Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 923 · 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 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 18 (c) 12 (d) 6
2. 2.A bag has 7 green balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 9 (b) 8 (c) 2 (d) 16
3. 3.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 55° (c) 90° (d) 45°
4. 4.A bag has 11 yellow balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 20 (b) 12 (c) 2 (d) 13
5. 5.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 27 times (c) 3 times (d) 6 times
6. 6.What is the mode of 1, 10, 1, 1, 15, 9 and 10? (a) 9 (b) 10 (c) 1 (d) 15
7. 7.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 155° (b) 55° (c) 150° (d) 125°
8. 8.A bag has 6 green balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 17 (d) 12
9. 9.In a class of 36 children, 22 like cricket, 8 like football and 8 like neither. How many like both? (a) 28 (b) 3 (c) 8 (d) 2
10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
11. 11.How many factors does 114 have? (a) 8 (b) 9 (c) 6 (d) 7
12. 12.In a class of 27 children, 9 like tea, 18 like coffee and 4 like both. How many like at least one of the two? (a) 27 (b) 19 (c) 24 (d) 23
13. 13.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
14. 14.In a class of 27 children, 13 like maths, 13 like science and 3 like both. How many like at least one of the two? (a) 27 (b) 20 (c) 26 (d) 23
15. 15.What is the sum of the first 10 terms of the AP 9, 14, 19, …? (a) 315 (b) 54 (c) 340 (d) 630
16. 16.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 69 (c) 22 (d) 198
17. 17.What is the midpoint of the line joining (2, 9) and (4, 17)? (a) (3, 13) (b) (6, 26) (c) (13, 3) (d) (1, 4)
18. 18.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
19. 19.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 8)(x + 9) (c) (x + 1)(x + 72) (d) (x + 1)(x + 16)
20. 20.The mean of 7 numbers is 19. When the number 51 is added to them, what is the new mean? (a) 23 (b) 24 (c) 35 (d) 19
21. 21.In which quadrant does the point (−1, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
22. 22.A cube has edges of 7 cm. What is its total surface area? (a) 196 sq cm (b) 49 sq cm (c) 343 sq cm (d) 294 sq cm
23. 23.What is the sum of the first 10 terms of the AP 5, 9, 13, …? (a) 460 (b) 230 (c) 41 (d) 250
24. 24.What is the midpoint of the line joining (7, 17) and (19, 7)? (a) (6, 5) (b) (26, 24) (c) (13, 12) (d) (12, 13)
25. 25.If a + b = 11 and ab = 18, what is (a − b)²? (a) 85 (b) 7 (c) 49 (d) 121
26. 26.In a class of 37 children, 28 like mangoes, 14 like bananas and 11 like both. How many like only mangoes? (a) 3 (b) 28 (c) 17 (d) 23
27. 27.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 440 cm (c) 110 cm (d) 220 cm
28. 28.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 140° (c) 40° (d) 70°
29. 29.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 40° (d) 130°
30. 30.If a + b = 12 and ab = 27, what is a² + b²? (a) 198 (b) 90 (c) 144 (d) 117
31. 31.What is the 24th term of the AP 5, 8, 11, 14, …? (a) 72 (b) 74 (c) 69 (d) 77
32. 32.A drawer has lots of red, green, blue and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 5 (c) 2 (d) 4
33. 33.Two angles of a triangle are 20° and 70°. What is the third angle? (a) 90° (b) 110° (c) 270° (d) 160°
34. 34.In a class of 25 children, 14 like maths, 12 like science and 2 like neither. How many like both? (a) 3 (b) 2 (c) 23 (d) 1
35. 35.A bag has 2 white, 5 green and 3 yellow balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/10 (b) 3/5 (c) 1/2 (d) 1/3
36. 36.In a class of 18 children, 8 like maths, 9 like science and 4 like both. How many like at least one of the two? (a) 13 (b) 17 (c) 9 (d) 18
37. 37.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
38. 38.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 81 (c) 36 (d) 72
39. 39.What is the sum of the first 11 terms of the AP 10, 12, 14, …? (a) 30 (b) 440 (c) 220 (d) 231
40. 40.What is the missing term in the AP 6, 15, 24, ?, 42? (a) 42 (b) 33 (c) 34 (d) 32

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