Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 38 · 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.If a + b = 8 and ab = 12, what is a² + b²? (a) 64 (b) 88 (c) 52 (d) 40
2. 2.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 2464 sq cm (c) 88 sq cm (d) 616 sq cm
3. 3.5 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 15 (b) 7 (c) 10 (d) 20
4. 4.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
5. 5.A bag has 3 white, 7 red and 4 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 3/11 (b) 1/3 (c) 3/14 (d) 11/14
6. 6.A bag has 10 black 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) 2 (b) 12 (c) 11 (d) 21
7. 7.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 275° (d) 5°
8. 8.In a class of 20 children, 8 like cricket, 8 like football and 3 like both. How many like only cricket? (a) 12 (b) 3 (c) 8 (d) 5
9. 9.There are 8 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) 14 (b) 56 (c) 96 (d) 48
10. 10.What is the 12th term of the AP 10, 17, 24, 31, …? (a) 94 (b) 77 (c) 87 (d) 84
11. 11.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 1/8 (c) 1/4 (d) 3/8
12. 12.Two straight lines cross. One of the angles is 40°. What is the angle next to it on the same straight line? (a) 40° (b) 140° (c) 320° (d) 50°
13. 13.Using (a + b)² = a² + 2ab + b², what is 35²? (a) 625 (b) 1225 (c) 925 (d) 1235
14. 14.What is the sum of the first 9 terms of the AP 4, 9, 14, …? (a) 221 (b) 44 (c) 216 (d) 432
15. 15.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 48 (c) 16 (d) 144
16. 16.What is the missing term in the AP 19, ?, 31, 37, 43? (a) 26 (b) 31 (c) 24 (d) 25
17. 17.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 25° (c) 30° (d) 15°
18. 18.A bag has 9 blue balls and 11 white 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) 12 (c) 10 (d) 20
19. 19.What is the 17th term of the AP 4, 10, 16, 22, …? (a) 100 (b) 106 (c) 96 (d) 102
20. 20.What is the sum of all the whole numbers from 1 to 43? (a) 1892 (b) 947 (c) 946 (d) 903
21. 21.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 21 (b) 14 (c) 15 (d) 22
22. 22.What is the sum of the first 6 terms of the AP 9, 13, 17, …? (a) 126 (b) 114 (c) 29 (d) 228
23. 23.In which quadrant does the point (5, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
24. 24.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 8) (b) (x + 4)(x + 5) (c) (x + 1)(x + 20) (d) (x − 4)(x − 5)
25. 25.Which is the correct factorisation of x² + 11x + 28? (a) (x + 1)(x + 10) (b) (x − 4)(x − 7) (c) (x + 1)(x + 28) (d) (x + 4)(x + 7)
26. 26.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 1/4 (c) 1/8 (d) 3/4
27. 27.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 30 (c) 15 (d) 12
28. 28.What is the midpoint of the line joining (3, 9) and (13, 19)? (a) (14, 8) (b) (8, 14) (c) (5, 5) (d) (16, 28)
29. 29.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 28 (c) 22 (d) 21
30. 30.In a class of 42 children, 29 like mangoes, 14 like bananas and 8 like neither. How many like both? (a) 34 (b) 8 (c) 1 (d) 9
31. 31.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 50° (c) 100° (d) 51°
32. 32.A drawer has lots of blue, green 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) 2 (b) 3 (c) 6 (d) 4
33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 20 (d) 19
34. 34.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 100° (b) 105° (c) 155° (d) 75°
35. 35.A drawer has lots of red 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) 4 (b) 5 (c) 3 (d) 2
36. 36.In a league, 9 teams each play every other team once. How many matches are played? (a) 45 (b) 81 (c) 36 (d) 72
37. 37.Which is the correct factorisation of x² + 8x + 12? (a) (x + 1)(x + 7) (b) (x + 1)(x + 12) (c) (x − 2)(x − 6) (d) (x + 2)(x + 6)
38. 38.What is the prime factorisation of 72? (a) 2⁴ × 3² (b) 2² × 3² (c) 2² × 3³ (d) 2³ × 3²
39. 39.What is the distance between the points (5, 2) and (9, 5)? (a) 5 (b) 6 (c) 25 (d) 7
40. 40.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10

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