Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 212 · 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.How many factors does 93 have? (a) 4 (b) 5 (c) 3 (d) 2
2. 2.The mean of 3 numbers is 36. When the number 48 is added to them, what is the new mean? (a) 36 (b) 39 (c) 40 (d) 42
3. 3.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 4/11 (c) 1/9 (d) 1/11
4. 4.A canteen sells 3 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 6 (c) 5 (d) 9
5. 5.A bag has 3 black balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 8 (c) 10 (d) 2
6. 6.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 20° (c) 11° (d) 10°
7. 7.What is the sum of all the whole numbers from 1 to 34? (a) 595 (b) 578 (c) 561 (d) 1190
8. 8.What is the sum of the first 8 terms of the AP 8, 11, 14, …? (a) 160 (b) 29 (c) 148 (d) 296
9. 9.What is the missing term in the AP 10, 16, 22, ?, 34? (a) 29 (b) 34 (c) 28 (d) 27
10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
11. 11.A bag has 9 black balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 10 (b) 2 (c) 17 (d) 11
12. 12.Two angles of a triangle are 40° and 45°. What is the exterior angle at the third corner? (a) 85° (b) 95° (c) 135° (d) 140°
13. 13.What is the sum of the first 7 terms of the AP 9, 10, 11, …? (a) 168 (b) 84 (c) 85 (d) 15
14. 14.If a + b = 11 and ab = 24, what is (a − b)²? (a) 5 (b) 25 (c) 121 (d) 73
15. 15.In a class of 29 children, 11 like cricket, 17 like football and 8 like both. How many like at least one of the two? (a) 28 (b) 29 (c) 20 (d) 12
16. 16.A drawer has lots of green, black, blue, yellow and red 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
17. 17.What is the mode of 7, 15, 10, 10, 10, 5 and 7? (a) 5 (b) 10 (c) 7 (d) 15
18. 18.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 50° (c) 100° (d) 80°
19. 19.Which is the correct factorisation of x² + 12x + 27? (a) (x + 3)(x + 9) (b) (x + 1)(x + 11) (c) (x − 3)(x − 9) (d) (x + 1)(x + 27)
20. 20.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 320° (b) 140° (c) 160° (d) 20°
21. 21.What is the smallest prime factor of 403? (a) 13 (b) 31 (c) 1 (d) 2
22. 22.What is the sum of the first 8 terms of the AP 9, 14, 19, …? (a) 424 (b) 44 (c) 232 (d) 212
23. 23.A bag has 2 green, 4 blue and 9 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 1/3 (b) 3/5 (c) 2/5 (d) 2/3
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/9 (c) 1/11 (d) 1/12
25. 25.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
26. 26.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
27. 27.Using (a − b)² = a² − 2ab + b², what is 15²? (a) 625 (b) 235 (c) 225 (d) 375
28. 28.What is the mean of 9, 14, 13, 8 and 6? (a) 11 (b) 10 (c) 12 (d) 9
29. 29.What is the sum of the roots of x² − 15x + 56 = 0? (a) 56 (b) 16 (c) 14 (d) 15
30. 30.What is the mode of 4, 5, 7, 7, 14, 7 and 5? (a) 5 (b) 4 (c) 14 (d) 7
31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 19 (b) 18 (c) 7 (d) 17
32. 32.What is the midpoint of the line joining (3, 15) and (7, 9)? (a) (2, 3) (b) (5, 12) (c) (10, 24) (d) (12, 5)
33. 33.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/2 (c) 1/3 (d) 1/4
34. 34.How many factors does 109 have? (a) 4 (b) 2 (c) 1 (d) 3
35. 35.In a class of 44 children, 14 like maths, 31 like science and 11 like both. How many like at least one of the two? (a) 45 (b) 44 (c) 34 (d) 23
36. 36.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
37. 37.What is the mean of 7, 10, 9 and 6? (a) 9 (b) 7 (c) 10 (d) 8
38. 38.A bag has 4 yellow, 5 red and 7 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 3/4 (b) 1/3 (c) 1/4 (d) 13/16
39. 39.What is the midpoint of the line joining (10, 20) and (12, 10)? (a) (15, 11) (b) (1, 5) (c) (22, 30) (d) (11, 15)
40. 40.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3

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