Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 475 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.A bag has 7 red, 3 green and 8 yellow balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 7/18 (c) 2/3 (d) 11/18
2. 2.What is the midpoint of the line joining (10, 9) and (22, 7)? (a) (8, 16) (b) (16, 8) (c) (6, 1) (d) (32, 16)
3. 3.How many prime numbers are there between 40 and 70? (a) 8 (b) 9 (c) 7 (d) 6
4. 4.In a class of 32 children, 12 like maths, 19 like science and 8 like neither. How many like both? (a) 8 (b) 6 (c) 7 (d) 24
5. 5.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
6. 6.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 107 (c) 98 (d) 108
7. 7.What is the prime factorisation of 56? (a) 2⁴ × 7 (b) 2 × 7³ (c) 2³ × 7 (d) 2² × 7
8. 8.Two straight lines cross. Two vertically opposite angles add up to 160°. What is each of the other two angles? (a) 200° (b) 80° (c) 20° (d) 100°
9. 9.How many factors does 12 have? (a) 4 (b) 7 (c) 5 (d) 6
10. 10.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 30 (c) 12 (d) 36
11. 11.In which quadrant does the point (2, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
12. 12.Which is the correct factorisation of x² + 7x + 12? (a) (x + 1)(x + 12) (b) (x + 1)(x + 6) (c) (x − 3)(x − 4) (d) (x + 3)(x + 4)
13. 13.Two angles of a triangle are 45° and 100°. What is the exterior angle at the third corner? (a) 145° (b) 80° (c) 135° (d) 35°
14. 14.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 81 (c) 9 (d) 30
15. 15.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 8)(x + 9) (d) (x + 1)(x + 16)
16. 16.A cuboid is 3 cm long, 2 cm wide and 4 cm high. What is its total surface area? (a) 52 sq cm (b) 24 sq cm (c) 104 sq cm (d) 26 sq cm
17. 17.7 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 14 (b) 49 (c) 56 (d) 98
18. 18.In a class of 33 children, 20 like cricket, 14 like football and 3 like both. How many like only cricket? (a) 19 (b) 11 (c) 20 (d) 17
19. 19.A bag has 9 red, 7 green and 9 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 16/25 (b) 1/3 (c) 9/16 (d) 9/25
20. 20.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 48 (c) 12 (d) 16
21. 21.What is the distance between the points (0, 8) and (9, 20)? (a) 15 (b) 225 (c) 21 (d) 16
22. 22.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 335° (d) 65°
23. 23.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 21 (c) 42 (d) 10
24. 24.What is the missing term in the AP 1, ?, 5, 7, 9? (a) 5 (b) 4 (c) 3 (d) 2
25. 25.What is the prime factorisation of 168? (a) 2⁴ × 3 × 7 (b) 2² × 3 × 7 (c) 2 × 3 × 7³ (d) 2³ × 3 × 7
26. 26.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 155° (b) 100° (c) 105° (d) 80°
27. 27.What is the missing term in the AP 14, ?, 20, 23, 26? (a) 18 (b) 17 (c) 16 (d) 20
28. 28.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 453 (c) 454 (d) 374
29. 29.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 25 (c) 13 (d) 12
30. 30.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
31. 31.What is the median of 21, 25, 1, 16 and 2? (a) 1 (b) 13 (c) 16 (d) 21
32. 32.Using (a + b)² = a² + 2ab + b², what is 45²? (a) 2025 (b) 2035 (c) 1225 (d) 1625
33. 33.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 17 (c) 54 (d) 51
34. 34.What is the sum of the roots of x² − 9x + 18 = 0? (a) 8 (b) 9 (c) 10 (d) 18
35. 35.What is the mode of 2, 16, 7, 16, 2, 16 and 17? (a) 16 (b) 7 (c) 17 (d) 2
36. 36.What is the mode of 10, 11, 5, 3, 11, 3 and 11? (a) 5 (b) 11 (c) 3 (d) 10
37. 37.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
38. 38.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 372 (c) 451 (d) 450
39. 39.A cuboid is 12 cm long, 7 cm wide and 8 cm high. What is its total surface area? (a) 672 sq cm (b) 472 sq cm (c) 944 sq cm (d) 236 sq cm
40. 40.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10

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