Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 422 · 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.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) 160° (d) 100°
2. 2.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 90° (c) 46° (d) 45°
3. 3.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 140° (b) 150° (c) 70° (d) 110°
4. 4.In a class of 39 children, 23 like maths, 19 like science and 9 like both. How many like only maths? (a) 23 (b) 14 (c) 20 (d) 10
5. 5.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 9 (c) 18 (d) 36
6. 6.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 144 (b) 24 (c) 66 (d) 132
7. 7.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 264 cm (d) 132 cm
8. 8.Which term of the AP 14, 17, 20, 23, … is 71? (a) 19th (b) 22nd (c) 20th (d) 21st
9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 1/11 (c) 4/11 (d) 5/36
10. 10.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 5 (b) 12 (c) 9 (d) 6
11. 11.In a class of 39 children, 16 like dance, 18 like music and 10 like neither. How many like both? (a) 6 (b) 5 (c) 29 (d) 10
12. 12.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
13. 13.The mean of 4 numbers is 17. When the number 7 is added to them, what is the new mean? (a) 12 (b) 17 (c) 16 (d) 15
14. 14.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 50° (b) 130° (c) 110° (d) 120°
15. 15.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
16. 16.What is the mode of 9, 9, 9, 11, 3, 19 and 11? (a) 11 (b) 19 (c) 9 (d) 3
17. 17.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 16 (d) 24
18. 18.3 T-shirts and 4 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) 7 (c) 15 (d) 12
19. 19.A bag has 3 black balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 4 (c) 12 (d) 5
20. 20.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 42) (b) (x + 1)(x + 12) (c) (x − 6)(x − 7) (d) (x + 6)(x + 7)
21. 21.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/8 (b) 3/4 (c) 1/4 (d) 3/8
22. 22.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 332 (c) 390 (d) 391
23. 23.A bag has 11 white balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 19 (b) 12 (c) 13 (d) 2
24. 24.A bag has 3 red balls and 6 blue 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) 4 (c) 7 (d) 9
25. 25.In a class of 31 children, 10 like dance, 20 like music and 6 like neither. How many like both? (a) 6 (b) 5 (c) 25 (d) 4
26. 26.In a class of 26 children, 9 like dance, 12 like music and 5 like both. How many like neither? (a) 11 (b) 15 (c) 10 (d) 5
27. 27.What is the mean of 2, 4, 15, 16 and 23? (a) 15 (b) 12 (c) 10 (d) 13
28. 28.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
29. 29.In a class of 29 children, 13 like dance, 15 like music and 9 like both. How many like only dance? (a) 13 (b) 4 (c) 14 (d) 6
30. 30.A cube has edges of 12 cm. What is its volume? (a) 576 cu cm (b) 864 cu cm (c) 36 cu cm (d) 1728 cu cm
31. 31.Two angles of a triangle are 80° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 65° (c) 100° (d) 115°
32. 32.What is the mean of 18, 16, 14, 4 and 23? (a) 17 (b) 14 (c) 15 (d) 16
33. 33.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 36 sq cm (b) 144 sq cm (c) 73 sq cm (d) 72 sq cm
34. 34.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2 × 3² × 5³ (c) 2³ × 3² × 5 (d) 2⁴ × 3² × 5
35. 35.A bag has 8 green, 4 white and 2 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/7 (b) 13/14 (c) 6/7 (d) 1/3
36. 36.A bag has 5 red balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 11 (b) 2 (c) 7 (d) 6
37. 37.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 24 (d) 12
38. 38.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 20° (c) 11° (d) 160°
39. 39.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
40. 40.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4

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