Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 546 · 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 coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/4
2. 2.In which quadrant does the point (−2, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
3. 3.What is the prime factorisation of 120? (a) 2⁴ × 3 × 5 (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5³
4. 4.A bag has 3 blue, 8 yellow and 2 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 9/13 (b) 8/13 (c) 5/13 (d) 1/3
5. 5.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 85° (b) 105° (c) 10° (d) 170°
6. 6.In a class of 34 children, 19 like cricket, 24 like football and 12 like both. How many like at least one of the two? (a) 43 (b) 31 (c) 34 (d) 19
7. 7.What is the 20th term of the AP 3, 7, 11, 15, …? (a) 76 (b) 83 (c) 80 (d) 79
8. 8.What is the smallest prime factor of 93? (a) 2 (b) 1 (c) 3 (d) 31
9. 9.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 5 (c) 45 (d) 18
10. 10.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 6 (c) 3 (d) 12
11. 11.A bag has 5 white balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 8 (c) 2 (d) 6
12. 12.The mean of 7 numbers is 36. When the number 12 is added to them, what is the new mean? (a) 33 (b) 36 (c) 24 (d) 34
13. 13.What is the sum of all the whole numbers from 1 to 18? (a) 342 (b) 153 (c) 162 (d) 171
14. 14.Two angles of a triangle are 20° and 20°. What is the third angle? (a) 140° (b) 40° (c) 160° (d) 320°
15. 15.Two angles of a triangle are 70° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 110° (c) 145° (d) 75°
16. 16.If a + b = 16 and ab = 60, what is a² + b²? (a) 136 (b) 196 (c) 256 (d) 376
17. 17.What is the sum of the first 7 terms of the AP 3, 7, 11, …? (a) 119 (b) 27 (c) 210 (d) 105
18. 18.What is the mean of 18, 15, 7 and 12? (a) 14 (b) 12 (c) 13 (d) 15
19. 19.A bag has 8 green, 8 red and 4 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 2/3 (b) 3/5 (c) 1/3 (d) 2/5
20. 20.A cube has edges of 3 cm. What is its volume? (a) 54 cu cm (b) 27 cu cm (c) 36 cu cm (d) 9 cu cm
21. 21.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 264 sq cm (b) 132 sq cm (c) 80 sq cm (d) 66 sq cm
22. 22.A bag has 12 blue balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 22 (b) 13 (c) 2 (d) 11
23. 23.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
24. 24.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
25. 25.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 44 cm (d) 154 cm
26. 26.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 30 (c) 36 (d) 15
27. 27.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 300 (c) 576 (d) 600
28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 2 (b) 3 (c) 5 (d) 4
29. 29.A drawer has lots of yellow 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) 5 (b) 4 (c) 3 (d) 2
30. 30.What is the mean of 18, 5, 15, 12, 4 and 18? (a) 14 (b) 13 (c) 11 (d) 12
31. 31.What is the median of 15, 23, 13, 24, 3, 6 and 32? (a) 15 (b) 24 (c) 23 (d) 13
32. 32.What is the median of 5, 38, 21, 10, 6, 17 and 1? (a) 10 (b) 6 (c) 14 (d) 17
33. 33.A bag has 11 blue balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 13 (b) 12 (c) 19 (d) 2
34. 34.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 12 (c) 24 (d) 48
35. 35.What is the sum of all the whole numbers from 1 to 13? (a) 78 (b) 182 (c) 92 (d) 91
36. 36.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 80° (c) 100° (d) 81°
37. 37.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
38. 38.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/11 (c) 3/11 (d) 1/12
39. 39.In a class of 31 children, 14 like maths, 18 like science and 8 like both. How many like neither? (a) 6 (b) 15 (c) 7 (d) 8
40. 40.In a class of 46 children, 24 like cricket, 16 like football and 4 like both. How many like at least one of the two? (a) 40 (b) 32 (c) 36 (d) 46

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