Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 759 · 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 two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/9 (c) 1/12 (d) 1/11
3. 3.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 23 (b) 22 (c) 29 (d) 24
4. 4.What is the distance between the points (0, 9) and (6, 17)? (a) 10 (b) 14 (c) 11 (d) 100
5. 5.Which term of the AP 5, 11, 17, 23, … is 197? (a) 33rd (b) 34th (c) 32nd (d) 35th
6. 6.Using (a − b)² = a² − 2ab + b², what is 85²? (a) 7235 (b) 9025 (c) 7225 (d) 8075
7. 7.In which quadrant does the point (8, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
8. 8.In a class of 43 children, 23 like dance, 21 like music and 6 like both. How many like only dance? (a) 17 (b) 15 (c) 22 (d) 23
9. 9.What is the distance between the points (2, 8) and (14, 17)? (a) 15 (b) 21 (c) 16 (d) 225
10. 10.Two angles of a triangle are 25° and 95°. What is the exterior angle at the third corner? (a) 155° (b) 60° (c) 85° (d) 120°
11. 11.What is the midpoint of the line joining (10, 11) and (20, 5)? (a) (8, 15) (b) (5, 3) (c) (30, 16) (d) (15, 8)
12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/18 (c) 1/12 (d) 1/36
13. 13.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 80° (b) 100° (c) 135° (d) 125°
14. 14.In which quadrant does the point (−6, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
15. 15.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
16. 16.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 24) (b) (x − 4)(x − 6) (c) (x + 4)(x + 6) (d) (x + 1)(x + 9)
17. 17.In a class of 26 children, 10 like maths, 10 like science and 2 like both. How many like only maths? (a) 10 (b) 16 (c) 2 (d) 8
18. 18.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 506 (c) 43 (d) 253
19. 19.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 15) (b) (x + 7)(x + 9) (c) (x + 1)(x + 63) (d) (x − 7)(x − 9)
20. 20.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 36 (d) 64
21. 21.In a class of 47 children, 19 like dance, 22 like music and 2 like both. How many like only dance? (a) 20 (b) 17 (c) 25 (d) 19
22. 22.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 37 (b) 49 (c) 48 (d) 36
23. 23.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
24. 24.What is the midpoint of the line joining (9, 6) and (13, 2)? (a) (11, 4) (b) (4, 11) (c) (2, 2) (d) (22, 8)
25. 25.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 66 cm (d) 132 cm
26. 26.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 100 (c) 45 (d) 90
27. 27.What is the mean of 12, 5, 2, 13, 14 and 20? (a) 11 (b) 12 (c) 10 (d) 13
28. 28.How many prime numbers are there between 20 and 50? (a) 9 (b) 8 (c) 7 (d) 6
29. 29.What is the mean of 16, 17, 19, 3, 2 and 3? (a) 11 (b) 12 (c) 9 (d) 10
30. 30.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 25 times (b) 10 times (c) 125 times (d) 5 times
31. 31.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 10 (b) 60 (c) 30 (d) 35
32. 32.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 55° (b) 110° (c) 35° (d) 145°
33. 33.What is the distance between the points (9, 3) and (12, 7)? (a) 6 (b) 7 (c) 25 (d) 5
34. 34.What are the roots of x² − 10x + 21 = 0? (a) 1 and 21 (b) 2 and 8 (c) 3 and 7 (d) 1 and 9
35. 35.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
36. 36.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 15 (d) 10
37. 37.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
38. 38.What are the roots of x² − 13x + 40 = 0? (a) 5 and 8 (b) 2 and 20 (c) 1 and 12 (d) 1 and 40
39. 39.In a league, 7 teams each play every other team once. How many matches are played? (a) 28 (b) 49 (c) 42 (d) 21
40. 40.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 85° (c) 265° (d) 95°

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