Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 213 · 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.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 50° (b) 130° (c) 230° (d) 115°
2. 2.What is the distance between the points (5, 9) and (14, 21)? (a) 16 (b) 15 (c) 21 (d) 225
3. 3.Which is the correct factorisation of x² + 5x + 6? (a) (x − 2)(x − 3) (b) (x + 1)(x + 4) (c) (x + 1)(x + 6) (d) (x + 2)(x + 3)
4. 4.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
5. 5.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 30 (c) 18 (d) 8
6. 6.What is the missing term in the AP 10, 17, ?, 31, 38? (a) 24 (b) 31 (c) 23 (d) 25
7. 7.There are 3 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 7 (c) 15 (d) 12
8. 8.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 55 (c) 90 (d) 45
9. 9.A bag has 9 yellow balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 10 (c) 11 (d) 21
10. 10.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 7/8 (c) 3/8 (d) 1/8
11. 11.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) 198 (b) 69 (c) 22 (d) 66
12. 12.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 351 (d) 702
13. 13.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 340° (c) 160° (d) 20°
14. 14.A bag has 9 blue balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 21 (d) 13
15. 15.What is the sum of the roots of x² − 11x + 18 = 0? (a) 11 (b) 10 (c) 12 (d) 18
16. 16.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 45° (b) 155° (c) 160° (d) 135°
17. 17.The mean of 6 numbers is 34. When the number 6 is added to them, what is the new mean? (a) 30 (b) 31 (c) 20 (d) 34
18. 18.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
19. 19.The mean of 9 numbers is 32. When the number 2 is added to them, what is the new mean? (a) 30 (b) 32 (c) 29 (d) 17
20. 20.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 11 (c) 25 (d) 20
21. 21.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 30° (c) 20° (d) 40°
22. 22.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 2464 cm (d) 88 cm
23. 23.How many factors does 37 have? (a) 3 (b) 1 (c) 4 (d) 2
24. 24.A bag has 3 yellow, 5 blue and 3 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 5/11 (b) 6/11 (c) 7/11 (d) 1/3
25. 25.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 130° (c) 155° (d) 50°
26. 26.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) 12 (b) 24 (c) 18 (d) 8
27. 27.There are 3 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 9 (b) 21 (c) 36 (d) 18
28. 28.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 2/3 (d) 1/3
29. 29.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 9) (b) (x + 4)(x + 6) (c) (x − 4)(x − 6) (d) (x + 1)(x + 24)
30. 30.The mean of 6 numbers is 35. When the number 28 is added to them, what is the new mean? (a) 36 (b) 33 (c) 35 (d) 34
31. 31.A bag has 5 white balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 7 (c) 8 (d) 6
32. 32.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 40° (d) 50°
33. 33.What is the distance between the points (9, 12) and (25, 0)? (a) 400 (b) 20 (c) 21 (d) 28
34. 34.Two angles of a triangle are 65° and 80°. What is the third angle? (a) 35° (b) 145° (c) 100° (d) 115°
35. 35.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
36. 36.What is the mean of 18, 10, 2 and 18? (a) 16 (b) 12 (c) 11 (d) 13
37. 37.What is the median of 17, 34, 33, 8, 18, 4 and 20? (a) 18 (b) 17 (c) 20 (d) 8
38. 38.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 315 (c) 306 (d) 316
39. 39.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 70 (b) 35 (c) 40 (d) 12
40. 40.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 2 times (c) 4 times (d) 6 times

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