Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 961 · 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.What is the mean of 11, 9, 3, 13, 20 and 16? (a) 12 (b) 11 (c) 14 (d) 13
2. 2.What is the mode of 3, 3, 8, 20, 3, 8 and 14? (a) 20 (b) 14 (c) 3 (d) 8
3. 3.What is the missing term in the AP 8, 14, 20, ?, 32? (a) 27 (b) 25 (c) 32 (d) 26
4. 4.Using (a + b)² = a² + 2ab + b², what is 64²? (a) 3136 (b) 4096 (c) 4106 (d) 3616
5. 5.A bag has 4 green balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 6 (b) 10 (c) 5 (d) 2
6. 6.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
7. 7.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
8. 8.If a + b = 9 and ab = 20, what is a² + b²? (a) 61 (b) 121 (c) 41 (d) 81
9. 9.A bag has 5 white, 5 green and 3 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/3 (b) 5/13 (c) 8/13 (d) 9/13
10. 10.What is the midpoint of the line joining (0, 1) and (6, 3)? (a) (3, 2) (b) (6, 4) (c) (2, 3) (d) (3, 1)
11. 11.A cube has edges of 9 cm. What is its volume? (a) 27 cu cm (b) 324 cu cm (c) 486 cu cm (d) 729 cu cm
12. 12.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
13. 13.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 30 (c) 36 (d) 15
14. 14.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 120 (b) 225 (c) 210 (d) 105
15. 15.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 235 (c) 225 (d) 228
16. 16.What are the roots of x² − 9x + 18 = 0? (a) 2 and 9 (b) 1 and 18 (c) 1 and 8 (d) 3 and 6
17. 17.A bag has 8 black balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 9 (b) 19 (c) 10 (d) 2
18. 18.In a class of 35 children, 25 like cricket, 11 like football and 6 like both. How many like at least one of the two? (a) 36 (b) 24 (c) 35 (d) 30
19. 19.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 288 (c) 279 (d) 264
20. 20.What is the distance between the points (1, 0) and (6, 12)? (a) 13 (b) 17 (c) 14 (d) 169
21. 21.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 48 (b) 49 (c) 37 (d) 36
22. 22.What is the sum of all the whole numbers from 1 to 21? (a) 462 (b) 210 (c) 232 (d) 231
23. 23.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 40° (d) 50°
24. 24.Two angles of a triangle are 65° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 50° (c) 130° (d) 230°
25. 25.A bag has 4 blue balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 6 (b) 5 (c) 7 (d) 2
26. 26.Two angles of a triangle are 30° and 120°. What is the exterior angle at the third corner? (a) 30° (b) 210° (c) 150° (d) 60°
27. 27.A bag has 7 white balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 7 (d) 13
28. 28.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 17 (b) 45 (c) 81 (d) 90
29. 29.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2³ × 3 × 5 (c) 2 × 3 × 5 (d) 2 × 3 × 5²
30. 30.What is the midpoint of the line joining (6, 15) and (16, 3)? (a) (9, 11) (b) (5, 6) (c) (11, 9) (d) (22, 18)
31. 31.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
32. 32.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 32 (c) 10 (d) 16
33. 33.Two angles of a triangle are 20° and 60°. What is the third angle? (a) 160° (b) 120° (c) 80° (d) 100°
34. 34.What is the 16th term of the AP 2, 11, 20, 29, …? (a) 146 (b) 137 (c) 144 (d) 135
35. 35.What is the sum of the first 5 terms of the AP 6, 10, 14, …? (a) 70 (b) 80 (c) 140 (d) 22
36. 36.In a class of 19 children, 10 like maths, 14 like science and 7 like both. How many like only maths? (a) 10 (b) 7 (c) 5 (d) 3
37. 37.A drawer has lots of blue and red 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) 4 (c) 5 (d) 3
38. 38.Using (a + b)² = a² + 2ab + b², what is 63²? (a) 3979 (b) 3249 (c) 3609 (d) 3969
39. 39.A bag has 11 white balls and 10 black 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) 21 (c) 12 (d) 11
40. 40.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 528 (c) 562 (d) 1122

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