Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 314 · 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 sum of the first 7 terms of the AP 9, 10, 11, …? (a) 15 (b) 84 (c) 168 (d) 85
2. 2.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
3. 3.In a class of 22 children, 10 like maths, 11 like science and 6 like both. How many like at least one of the two? (a) 15 (b) 21 (c) 22 (d) 9
4. 4.The mean of 8 numbers is 16. When the number 7 is added to them, what is the new mean? (a) 14 (b) 17 (c) 16 (d) 15
5. 5.What is the midpoint of the line joining (5, 11) and (7, 5)? (a) (12, 16) (b) (8, 6) (c) (1, 3) (d) (6, 8)
6. 6.A bag has 3 blue balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 2 (c) 12 (d) 4
7. 7.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 48 (c) 24 (d) 12
8. 8.A bag has 6 white balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 7 (c) 10 (d) 2
9. 9.What is the sum of the first 7 terms of the AP 2, 5, 8, …? (a) 80 (b) 77 (c) 154 (d) 20
10. 10.A bag has 3 green, 3 white and 5 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 8/11 (b) 3/11 (c) 1/3 (d) 9/11
11. 11.A cuboid is 6 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 144 cu cm (b) 168 cu cm (c) 16 cu cm (d) 24 cu cm
12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 17 (d) 6
13. 13.8 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) 112 (b) 15 (c) 64 (d) 56
14. 14.In a class of 30 children, 16 like mangoes, 13 like bananas and 6 like neither. How many like both? (a) 24 (b) 6 (c) 4 (d) 5
15. 15.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
16. 16.What is the distance between the points (9, 7) and (15, 15)? (a) 10 (b) 100 (c) 11 (d) 14
17. 17.A drawer has lots of blue, red, yellow and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 8 (d) 4
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/9 (c) 1/11 (d) 1/12
19. 19.In a class of 33 children, 23 like dance, 19 like music and 12 like both. How many like only dance? (a) 23 (b) 14 (c) 7 (d) 11
20. 20.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 90 (d) 45
21. 21.Two angles of a triangle are 35° and 85°. What is the exterior angle at the third corner? (a) 60° (b) 95° (c) 145° (d) 120°
22. 22.If a + b = 5 and ab = 4, what is (a − b)²? (a) 3 (b) 25 (c) 9 (d) 17
23. 23.A cube has edges of 3 cm. What is its total surface area? (a) 54 sq cm (b) 27 sq cm (c) 9 sq cm (d) 36 sq cm
24. 24.What is the prime factorisation of 336? (a) 2⁴ × 3 × 7 (b) 2 × 3 × 7⁴ (c) 2⁵ × 3 × 7 (d) 2³ × 3 × 7
25. 25.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 326 (c) 650 (d) 300
26. 26.In a class of 48 children, 21 like tea, 26 like coffee and 7 like neither. How many like both? (a) 6 (b) 7 (c) 5 (d) 41
27. 27.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 49 (b) 56 (c) 98 (d) 14
28. 28.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 2464 cm (c) 88 cm (d) 352 cm
29. 29.What is the smallest prime factor of 299? (a) 23 (b) 13 (c) 2 (d) 1
30. 30.What is the mean of 7, 20, 11 and 10? (a) 11 (b) 12 (c) 13 (d) 16
31. 31.How many prime numbers are there between 40 and 60? (a) 4 (b) 5 (c) 7 (d) 6
32. 32.A bag has 2 white, 4 red and 5 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 2/9 (b) 1/3 (c) 9/11 (d) 2/11
33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 8 (d) 20
34. 34.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 9 (c) 15 (d) 25
35. 35.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 64 cu cm (c) 12 cu cm (d) 96 cu cm
36. 36.A drawer has lots of yellow and black 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) 5 (d) 2
37. 37.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 65° (b) 115° (c) 25° (d) 295°
38. 38.What is the midpoint of the line joining (5, 3) and (9, 1)? (a) (14, 4) (b) (2, 1) (c) (7, 2) (d) (2, 7)
39. 39.What is the mode of 2, 2, 6, 6, 6, 18 and 15? (a) 2 (b) 6 (c) 15 (d) 18
40. 40.How many prime numbers are there between 10 and 20? (a) 4 (b) 6 (c) 5 (d) 3

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