Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 540 · 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.Two angles of a triangle are 35° and 65°. What is the third angle? (a) 100° (b) 115° (c) 80° (d) 145°
2. 2.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
3. 3.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)
4. 4.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 841 (c) 870 (d) 57
5. 5.How many prime numbers are there between 10 and 20? (a) 6 (b) 5 (c) 3 (d) 4
6. 6.What is the mean of 7, 18, 20, 3 and 7? (a) 12 (b) 10 (c) 13 (d) 11
7. 7.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 176 cm (d) 88 cm
8. 8.What is the midpoint of the line joining (9, 22) and (19, 10)? (a) (5, 6) (b) (14, 16) (c) (16, 14) (d) (28, 32)
9. 9.In a class of 27 children, 16 like cricket, 14 like football and 4 like both. How many like at least one of the two? (a) 22 (b) 26 (c) 30 (d) 27
10. 10.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
11. 11.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 3/4 (c) 1/8 (d) 1/4
12. 12.How many factors does 93 have? (a) 5 (b) 4 (c) 3 (d) 2
13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 16 (d) 15
14. 14.There are 7 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 21 (c) 14 (d) 28
15. 15.What is the distance between the points (9, 6) and (13, 9)? (a) 25 (b) 5 (c) 7 (d) 6
16. 16.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 25 (c) 10 (d) 20
17. 17.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 65° (b) 160° (c) 135° (d) 115°
18. 18.A bag has 5 green balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 10 (b) 6 (c) 7 (d) 2
19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 9 (b) 19 (c) 20 (d) 21
20. 20.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
21. 21.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
22. 22.What is the sum of the first 10 terms of the AP 8, 11, 14, …? (a) 430 (b) 35 (c) 230 (d) 215
23. 23.In a class of 32 children, 18 like dance, 17 like music and 3 like neither. How many like both? (a) 7 (b) 29 (c) 3 (d) 6
24. 24.What is the midpoint of the line joining (0, 3) and (4, 7)? (a) (4, 10) (b) (2, 2) (c) (2, 5) (d) (5, 2)
25. 25.If a + b = 14 and ab = 40, what is (a − b)²? (a) 36 (b) 116 (c) 196 (d) 6
26. 26.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 55 (d) 110
27. 27.A bag has 9 red balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 10 (c) 9 (d) 2
28. 28.In a class of 32 children, 15 like tea, 10 like coffee and 9 like neither. How many like both? (a) 3 (b) 23 (c) 9 (d) 2
29. 29.A bag has 10 red balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 11 (b) 2 (c) 16 (d) 12
30. 30.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 72 (b) 12 (c) 42 (d) 36
31. 31.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 14 (c) 42 (d) 45
32. 32.What is the median of 18, 40, 12, 4 and 38? (a) 19 (b) 38 (c) 18 (d) 12
33. 33.How many prime numbers are there between 20 and 30? (a) 1 (b) 3 (c) 4 (d) 2
34. 34.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 100 (c) 55 (d) 45
35. 35.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 42 (c) 28 (d) 21
36. 36.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 6 (b) 9 (c) 12 (d) 5
37. 37.Two angles of a triangle are 25° and 75°. What is the exterior angle at the third corner? (a) 80° (b) 155° (c) 100° (d) 105°
38. 38.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 90 (b) 45 (c) 81 (d) 17
39. 39.The mean of 5 numbers is 30. When the number 36 is added to them, what is the new mean? (a) 30 (b) 33 (c) 31 (d) 32
40. 40.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 105 (c) 225 (d) 120

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