Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 766 · 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.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) 17 (b) 54 (c) 51 (d) 153
2. 2.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 88 cm (c) 352 cm (d) 2464 cm
3. 3.What is the median of 1, 33, 24, 13 and 25? (a) 13 (b) 23 (c) 24 (d) 25
4. 4.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 150° (b) 70° (c) 110° (d) 100°
5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 18 (b) 16 (c) 6 (d) 17
6. 6.What is the mode of 1, 1, 19, 19, 14, 19 and 9? (a) 1 (b) 14 (c) 9 (d) 19
7. 7.What is the midpoint of the line joining (2, 1) and (4, 3)? (a) (1, 1) (b) (6, 4) (c) (2, 3) (d) (3, 2)
8. 8.A bag has 7 red balls and 8 black 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) 15 (c) 8 (d) 9
9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 20 (d) 8
10. 10.What is the product of the roots of x² − 5x + 6 = 0? (a) 6 (b) 8 (c) 7 (d) 5
11. 11.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/11 (c) 1/18 (d) 1/36
12. 12.Using (a − b)² = a² − 2ab + b², what is 99²? (a) 9999 (b) 9811 (c) 10201 (d) 9801
13. 13.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x − 7)(x − 8) (c) (x + 1)(x + 14) (d) (x + 7)(x + 8)
14. 14.A drawer has lots of red, white 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) 2 (b) 3 (c) 6 (d) 4
15. 15.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) 1/4 (d) 1/8
16. 16.A drawer has lots of red, black, white 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) 5 (b) 4 (c) 8 (d) 2
17. 17.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 36 (c) 21 (d) 18
18. 18.What is the sum of the first 11 terms of the AP 7, 11, 15, …? (a) 297 (b) 594 (c) 47 (d) 319
19. 19.How many prime numbers are there between 10 and 30? (a) 5 (b) 6 (c) 8 (d) 7
20. 20.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
21. 21.A drawer has lots of red, green, yellow, 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) 10 (b) 5 (c) 6 (d) 2
22. 22.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 25° (c) 50° (d) 130°
23. 23.A bag has 7 red, 3 white and 3 yellow balls. One ball is taken out without looking. What is the probability that it is not white? (a) 11/13 (b) 1/3 (c) 10/13 (d) 3/13
24. 24.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 2/3 (c) 1/3 (d) 1/4
25. 25.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
26. 26.In which quadrant does the point (−2, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
27. 27.What is the distance between the points (8, 14) and (24, 2)? (a) 400 (b) 28 (c) 20 (d) 21
28. 28.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 80° (c) 130° (d) 100°
29. 29.What is the missing term in the AP 9, 12, ?, 18, 21? (a) 18 (b) 15 (c) 14 (d) 16
30. 30.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 24 (c) 12 (d) 18
31. 31.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 5/11 (c) 1/6 (d) 1/11
32. 32.In a class of 31 children, 11 like dance, 20 like music and 4 like both. How many like only dance? (a) 11 (b) 4 (c) 16 (d) 7
33. 33.A drawer has lots of white, green, yellow, black and blue 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) 10 (c) 6 (d) 2
34. 34.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
35. 35.A bag has 7 red balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 11 (d) 5
36. 36.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 90° (c) 45° (d) 55°
37. 37.Using (a + b)² = a² + 2ab + b², what is 41²? (a) 1601 (b) 1521 (c) 1691 (d) 1681
38. 38.What is the sum of the first 7 terms of the AP 6, 11, 16, …? (a) 147 (b) 294 (c) 152 (d) 36
39. 39.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 22 cm (d) 88 cm
40. 40.In which quadrant does the point (−3, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant

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