Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 469 · 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 9, 3, 17, 7, 6 and 6? (a) 9 (b) 7 (c) 8 (d) 10
2. 2.In a class of 41 children, 13 like mangoes, 21 like bananas and 9 like neither. How many like both? (a) 3 (b) 9 (c) 2 (d) 32
3. 3.What is the distance between the points (5, 1) and (12, 25)? (a) 25 (b) 26 (c) 31 (d) 625
4. 4.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) 32 (b) 28 (c) 11 (d) 56
5. 5.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 16 (b) 51 (c) 144 (d) 48
6. 6.In a class of 26 children, 19 like dance, 9 like music and 5 like both. How many like only dance? (a) 4 (b) 14 (c) 17 (d) 19
7. 7.In a class of 24 children, 7 like dance, 18 like music and 4 like both. How many like at least one of the two? (a) 24 (b) 17 (c) 25 (d) 21
8. 8.What is the prime factorisation of 36? (a) 2 × 3² (b) 2³ × 3² (c) 2² × 3³ (d) 2² × 3²
9. 9.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
10. 10.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 5/11 (c) 1/11 (d) 5/36
12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 3 (d) 4
13. 13.What is the smallest prime factor of 145? (a) 5 (b) 29 (c) 2 (d) 1
14. 14.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 25° (b) 130° (c) 50° (d) 35°
15. 15.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
16. 16.In a class of 28 children, 14 like mangoes, 12 like bananas and 6 like both. How many like at least one of the two? (a) 14 (b) 20 (c) 28 (d) 26
17. 17.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 81 (b) 90 (c) 17 (d) 45
18. 18.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/3 (c) 2/3 (d) 1/2
19. 19.A bag has 5 red balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 17 (b) 2 (c) 7 (d) 6
20. 20.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
21. 21.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/3 (d) 1/4
22. 22.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 145° (d) 110°
23. 23.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 63 (c) 21 (d) 7
24. 24.How many factors does 84 have? (a) 12 (b) 13 (c) 10 (d) 11
25. 25.What is the mode of 2, 2, 1, 16, 3, 16 and 16? (a) 2 (b) 16 (c) 3 (d) 1
26. 26.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
28. 28.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 21 (c) 42 (d) 28
29. 29.A bag has 4 red, 7 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 2/13 (b) 11/13 (c) 12/13 (d) 1/3
30. 30.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
31. 31.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
32. 32.What is the midpoint of the line joining (3, 8) and (11, 18)? (a) (7, 13) (b) (13, 7) (c) (14, 26) (d) (4, 5)
33. 33.What is the median of 26, 10, 19, 14 and 6? (a) 15 (b) 19 (c) 14 (d) 10
34. 34.Two angles of a triangle are 80° and 55°. What is the exterior angle at the third corner? (a) 45° (b) 125° (c) 135° (d) 100°
35. 35.What is the median of 15, 25, 18, 21, 24, 20 and 8? (a) 21 (b) 20 (c) 19 (d) 18
36. 36.The mean of 9 numbers is 27. When the number 17 is added to them, what is the new mean? (a) 22 (b) 26 (c) 25 (d) 27
37. 37.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 21 (c) 63 (d) 189
38. 38.What is the median of 18, 13, 8, 15, 9, 11 and 16? (a) 15 (b) 14 (c) 13 (d) 11
39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 17 (d) 15
40. 40.How many prime numbers are there between 70 and 80? (a) 4 (b) 2 (c) 3 (d) 5

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