Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 804 · 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 distance between the points (9, 21) and (18, 9)? (a) 225 (b) 21 (c) 16 (d) 15
2. 2.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 25 (c) 36 (d) 37
3. 3.What is the mean of 11, 19, 8 and 10? (a) 13 (b) 11 (c) 12 (d) 16
4. 4.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 190° (b) 85° (c) 10° (d) 95°
5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/18 (c) 1/11 (d) 1/12
6. 6.A drawer has lots of black 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) 4 (b) 5 (c) 3 (d) 2
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 1/11 (c) 1/9 (d) 4/11
8. 8.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 22 (c) 21 (d) 28
9. 9.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 1/4 (c) 2/3 (d) 1/2
10. 10.What is the midpoint of the line joining (7, 20) and (15, 10)? (a) (4, 5) (b) (15, 11) (c) (11, 15) (d) (22, 30)
11. 11.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/4 (c) 1/2 (d) 3/4
12. 12.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 484 (c) 483 (d) 474
13. 13.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 135° (b) 130° (c) 95° (d) 85°
14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
15. 15.What is the midpoint of the line joining (4, 3) and (6, 11)? (a) (5, 7) (b) (1, 4) (c) (7, 5) (d) (10, 14)
16. 16.If a + b = 13 and ab = 40, what is (a − b)²? (a) 89 (b) 9 (c) 3 (d) 169
17. 17.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
18. 18.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 21 (d) 42
19. 19.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 40° (c) 50° (d) 100°
20. 20.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
21. 21.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 7/8 (c) 1/4 (d) 1/8
22. 22.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 693 sq cm
23. 23.In a class of 49 children, 23 like maths, 28 like science and 12 like both. How many like at least one of the two? (a) 49 (b) 27 (c) 39 (d) 51
24. 24.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
25. 25.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 7/8 (c) 1/4 (d) 1/8
26. 26.A bag has 8 blue, 2 red and 6 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 3/5 (c) 5/8 (d) 3/8
27. 27.In a class of 51 children, 30 like cricket, 31 like football and 1 like neither. How many like both? (a) 50 (b) 1 (c) 10 (d) 11
28. 28.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 51 (c) 17 (d) 153
29. 29.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11
30. 30.How many factors does 119 have? (a) 2 (b) 3 (c) 4 (d) 5
31. 31.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 402 (c) 346 (d) 411
32. 32.In a class of 29 children, 9 like maths, 21 like science and 5 like both. How many like neither? (a) 9 (b) 4 (c) 3 (d) 5
33. 33.Two angles of a triangle are 25° and 20°. What is the exterior angle at the third corner? (a) 45° (b) 135° (c) 160° (d) 155°
34. 34.Two angles of a triangle are 20° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 65° (c) 115° (d) 160°
35. 35.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
36. 36.A drawer has lots of white, blue 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) 6 (c) 2 (d) 4
37. 37.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 65° (c) 130° (d) 25°
38. 38.4 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) 9 (b) 20 (c) 24 (d) 40
39. 39.A cuboid is 10 cm long, 5 cm wide and 9 cm high. What is its total surface area? (a) 450 sq cm (b) 370 sq cm (c) 740 sq cm (d) 185 sq cm
40. 40.7 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) 70 (b) 12 (c) 42 (d) 35

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