Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 856 · 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 canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 30 (b) 60 (c) 11 (d) 35
2. 2.In which quadrant does the point (−8, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
3. 3.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
4. 4.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 55° (b) 130° (c) 105° (d) 125°
5. 5.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 70° (b) 110° (c) 290° (d) 145°
6. 6.A bag has 7 green balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 11 (c) 9 (d) 8
7. 7.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
8. 8.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1129 (c) 2256 (d) 1128
9. 9.A canteen sells 4 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 16 (c) 32 (d) 8
10. 10.In a class of 37 children, 16 like tea, 24 like coffee and 8 like both. How many like at least one of the two? (a) 24 (b) 32 (c) 40 (d) 37
11. 11.If a + b = 7 and ab = 6, what is a² + b²? (a) 61 (b) 49 (c) 43 (d) 37
12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 4 (b) 7 (c) 5 (d) 6
13. 13.What is the mode of 4, 20, 10, 20, 5, 10 and 20? (a) 20 (b) 4 (c) 10 (d) 5
14. 14.Two angles of a triangle are 60° and 45°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 135° (d) 120°
15. 15.In which quadrant does the point (9, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
16. 16.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 140° (b) 45° (c) 85° (d) 135°
17. 17.How many prime numbers are there between 80 and 90? (a) 2 (b) 4 (c) 1 (d) 3
18. 18.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 2/3 (d) 1/3
19. 19.What is the sum of the first 29 odd numbers (1 + 3 + 5 + …)? (a) 435 (b) 57 (c) 841 (d) 870
20. 20.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 12 (c) 16 (d) 24
21. 21.What is the sum of all the whole numbers from 1 to 39? (a) 741 (b) 1560 (c) 780 (d) 781
22. 22.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 55 (c) 100 (d) 90
23. 23.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 220 cm (d) 110 cm
24. 24.What is the prime factorisation of 168? (a) 2 × 3 × 7³ (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2⁴ × 3 × 7
25. 25.A bag has 7 red, 4 green and 3 white balls. One ball is taken out without looking. What is the probability that it is red? (a) 4/7 (b) 1/2 (c) 1/3 (d) 1/14
26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 13 (b) 4 (c) 14 (d) 15
27. 27.What is the median of 35, 21, 29, 31, 39, 10 and 24? (a) 24 (b) 27 (c) 29 (d) 31
28. 28.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 66 (d) 24
29. 29.8 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 32 (c) 10 (d) 16
30. 30.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 270° (b) 160° (c) 110° (d) 90°
31. 31.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
32. 32.Using (a + b)² = a² + 2ab + b², what is 102²? (a) 10004 (b) 10414 (c) 10404 (d) 9604
33. 33.What is the mean of 5, 12, 19, 17 and 7? (a) 12 (b) 13 (c) 15 (d) 10
34. 34.In a class of 28 children, 12 like dance, 23 like music and 1 like neither. How many like both? (a) 8 (b) 7 (c) 1 (d) 27
35. 35.What is the mean of 18, 7, 12, 10 and 3? (a) 12 (b) 9 (c) 10 (d) 11
36. 36.What is the mean of 15, 17, 16, 17 and 15? (a) 15 (b) 20 (c) 16 (d) 17
37. 37.A cube has edges of 4 cm. What is its total surface area? (a) 97 sq cm (b) 64 sq cm (c) 16 sq cm (d) 96 sq cm
38. 38.A drawer has lots of blue, red, black, yellow and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 5 (d) 2
39. 39.A bag has 4 red, 7 yellow and 3 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 3/11 (b) 1/3 (c) 11/14 (d) 3/14
40. 40.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 44 sq cm (d) 154 sq cm

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