Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 999 · 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.How many prime numbers are there between 50 and 70? (a) 6 (b) 3 (c) 4 (d) 5
2. 2.If a + b = 10 and ab = 24, what is a² + b²? (a) 76 (b) 100 (c) 148 (d) 52
3. 3.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 96 cu cm (d) 12 cu cm
4. 4.How many factors does 110 have? (a) 9 (b) 8 (c) 6 (d) 7
5. 5.In a league, 5 teams each play every other team once. How many matches are played? (a) 15 (b) 20 (c) 10 (d) 25
6. 6.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 95° (c) 85° (d) 170°
7. 7.In a class of 40 children, 14 like cricket, 21 like football and 4 like both. How many like neither? (a) 5 (b) 13 (c) 9 (d) 4
8. 8.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 2 times (c) 4 times (d) 8 times
9. 9.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 35° (b) 45° (c) 70° (d) 110°
10. 10.A drawer has lots of blue and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 3 (d) 4
11. 11.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 1/4 (d) 2/3
12. 12.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) 37 (b) 36 (c) 49 (d) 48
13. 13.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
14. 14.In a class of 48 children, 22 like cricket, 24 like football and 8 like both. How many like at least one of the two? (a) 38 (b) 30 (c) 46 (d) 48
15. 15.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 120° (b) 105° (c) 75° (d) 135°
16. 16.What is the median of 11, 8, 21, 23, 15, 13 and 24? (a) 21 (b) 13 (c) 23 (d) 15
17. 17.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 25° (d) 130°
18. 18.A bag has 3 yellow balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 2 (c) 4 (d) 15
19. 19.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 48 (d) 24
20. 20.The mean of 5 numbers is 19. When the number 7 is added to them, what is the new mean? (a) 18 (b) 13 (c) 19 (d) 17
21. 21.If a + b = 14 and ab = 48, what is a² + b²? (a) 148 (b) 292 (c) 196 (d) 100
22. 22.In a class of 26 children, 17 like dance, 12 like music and 8 like both. How many like only dance? (a) 14 (b) 4 (c) 17 (d) 9
23. 23.In a class of 39 children, 20 like maths, 15 like science and 6 like both. How many like at least one of the two? (a) 23 (b) 29 (c) 35 (d) 39
24. 24.In a league, 12 teams each play every other team once. How many matches are played? (a) 132 (b) 66 (c) 78 (d) 144
25. 25.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56
26. 26.What is the distance between the points (7, 5) and (10, 1)? (a) 5 (b) 25 (c) 7 (d) 6
27. 27.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
28. 28.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
29. 29.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 154 cm (d) 44 cm
30. 30.Two angles of a triangle are 20° and 90°. What is the third angle? (a) 90° (b) 70° (c) 160° (d) 110°
31. 31.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
32. 32.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 18 (c) 81 (d) 36
33. 33.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 210 (b) 120 (c) 225 (d) 105
34. 34.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
35. 35.In a class of 31 children, 24 like dance, 15 like music and 1 like neither. How many like both? (a) 8 (b) 30 (c) 1 (d) 9
36. 36.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 150° (b) 30° (c) 115° (d) 95°
37. 37.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 160° (c) 100° (d) 80°
38. 38.A bag has 6 red, 3 yellow and 6 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 4/5 (b) 1/5 (c) 1/3 (d) 1/4
39. 39.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 13 (b) 24 (c) 25 (d) 12
40. 40.What is the product of the roots of x² − 9x + 20 = 0? (a) 21 (b) 20 (c) 9 (d) 19

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