Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 216 · 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 fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
2. 2.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
3. 3.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 5° (b) 85° (c) 95° (d) 10°
4. 4.What are the roots of x² − 13x + 40 = 0? (a) 2 and 20 (b) 1 and 12 (c) 1 and 40 (d) 5 and 8
5. 5.How many factors does 74 have? (a) 5 (b) 3 (c) 2 (d) 4
6. 6.If a + b = 19 and ab = 88, what is a² + b²? (a) 361 (b) 273 (c) 537 (d) 185
7. 7.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 42 (c) 21 (d) 49
8. 8.The mean of 4 numbers is 19. When the number 14 is added to them, what is the new mean? (a) 18 (b) 17 (c) 19 (d) 20
9. 9.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4
10. 10.The mean of 7 numbers is 38. When the number 46 is added to them, what is the new mean? (a) 40 (b) 39 (c) 42 (d) 38
11. 11.What is the 36th term of the AP 7, 9, 11, 13, …? (a) 72 (b) 70 (c) 79 (d) 77
12. 12.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
13. 13.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 300° (b) 30° (c) 60° (d) 120°
14. 14.Two angles of a triangle are 20° and 30°. What is the exterior angle at the third corner? (a) 130° (b) 150° (c) 160° (d) 50°
15. 15.Two angles of a triangle are 45° and 80°. What is the exterior angle at the third corner? (a) 125° (b) 135° (c) 55° (d) 100°
16. 16.What is the mean of 13, 19, 11, 19, 16 and 18? (a) 18 (b) 16 (c) 17 (d) 15
17. 17.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 105° (c) 285° (d) 75°
18. 18.A bag has 4 yellow balls and 5 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 5 (c) 9 (d) 6
19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 17 (b) 18 (c) 19 (d) 7
20. 20.What is the midpoint of the line joining (0, 9) and (4, 7)? (a) (8, 2) (b) (4, 16) (c) (2, 1) (d) (2, 8)
21. 21.What is the 11th term of the AP 18, 23, 28, 33, …? (a) 50 (b) 68 (c) 73 (d) 55
22. 22.In a class of 26 children, 20 like tea, 11 like coffee and 6 like both. How many like neither? (a) 2 (b) 7 (c) 1 (d) 6
23. 23.How many prime numbers are there between 50 and 80? (a) 8 (b) 9 (c) 7 (d) 6
24. 24.What is the sum of the first 12 terms of the AP 9, 10, 11, …? (a) 180 (b) 348 (c) 174 (d) 20
25. 25.What is the midpoint of the line joining (5, 8) and (15, 14)? (a) (5, 3) (b) (10, 11) (c) (11, 10) (d) (20, 22)
26. 26.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 25 (c) 36 (d) 37
27. 27.What is the missing term in the AP 16, 19, ?, 25, 28? (a) 23 (b) 25 (c) 22 (d) 21
28. 28.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 6 (d) 15
29. 29.How many factors does 73 have? (a) 2 (b) 1 (c) 4 (d) 3
30. 30.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
31. 31.What is the mode of 18, 11, 11, 5, 5, 4 and 5? (a) 4 (b) 11 (c) 18 (d) 5
32. 32.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 110° (b) 70° (c) 140° (d) 250°
33. 33.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
34. 34.In a class of 35 children, 23 like cricket, 18 like football and 7 like both. How many like neither? (a) 2 (b) 7 (c) 1 (d) 8
35. 35.What is the prime factorisation of 63? (a) 3³ × 7 (b) 3² × 7 (c) 3 × 7² (d) 3 × 7
36. 36.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
37. 37.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 484 (c) 43 (d) 253
38. 38.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
39. 39.In a class of 20 children, 6 like maths, 7 like science and 3 like both. How many like neither? (a) 3 (b) 7 (c) 10 (d) 13
40. 40.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 60° (b) 140° (c) 100° (d) 120°

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