Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 501 · 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 17, 5, 11, 15 and 17? (a) 14 (b) 13 (c) 15 (d) 12
2. 2.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 210° (b) 31° (c) 30° (d) 150°
3. 3.What is the prime factorisation of 21? (a) 3 × 7² (b) 3² × 7 (c) 3 × 7 (d) 3³ × 7
4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
5. 5.What is the median of 40, 38, 37, 3 and 39? (a) 37 (b) 38 (c) 39 (d) 40
6. 6.A drawer has lots of red, black and yellow 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) 3 (c) 4 (d) 6
7. 7.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
8. 8.If a + b = 9 and ab = 14, what is (a − b)²? (a) 53 (b) 81 (c) 25 (d) 5
9. 9.In which quadrant does the point (−7, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
10. 10.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/4 (c) 2/3 (d) 1/3
11. 11.What is the midpoint of the line joining (0, 6) and (4, 0)? (a) (3, 3) (b) (4, 6) (c) (3, 2) (d) (2, 3)
12. 12.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 55° (b) 70° (c) 125° (d) 250°
13. 13.What are the roots of x² − 15x + 54 = 0? (a) 2 and 27 (b) 6 and 9 (c) 1 and 54 (d) 1 and 14
14. 14.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 15 (c) 30 (d) 8
15. 15.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 100 (c) 90 (d) 20
16. 16.What is the sum of the first 9 terms of the AP 6, 9, 12, …? (a) 30 (b) 165 (c) 324 (d) 162
17. 17.What is the sum of the first 5 terms of the AP 1, 5, 9, …? (a) 17 (b) 90 (c) 55 (d) 45
18. 18.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 121 (c) 110 (d) 55
19. 19.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
20. 20.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
21. 21.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 110° (b) 130° (c) 120° (d) 70°
22. 22.The mean of 9 numbers is 22. When the number 12 is added to them, what is the new mean? (a) 17 (b) 21 (c) 22 (d) 20
23. 23.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/5 (b) 5/6 (c) 1/6 (d) 1/3
24. 24.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2² × 3² × 5 (d) 2 × 3² × 5
25. 25.In a class of 40 children, 32 like cricket, 19 like football and 1 like neither. How many like both? (a) 39 (b) 12 (c) 11 (d) 1
26. 26.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
27. 27.What is the distance between the points (6, 8) and (14, 14)? (a) 11 (b) 10 (c) 100 (d) 14
28. 28.What is the mode of 10, 16, 9, 10, 11, 9 and 9? (a) 10 (b) 11 (c) 16 (d) 9
29. 29.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 1/4 (c) 3/8 (d) 3/4
30. 30.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 3/4 (c) 1/4 (d) 1/3
31. 31.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 255° (b) 75° (c) 76° (d) 105°
32. 32.The mean of 4 numbers is 19. When the number 14 is added to them, what is the new mean? (a) 17 (b) 20 (c) 18 (d) 19
33. 33.A bag has 11 black balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 12 (b) 2 (c) 13 (d) 20
34. 34.In a class of 52 children, 32 like dance, 25 like music and 12 like both. How many like neither? (a) 8 (b) 19 (c) 7 (d) 12
35. 35.In a class of 50 children, 29 like dance, 24 like music and 10 like both. How many like only dance? (a) 26 (b) 29 (c) 14 (d) 19
36. 36.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
37. 37.Using (a − b)² = a² − 2ab + b², what is 89²? (a) 8281 (b) 7921 (c) 8099 (d) 7931
38. 38.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 66 (c) 121 (d) 110
39. 39.In which quadrant does the point (−2, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
40. 40.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 18 (c) 15 (d) 45

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