Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 631 · 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.The mean of 4 numbers is 18. When the number 8 is added to them, what is the new mean? (a) 17 (b) 13 (c) 18 (d) 16
2. 2.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 30° (b) 70° (c) 120° (d) 60°
3. 3.In a class of 44 children, 29 like dance, 22 like music and 11 like both. How many like only dance? (a) 11 (b) 18 (c) 29 (d) 22
4. 4.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
5. 5.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 95° (b) 130° (c) 135° (d) 45°
6. 6.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
7. 7.What is the mode of 12, 5, 13, 19, 19, 13 and 19? (a) 12 (b) 13 (c) 19 (d) 5
8. 8.In a class of 28 children, 10 like tea, 19 like coffee and 3 like both. How many like only tea? (a) 16 (b) 7 (c) 9 (d) 10
9. 9.If a + b = 17 and ab = 60, what is a² + b²? (a) 289 (b) 229 (c) 169 (d) 409
10. 10.In a class of 33 children, 18 like dance, 17 like music and 4 like both. How many like only dance? (a) 13 (b) 18 (c) 14 (d) 16
11. 11.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/4 (c) 3/4 (d) 1/2
12. 12.How many prime numbers are there between 80 and 90? (a) 1 (b) 4 (c) 2 (d) 3
13. 13.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
14. 14.What is the prime factorisation of 126? (a) 2³ × 3² × 7 (b) 2² × 3² × 7 (c) 2 × 3² × 7 (d) 2 × 3² × 7²
15. 15.How many factors does 55 have? (a) 4 (b) 3 (c) 5 (d) 2
16. 16.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 55 (d) 110
17. 17.Two angles of a triangle are 40° and 60°. What is the third angle? (a) 80° (b) 100° (c) 140° (d) 120°
18. 18.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 130° (c) 25° (d) 35°
19. 19.A cube has edges of 2 cm. What is its volume? (a) 24 cu cm (b) 8 cu cm (c) 16 cu cm (d) 6 cu cm
20. 20.In which quadrant does the point (−2, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
21. 21.What is the sum of the first 5 terms of the AP 8, 10, 12, …? (a) 16 (b) 60 (c) 120 (d) 65
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/9 (c) 1/11 (d) 4/11
23. 23.What is the median of 31, 14, 1, 35 and 21? (a) 1 (b) 14 (c) 31 (d) 21
24. 24.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2 × 5 × 7 (c) 2² × 5 × 7 (d) 2³ × 5 × 7
25. 25.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) 4 (b) 3 (c) 6 (d) 2
26. 26.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
27. 27.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
28. 28.A bag has 10 red balls and 11 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 12 (b) 2 (c) 21 (d) 11
29. 29.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 2464 cm (c) 176 cm (d) 352 cm
30. 30.A bag has 4 black balls and 3 green 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) 7 (d) 4
31. 31.What is the 17th term of the AP 14, 18, 22, 26, …? (a) 64 (b) 78 (c) 68 (d) 82
32. 32.Two angles of a triangle are 60° and 35°. What is the third angle? (a) 85° (b) 120° (c) 145° (d) 95°
33. 33.In a class of 35 children, 15 like tea, 27 like coffee and 10 like both. How many like neither? (a) 10 (b) 3 (c) 13 (d) 4
34. 34.In a class of 19 children, 13 like maths, 7 like science and 2 like neither. How many like both? (a) 2 (b) 3 (c) 17 (d) 1
35. 35.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 14 (c) 22 (d) 15
36. 36.In a class of 40 children, 18 like mangoes, 25 like bananas and 5 like both. How many like at least one of the two? (a) 33 (b) 40 (c) 43 (d) 38
37. 37.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 14 (c) 15 (d) 7
38. 38.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) 25 (b) 24 (c) 13 (d) 12
39. 39.A cube has edges of 11 cm. What is its total surface area? (a) 1331 sq cm (b) 726 sq cm (c) 121 sq cm (d) 484 sq cm
40. 40.In a class of 17 children, 5 like mangoes, 10 like bananas and 2 like both. How many like neither? (a) 5 (b) 6 (c) 4 (d) 2

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