Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 767 · 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 7 red balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 11 (d) 8
2. 2.4 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) 28 (b) 56 (c) 11 (d) 32
3. 3.What is the mode of 18, 14, 1, 1, 14, 7 and 1? (a) 14 (b) 7 (c) 18 (d) 1
4. 4.Two angles of a triangle are 65° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 45° (c) 115° (d) 135°
5. 5.Which term of the AP 7, 15, 23, 31, … is 103? (a) 13th (b) 12th (c) 15th (d) 14th
6. 6.How many prime numbers are there between 40 and 60? (a) 6 (b) 7 (c) 5 (d) 4
7. 7.A bag has 10 black balls and 5 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) 2 (c) 15 (d) 11
8. 8.How many factors does 33 have? (a) 3 (b) 5 (c) 2 (d) 4
9. 9.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 120 (c) 105 (d) 210
10. 10.What is the 26th term of the AP 11, 18, 25, 32, …? (a) 175 (b) 193 (c) 182 (d) 186
11. 11.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
12. 12.A canteen sells 6 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 10 (c) 30 (d) 24
13. 13.What is the sum of all the whole numbers from 1 to 24? (a) 300 (b) 288 (c) 600 (d) 276
14. 14.What is the sum of all the whole numbers from 1 to 77? (a) 2926 (b) 3003 (c) 3004 (d) 6006
15. 15.In a class of 38 children, 27 like dance, 17 like music and 11 like both. How many like only dance? (a) 16 (b) 6 (c) 21 (d) 27
16. 16.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 5/6 (c) 2/3 (d) 1/4
17. 17.A bag has 6 white, 7 green and 6 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 6/19 (b) 13/19 (c) 14/19 (d) 1/3
18. 18.A drawer has lots of white 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) 3 (b) 4 (c) 2 (d) 5
19. 19.What is the prime factorisation of 126? (a) 2² × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7² (d) 2 × 3² × 7
20. 20.7 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 42 (b) 70 (c) 12 (d) 35
21. 21.In a class of 47 children, 20 like tea, 27 like coffee and 10 like both. How many like at least one of the two? (a) 47 (b) 38 (c) 37 (d) 27
22. 22.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 176 sq cm (d) 2464 sq cm
23. 23.A cuboid is 5 cm long, 2 cm wide and 10 cm high. What is its volume? (a) 10 cu cm (b) 100 cu cm (c) 17 cu cm (d) 160 cu cm
24. 24.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 2/3 (c) 1/3 (d) 1/2
25. 25.Two straight lines cross. One of the angles is 135°. What is the angle next to it on the same straight line? (a) 135° (b) 46° (c) 225° (d) 45°
26. 26.In how many different ways can the letters of the word PLANT be arranged? (a) 120 (b) 20 (c) 240 (d) 25
27. 27.How many prime numbers are there between 10 and 40? (a) 7 (b) 8 (c) 9 (d) 10
28. 28.A bag has 4 blue balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 10 (b) 6 (c) 5 (d) 2
29. 29.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 100 (c) 92 (d) 91
30. 30.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 10° (d) 100°
31. 31.Which term of the AP 9, 15, 21, 27, … is 75? (a) 12th (b) 13th (c) 11th (d) 14th
32. 32.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 18 (c) 15 (d) 5
33. 33.Two angles of a triangle are 75° and 35°. What is the third angle? (a) 110° (b) 70° (c) 105° (d) 145°
34. 34.How many factors does 62 have? (a) 4 (b) 3 (c) 5 (d) 2
35. 35.What is the midpoint of the line joining (0, 0) and (8, 4)? (a) (4, 2) (b) (2, 4) (c) (5, 2) (d) (8, 4)
36. 36.In a class of 37 children, 11 like tea, 19 like coffee and 2 like both. How many like only tea? (a) 18 (b) 17 (c) 11 (d) 9
37. 37.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/8 (c) 3/5 (d) 1/4
38. 38.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
39. 39.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
40. 40.A bag has 11 green balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 12 (c) 17 (d) 13

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