Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 399 · 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.In a class of 22 children, 13 like mangoes, 14 like bananas and 9 like both. How many like at least one of the two? (a) 9 (b) 18 (c) 22 (d) 27
2. 2.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 12 (d) 3
3. 3.Two angles of a triangle are 75° and 75°. What is the third angle? (a) 150° (b) 105° (c) 210° (d) 30°
4. 4.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 156 (c) 91 (d) 78
5. 5.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/4
6. 6.There are 7 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 84 (b) 49 (c) 42 (d) 13
7. 7.A cube has edges of 5 cm. What is its volume? (a) 15 cu cm (b) 100 cu cm (c) 150 cu cm (d) 125 cu cm
8. 8.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 342 (d) 324
9. 9.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 86° (c) 95° (d) 170°
10. 10.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 36 cu cm (c) 9 cu cm (d) 54 cu cm
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
12. 12.Which is the correct factorisation of x² + 12x + 32? (a) (x − 4)(x − 8) (b) (x + 1)(x + 11) (c) (x + 1)(x + 32) (d) (x + 4)(x + 8)
13. 13.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 15° (c) 150° (d) 25°
14. 14.In a class of 40 children, 11 like cricket, 21 like football and 2 like both. How many like only cricket? (a) 2 (b) 11 (c) 19 (d) 9
15. 15.In a class of 36 children, 7 like cricket, 21 like football and 2 like both. How many like only cricket? (a) 7 (b) 5 (c) 19 (d) 15
16. 16.In a class of 35 children, 22 like tea, 12 like coffee and 5 like neither. How many like both? (a) 5 (b) 3 (c) 30 (d) 4
17. 17.What is the missing term in the AP 1, 6, ?, 16, 21? (a) 12 (b) 16 (c) 11 (d) 10
18. 18.What is the median of 7, 26, 4, 13 and 34? (a) 7 (b) 4 (c) 13 (d) 26
19. 19.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 140° (b) 40° (c) 220° (d) 41°
20. 20.A drawer has lots of black, white, yellow and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 8 (c) 4 (d) 5
21. 21.What are the roots of x² − 14x + 48 = 0? (a) 2 and 24 (b) 1 and 48 (c) 1 and 13 (d) 6 and 8
22. 22.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 30 (d) 15
23. 23.What is the mode of 17, 13, 2, 17, 13, 1 and 13? (a) 1 (b) 17 (c) 2 (d) 13
24. 24.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
25. 25.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 40° (b) 50° (c) 100° (d) 140°
26. 26.If a + b = 12 and ab = 35, what is a² + b²? (a) 109 (b) 214 (c) 144 (d) 74
27. 27.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 8)(x + 9) (c) (x + 1)(x + 72) (d) (x + 1)(x + 16)
28. 28.How many factors does 35 have? (a) 3 (b) 5 (c) 4 (d) 2
29. 29.In a class of 42 children, 30 like cricket, 19 like football and 12 like both. How many like at least one of the two? (a) 42 (b) 25 (c) 49 (d) 37
30. 30.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 6)(x + 7) (c) (x + 1)(x + 12) (d) (x − 6)(x − 7)
31. 31.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 2/3 (b) 5/6 (c) 1/3 (d) 1/4
32. 32.In a class of 36 children, 20 like dance, 14 like music and 8 like neither. How many like both? (a) 7 (b) 8 (c) 28 (d) 6
33. 33.In a league, 5 teams each play every other team once. How many matches are played? (a) 20 (b) 15 (c) 25 (d) 10
34. 34.What is the sum of the first 11 terms of the AP 3, 6, 9, …? (a) 201 (b) 33 (c) 396 (d) 198
35. 35.In a league, 10 teams each play every other team once. How many matches are played? (a) 55 (b) 100 (c) 90 (d) 45
36. 36.What is the midpoint of the line joining (10, 7) and (22, 17)? (a) (6, 5) (b) (16, 12) (c) (12, 16) (d) (32, 24)
37. 37.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 115° (b) 130° (c) 66° (d) 65°
38. 38.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 10 (c) 90 (d) 33
39. 39.What is the distance between the points (0, 12) and (8, 6)? (a) 11 (b) 14 (c) 100 (d) 10
40. 40.A bag has 5 yellow balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 4 (c) 8 (d) 2

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