Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 929 · 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 circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
2. 2.What is the midpoint of the line joining (9, 6) and (13, 8)? (a) (11, 7) (b) (2, 1) (c) (22, 14) (d) (7, 11)
3. 3.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
4. 4.In a class of 23 children, 15 like cricket, 14 like football and 11 like both. How many like neither? (a) 16 (b) 6 (c) 5 (d) 11
5. 5.What is the midpoint of the line joining (3, 6) and (7, 10)? (a) (5, 8) (b) (10, 16) (c) (8, 5) (d) (2, 2)
6. 6.A bag has 9 blue balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 19 (d) 11
7. 7.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 210° (c) 150° (d) 30°
8. 8.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 240 (c) 120 (d) 20
9. 9.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 5/6 (d) 2/3
10. 10.In a class of 38 children, 28 like mangoes, 11 like bananas and 8 like both. How many like neither? (a) 6 (b) 8 (c) 7 (d) 15
11. 11.Two angles of a triangle are 35° and 35°. What is the third angle? (a) 145° (b) 290° (c) 70° (d) 110°
12. 12.What is the sum of the first 7 terms of the AP 5, 11, 17, …? (a) 182 (b) 41 (c) 322 (d) 161
13. 13.What is the mode of 14, 14, 15, 14, 2, 15 and 5? (a) 5 (b) 15 (c) 14 (d) 2
14. 14.Using (a − b)² = a² − 2ab + b², what is 15²? (a) 235 (b) 625 (c) 225 (d) 375
15. 15.A bag has 3 green, 4 blue and 7 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 2/7 (c) 2/5 (d) 5/7
16. 16.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) 36 (b) 37 (c) 48 (d) 49
17. 17.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 207 (c) 23 (d) 72
18. 18.A canteen sells 4 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 28 (b) 32 (c) 11 (d) 56
19. 19.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 49 (c) 42 (d) 21
20. 20.Two angles of a triangle are 55° and 65°. What is the third angle? (a) 115° (b) 125° (c) 60° (d) 120°
21. 21.In a class of 35 children, 18 like cricket, 21 like football and 7 like both. How many like neither? (a) 4 (b) 10 (c) 7 (d) 3
22. 22.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 18 (c) 81 (d) 72
23. 23.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
24. 24.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
25. 25.What is the mean of 15, 11, 9, 9, 2 and 20? (a) 10 (b) 11 (c) 12 (d) 13
26. 26.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
27. 27.What is the smallest prime factor of 49? (a) 3 (b) 1 (c) 7 (d) 2
28. 28.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 25° (b) 26° (c) 155° (d) 50°
29. 29.What is the mean of 18, 15, 20, 15, 2 and 14? (a) 14 (b) 13 (c) 12 (d) 15
30. 30.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 33 (c) 90 (d) 10
31. 31.What is the mean of 20, 2, 15, 16 and 22? (a) 17 (b) 15 (c) 16 (d) 14
32. 32.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/3 (c) 1/2 (d) 1/4
33. 33.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 60 (c) 63 (d) 20
34. 34.Two angles of a triangle are 55° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 115° (c) 125° (d) 65°
35. 35.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
36. 36.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 155° (b) 25° (c) 110° (d) 95°
37. 37.4 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) 28 (b) 56 (c) 11 (d) 32
38. 38.How many factors does 102 have? (a) 9 (b) 6 (c) 8 (d) 7
39. 39.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 100° (b) 140° (c) 60° (d) 120°
40. 40.What is the midpoint of the line joining (4, 7) and (10, 1)? (a) (4, 7) (b) (14, 8) (c) (7, 4) (d) (3, 3)

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