Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 775 · 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 times is the digit 3 written when you write all the numbers from 1 to 49? (a) 4 (b) 14 (c) 15 (d) 16
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 2/11 (c) 1/11 (d) 1/18
3. 3.A drawer has lots of blue and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 4 (d) 3
4. 4.What is the midpoint of the line joining (5, 2) and (7, 12)? (a) (12, 14) (b) (6, 7) (c) (7, 6) (d) (1, 5)
5. 5.If a + b = 8 and ab = 12, what is (a − b)²? (a) 64 (b) 40 (c) 16 (d) 4
6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 19 (d) 18
7. 7.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 80° (c) 130° (d) 50°
8. 8.In an isosceles triangle, the angle between the two equal sides is 30°. What is each of the other two angles? (a) 150° (b) 30° (c) 75° (d) 60°
9. 9.What is the smallest prime factor of 87? (a) 29 (b) 1 (c) 2 (d) 3
10. 10.Two angles of a triangle are 75° and 30°. What is the third angle? (a) 75° (b) 150° (c) 105° (d) 255°
11. 11.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 394 (c) 474 (d) 483
12. 12.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 2464 cm (d) 352 cm
13. 13.What is the median of 6, 18, 15, 16, 8, 34 and 19? (a) 18 (b) 17 (c) 15 (d) 16
14. 14.What are the roots of x² − 5x + 6 = 0? (a) 1 and 6 (b) 1 and 4 (c) 2 and 3 (d) 2 and 4
15. 15.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 70° (c) 35° (d) 110°
16. 16.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 272 (c) 300 (d) 301
17. 17.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 22 (c) 55 (d) 121
18. 18.What is the prime factorisation of 12? (a) 2² × 3 (b) 2 × 3 (c) 2 × 3² (d) 2³ × 3
19. 19.Using (a + b)² = a² + 2ab + b², what is 61²? (a) 3481 (b) 3721 (c) 3731 (d) 3601
20. 20.In a class of 38 children, 24 like maths, 9 like science and 4 like both. How many like only maths? (a) 5 (b) 20 (c) 24 (d) 29
21. 21.What is the missing term in the AP 20, 27, ?, 41, 48? (a) 41 (b) 35 (c) 34 (d) 33
22. 22.There are 5 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 8 (c) 20 (d) 15
23. 23.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 3/8 (c) 1/8 (d) 1/4
24. 24.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 145° (b) 35° (c) 55° (d) 110°
25. 25.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 15° (b) 150° (c) 30° (d) 25°
26. 26.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 24 (b) 144 (c) 66 (d) 132
27. 27.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
28. 28.7 T-shirts and 3 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) 28 (c) 21 (d) 10
29. 29.What is the smallest prime factor of 69? (a) 23 (b) 1 (c) 3 (d) 2
30. 30.How many factors does 113 have? (a) 4 (b) 2 (c) 1 (d) 3
31. 31.Which is the correct factorisation of x² + 11x + 28? (a) (x + 1)(x + 28) (b) (x + 1)(x + 10) (c) (x + 4)(x + 7) (d) (x − 4)(x − 7)
32. 32.A cube has edges of 6 cm. What is its total surface area? (a) 217 sq cm (b) 36 sq cm (c) 144 sq cm (d) 216 sq cm
33. 33.In a class of 35 children, 7 like cricket, 21 like football and 2 like both. How many like only cricket? (a) 5 (b) 7 (c) 14 (d) 19
34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 6 (b) 15 (c) 17 (d) 16
35. 35.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 72 (c) 207 (d) 23
36. 36.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
37. 37.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 50° (b) 115° (c) 65° (d) 25°
38. 38.A bag has 9 green balls and 3 black 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) 2 (c) 12 (d) 10
39. 39.What is the sum of the first 7 terms of the AP 9, 14, 19, …? (a) 173 (b) 39 (c) 168 (d) 336
40. 40.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20

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