Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 994 · 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 dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 1/11 (c) 1/18 (d) 2/11
2. 2.A bag has 11 yellow balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 15 (c) 13 (d) 12
3. 3.A cuboid is 4 cm long, 3 cm wide and 3 cm high. What is its volume? (a) 66 cu cm (b) 36 cu cm (c) 12 cu cm (d) 10 cu cm
4. 4.Two angles of a triangle are 35° and 45°. What is the exterior angle at the third corner? (a) 80° (b) 145° (c) 100° (d) 135°
5. 5.What is the median of 24, 22, 9, 34 and 13? (a) 22 (b) 13 (c) 9 (d) 24
6. 6.What is the distance between the points (5, 5) and (13, 11)? (a) 10 (b) 11 (c) 14 (d) 100
7. 7.What is the sum of all the whole numbers from 1 to 43? (a) 946 (b) 903 (c) 1892 (d) 947
8. 8.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 24 (c) 16 (d) 12
9. 9.In a class of 31 children, 15 like cricket, 24 like football and 11 like both. How many like neither? (a) 4 (b) 3 (c) 14 (d) 11
10. 10.Two angles of a triangle are 80° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 105° (c) 75° (d) 100°
11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
12. 12.Which is the correct factorisation of x² + 15x + 56? (a) (x − 7)(x − 8) (b) (x + 1)(x + 56) (c) (x + 7)(x + 8) (d) (x + 1)(x + 14)
13. 13.How many factors does 64 have? (a) 8 (b) 7 (c) 6 (d) 5
14. 14.What is the mean of 7, 6, 8, 5 and 14? (a) 7 (b) 8 (c) 9 (d) 10
15. 15.Using (a − b)² = a² − 2ab + b², what is 98²? (a) 10404 (b) 9614 (c) 9604 (d) 9996
16. 16.In a class of 28 children, 21 like dance, 9 like music and 6 like both. How many like neither? (a) 5 (b) 6 (c) 10 (d) 4
17. 17.If a + b = 7 and ab = 10, what is a² + b²? (a) 39 (b) 49 (c) 69 (d) 29
18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 20 (b) 9 (c) 21 (d) 19
19. 19.A cuboid is 8 cm long, 4 cm wide and 5 cm high. What is its volume? (a) 32 cu cm (b) 184 cu cm (c) 17 cu cm (d) 160 cu cm
20. 20.What is the mode of 1, 11, 2, 1, 2, 6 and 1? (a) 11 (b) 6 (c) 1 (d) 2
21. 21.A bag has 3 red, 2 blue and 2 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 5/7 (b) 4/7 (c) 3/7 (d) 1/3
22. 22.In which quadrant does the point (1, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
23. 23.In a class of 24 children, 15 like dance, 7 like music and 4 like neither. How many like both? (a) 4 (b) 3 (c) 20 (d) 2
24. 24.Using (a − b)² = a² − 2ab + b², what is 49²? (a) 2411 (b) 2499 (c) 2601 (d) 2401
25. 25.What is the midpoint of the line joining (4, 12) and (12, 6)? (a) (4, 3) (b) (9, 8) (c) (16, 18) (d) (8, 9)
26. 26.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/11 (c) 1/18 (d) 1/36
27. 27.There are 8 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) 32 (b) 64 (c) 40 (d) 12
28. 28.A bag has 10 green balls and 7 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) 17 (c) 11 (d) 8
29. 29.What is the mode of 12, 5, 15, 10, 10, 15 and 10? (a) 5 (b) 15 (c) 12 (d) 10
30. 30.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 121 (c) 22 (d) 110
31. 31.A bag has 12 yellow balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 17 (b) 2 (c) 13 (d) 14
32. 32.What is the distance between the points (1, 8) and (9, 14)? (a) 10 (b) 100 (c) 14 (d) 11
33. 33.How many factors does 119 have? (a) 2 (b) 3 (c) 5 (d) 4
34. 34.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 240 (d) 120
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/12 (c) 1/9 (d) 1/11
36. 36.In a class of 34 children, 13 like maths, 14 like science and 3 like both. How many like at least one of the two? (a) 24 (b) 27 (c) 21 (d) 34
37. 37.A bag has 6 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) 7 (b) 13 (c) 18 (d) 2
38. 38.What is the missing term in the AP 9, ?, 15, 18, 21? (a) 15 (b) 13 (c) 12 (d) 11
39. 39.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 1728 sq cm (c) 144 sq cm (d) 576 sq cm
40. 40.What are the roots of x² − 13x + 40 = 0? (a) 1 and 40 (b) 2 and 20 (c) 1 and 12 (d) 5 and 8

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