Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 373 · 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.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) 22 (b) 14 (c) 21 (d) 15
2. 2.What are the roots of x² − 10x + 21 = 0? (a) 3 and 7 (b) 1 and 9 (c) 2 and 8 (d) 1 and 21
3. 3.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 3850 cm (d) 440 cm
4. 4.What is the midpoint of the line joining (10, 5) and (22, 3)? (a) (6, 1) (b) (16, 4) (c) (4, 16) (d) (32, 8)
5. 5.The mean of 9 numbers is 32. When the number 52 is added to them, what is the new mean? (a) 34 (b) 42 (c) 32 (d) 35
6. 6.What is the prime factorisation of 105? (a) 3 × 5 × 7 (b) 3³ × 5 × 7 (c) 3 × 5 × 7² (d) 3² × 5 × 7
7. 7.Two angles of a triangle are 20° and 40°. What is the third angle? (a) 120° (b) 140° (c) 60° (d) 160°
8. 8.A bag has 9 white balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 9 (c) 10 (d) 2
9. 9.In a class of 33 children, 15 like tea, 26 like coffee and 12 like both. How many like neither? (a) 4 (b) 12 (c) 16 (d) 5
10. 10.Two angles of a triangle are 30° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 150° (c) 110° (d) 70°
11. 11.A bag has 4 red balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 6 (b) 14 (c) 5 (d) 2
12. 12.Two angles of a triangle are 30° and 35°. What is the third angle? (a) 145° (b) 65° (c) 115° (d) 150°
13. 13.A cube has edges of 4 cm. What is its volume? (a) 65 cu cm (b) 96 cu cm (c) 12 cu cm (d) 64 cu cm
14. 14.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 15 (c) 8 (d) 14
15. 15.What is the prime factorisation of 14? (a) 2 × 7² (b) 2² × 7 (c) 2³ × 7 (d) 2 × 7
16. 16.Using (a − b)² = a² − 2ab + b², what is 87²? (a) 8091 (b) 7569 (c) 8649 (d) 7579
17. 17.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 1)(x + 72) (c) (x + 8)(x + 9) (d) (x − 8)(x − 9)
18. 18.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 100 (b) 90 (c) 45 (d) 20
19. 19.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 3/4
20. 20.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 160° (b) 10° (c) 20° (d) 11°
21. 21.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/4 (b) 5/6 (c) 2/3 (d) 1/3
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/36 (b) 1/11 (c) 1/6 (d) 5/11
23. 23.What is the sum of the first 5 terms of the AP 6, 12, 18, …? (a) 105 (b) 90 (c) 180 (d) 30
24. 24.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 3/8 (c) 1/8 (d) 1/4
25. 25.A drawer has lots of black, red, 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) 6 (b) 2 (c) 10 (d) 5
26. 26.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/4
27. 27.What is the sum of all the whole numbers from 1 to 28? (a) 812 (b) 378 (c) 406 (d) 392
28. 28.What is the sum of the roots of x² − 11x + 18 = 0? (a) 10 (b) 11 (c) 18 (d) 12
29. 29.Which is the correct factorisation of x² + 12x + 32? (a) (x + 1)(x + 32) (b) (x − 4)(x − 8) (c) (x + 4)(x + 8) (d) (x + 1)(x + 11)
30. 30.What is the midpoint of the line joining (7, 2) and (15, 10)? (a) (22, 12) (b) (4, 4) (c) (11, 6) (d) (6, 11)
31. 31.How many factors does 42 have? (a) 7 (b) 9 (c) 6 (d) 8
32. 32.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 66 cm (c) 1386 cm (d) 132 cm
33. 33.What is the mode of 16, 2, 2, 15, 4, 15 and 15? (a) 2 (b) 4 (c) 15 (d) 16
34. 34.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 25 (b) 24 (c) 37 (d) 36
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/11 (b) 5/11 (c) 1/6 (d) 5/36
36. 36.What is the sum of all the whole numbers from 1 to 58? (a) 1711 (b) 1682 (c) 3422 (d) 1653
37. 37.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
38. 38.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 33 (b) 289 (c) 306 (d) 153
39. 39.A drawer has lots of white 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) 2 (b) 5 (c) 3 (d) 4
40. 40.In a class of 32 children, 26 like tea, 12 like coffee and 3 like neither. How many like both? (a) 3 (b) 9 (c) 29 (d) 6

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