Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 436 · 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.There are 8 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 15 (b) 112 (c) 56 (d) 64
2. 2.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 100° (c) 10° (d) 20°
3. 3.What is the median of 27, 12, 35, 20 and 39? (a) 20 (b) 28 (c) 35 (d) 27
4. 4.5 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) 35 (b) 12 (c) 70 (d) 40
5. 5.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
6. 6.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 132 (c) 144 (d) 66
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 1/9 (c) 5/36 (d) 4/11
8. 8.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 156 (c) 91 (d) 78
9. 9.What is the smallest prime factor of 217? (a) 31 (b) 1 (c) 7 (d) 2
10. 10.Which is the correct factorisation of x² + 8x + 15? (a) (x + 1)(x + 7) (b) (x + 1)(x + 15) (c) (x − 3)(x − 5) (d) (x + 3)(x + 5)
11. 11.What is the missing term in the AP 7, 10, 13, ?, 19? (a) 17 (b) 16 (c) 15 (d) 19
12. 12.What is the product of the roots of x² − 16x + 63 = 0? (a) 62 (b) 16 (c) 64 (d) 63
13. 13.How many factors does 64 have? (a) 6 (b) 8 (c) 5 (d) 7
14. 14.In a class of 18 children, 11 like mangoes, 10 like bananas and 4 like both. How many like only mangoes? (a) 11 (b) 8 (c) 7 (d) 6
15. 15.In a class of 27 children, 20 like mangoes, 13 like bananas and 8 like both. How many like neither? (a) 2 (b) 10 (c) 8 (d) 3
16. 16.What is the mode of 4, 13, 4, 2, 4, 19 and 13? (a) 4 (b) 19 (c) 2 (d) 13
17. 17.What is the midpoint of the line joining (6, 5) and (8, 7)? (a) (1, 1) (b) (7, 6) (c) (6, 7) (d) (14, 12)
18. 18.How many factors does 25 have? (a) 4 (b) 2 (c) 3 (d) 1
19. 19.A bag has 5 red, 7 yellow and 9 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/2 (b) 8/21 (c) 1/3 (d) 2/3
20. 20.If a + b = 20 and ab = 96, what is (a − b)²? (a) 400 (b) 16 (c) 208 (d) 4
21. 21.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
22. 22.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 120 (c) 25 (d) 240
23. 23.What is the mean of 19, 3, 13, 8 and 12? (a) 11 (b) 13 (c) 12 (d) 10
24. 24.In a class of 40 children, 16 like maths, 25 like science and 11 like both. How many like only maths? (a) 14 (b) 5 (c) 15 (d) 16
25. 25.What is the sum of the roots of x² − 7x + 12 = 0? (a) 12 (b) 8 (c) 7 (d) 6
26. 26.What is the sum of all the whole numbers from 1 to 22? (a) 506 (b) 242 (c) 253 (d) 231
27. 27.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 781 (c) 1560 (d) 780
28. 28.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
29. 29.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 10 (d) 8
30. 30.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 90 (b) 100 (c) 45 (d) 20
31. 31.A bag has 7 yellow balls and 12 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 8 (c) 13 (d) 2
32. 32.Using (a − b)² = a² − 2ab + b², what is 96²? (a) 10816 (b) 9226 (c) 9216 (d) 9984
33. 33.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
34. 34.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 6 (d) 9
35. 35.In a class of 29 children, 17 like mangoes, 16 like bananas and 7 like neither. How many like both? (a) 22 (b) 4 (c) 7 (d) 11
36. 36.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 5/8 (c) 3/5 (d) 1/4
37. 37.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 484 sq cm (c) 121 sq cm (d) 726 sq cm
38. 38.What is the mode of 8, 8, 9, 9, 1, 8 and 20? (a) 9 (b) 8 (c) 1 (d) 20
39. 39.A cube has edges of 3 cm. What is its total surface area? (a) 36 sq cm (b) 54 sq cm (c) 27 sq cm (d) 9 sq cm
40. 40.What is the midpoint of the line joining (8, 16) and (10, 10)? (a) (18, 26) (b) (13, 9) (c) (1, 3) (d) (9, 13)

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