cut into four identical rectangles by three parallel cuts. What is the perimeter of one rectangle?
  11. 1 January 2026 is a Thursday. What day of the week is 1 March 2026?
  12. A, B, C and D are the corners of a parallelogram, in order. A is (1, 2), B is (5, 2) and C is (8, 6). What are the coordinates of D?
  13. A quadrilateral has diagonals that are equal in length and bisect each other, but they do not have to cross at right angles. Which quadrilateral must it be?
  14. A cube has a total surface area of 150 cm². What is its volume?
  15. A field is 0.4 km long and 250 m wide. What is its area in hectares? (1 hectare = 10,000 m²)
  16. A 6 cm by 4 cm rectangle is enlarged by a scale factor of 2.5. What is the area of the enlarged rectangle?
  17. Through how many degrees does the hour hand of a clock turn in 50 minutes?
  18. A pie chart shows how £400 was spent. The sector for Travel is 72° and the sector for Food is 108°. How much was spent on Food?
  19. A shopkeeper sells a lamp for £54, which gives a profit of 20% on what it cost her. How much did the lamp cost her?
  20. Two sides of an isosceles triangle are 7 cm and 3 cm long. What is its perimeter?
  21. A 2.4 kg bag of flour is used as follows: three eighths for bread and 450 g for a cake. The rest is put into packs of 100 g. How many full packs are made?
  22. The faces of a cuboid have areas 24 cm², 30 cm² and 20 cm². What is the volume of the cuboid?
  23. On a given day in autumn, the probability of rain is 0.35 and the probability of snow is 0.1. Rain and snow cannot happen together. What is the probability of neither?
  24. A ship sails 8 km north, then 6 km east, and then sails in a straight line back to its starting point. What is the total distance sailed?
  25. Which set of three lengths could be the sides of a triangle?
  26. What is the median of 14, 9, 21, 12, 17 and 9?
  27. The perimeter of a rectangle is 46 cm, and its length is 7 cm more than its width. What is its area?
  28. A flight leaves London at 21:40 on 3 March and takes 8 hours 25 minutes. The local time at the destination is 5 hours behind London. What is the local time and date when it lands?
  29. A square with a side of 9 cm and an equilateral triangle have the same perimeter. How long is each side of the triangle?
  30. A triangle has corners at (0, 0), (8, 0) and (3, 6). What is its area?
  31. What is 7.0462 written to 3 significant figures?
  32. A recipe needs 3/4 of a pint of milk. If 1 pint is 568 ml, how much milk is that, in ml?
  33. A trapezium has parallel sides of 9 cm and 15 cm, and a perpendicular height of 6 cm. What is its area?
  34. A car travels at 72 km/h. What is its speed in metres per second?
  35. A spinner lands on red with probability 0.3. It is spun 250 times. How many red results would you expect?
  36. A tank holds 80 litres and leaks 1.5 litres every hour. After how many hours will it hold only a quarter of the original amount?
  37. The bearing of B from A is 070°. What is the bearing of A from B?
  38. The point P(4, -1) is reflected in the line y = x. What are the coordinates of its image?
  39. A regular hexagon has sides of 8 cm. A square has the same perimeter. What is the area of the square?
  40. Alfie starts at a point O, cycles 9 km west and then 20 km north. Beth starts at O and cycles 6 km east. How far apart are they at the end?

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