Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 986 · 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.A bag has 10 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) 7 (b) 11 (c) 2 (d) 16
2. 2.A bag has 11 yellow balls and 12 red 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) 13 (c) 23 (d) 12
3. 3.In a class of 32 children, 10 like dance, 15 like music and 3 like both. How many like only dance? (a) 12 (b) 10 (c) 7 (d) 17
4. 4.In a class of 40 children, 30 like tea, 18 like coffee and 10 like both. How many like only tea? (a) 20 (b) 30 (c) 22 (d) 8
5. 5.In a class of 32 children, 19 like maths, 14 like science and 8 like neither. How many like both? (a) 8 (b) 1 (c) 24 (d) 9
6. 6.A bag has 5 blue balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 15 (c) 11 (d) 2
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 1/6 (c) 7/36 (d) 1/11
8. 8.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 40° (d) 100°
9. 9.If a + b = 11 and ab = 24, what is (a − b)²? (a) 5 (b) 73 (c) 121 (d) 25
10. 10.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 40 (c) 24 (d) 20
11. 11.Using (a + b)² = a² + 2ab + b², what is 54²? (a) 2516 (b) 2116 (c) 2916 (d) 2926
12. 12.What is the midpoint of the line joining (7, 7) and (13, 3)? (a) (5, 10) (b) (3, 2) (c) (20, 10) (d) (10, 5)
13. 13.What is the midpoint of the line joining (3, 10) and (13, 2)? (a) (16, 12) (b) (8, 6) (c) (6, 8) (d) (5, 4)
14. 14.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/11 (c) 1/9 (d) 5/36
16. 16.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
17. 17.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7³
18. 18.A cube has edges of 10 cm. What is its volume? (a) 1000 cu cm (b) 600 cu cm (c) 30 cu cm (d) 400 cu cm
19. 19.A bag has 8 blue balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 10 (b) 9 (c) 18 (d) 2
20. 20.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
21. 21.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90
22. 22.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 80° (b) 81° (c) 100° (d) 160°
23. 23.What is the smallest prime factor of 143? (a) 2 (b) 1 (c) 11 (d) 13
24. 24.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 8125 (b) 9035 (c) 7225 (d) 9025
25. 25.6 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 36 (b) 24 (c) 9 (d) 18
26. 26.What is the mode of 3, 13, 3, 4, 16, 4 and 4? (a) 16 (b) 13 (c) 4 (d) 3
27. 27.In a class of 39 children, 25 like dance, 22 like music and 10 like both. How many like at least one of the two? (a) 39 (b) 37 (c) 47 (d) 27
28. 28.In a class of 39 children, 20 like maths, 17 like science and 2 like both. How many like at least one of the two? (a) 39 (b) 37 (c) 33 (d) 35
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 3/11 (c) 1/12 (d) 1/9
30. 30.What is the missing term in the AP 10, ?, 16, 19, 22? (a) 14 (b) 12 (c) 16 (d) 13
31. 31.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 45 (c) 126 (d) 14
32. 32.In a class of 30 children, 20 like mangoes, 15 like bananas and 3 like neither. How many like both? (a) 3 (b) 8 (c) 27 (d) 5
33. 33.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 7482 (c) 3655 (d) 3741
34. 34.A bag has 3 green balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 10 (b) 2 (c) 4 (d) 5
35. 35.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 96 (b) 19 (c) 192 (d) 104
36. 36.In a class of 34 children, 19 like dance, 21 like music and 9 like both. How many like only dance? (a) 12 (b) 10 (c) 13 (d) 19
37. 37.How many factors does 46 have? (a) 4 (b) 3 (c) 2 (d) 5
38. 38.What is the smallest prime factor of 203? (a) 29 (b) 7 (c) 1 (d) 2
39. 39.What is the smallest prime factor of 115? (a) 23 (b) 5 (c) 1 (d) 2
40. 40.A bag has 11 green balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 13 (b) 14 (c) 2 (d) 12

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