Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 150 · 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 mean of 3, 11, 5, 18, 19 and 22? (a) 15 (b) 13 (c) 12 (d) 14
2. 2.In which quadrant does the point (−6, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
3. 3.What is the mode of 2, 12, 2, 19, 20, 19 and 2? (a) 19 (b) 12 (c) 2 (d) 20
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/12 (b) 2/11 (c) 1/11 (d) 1/18
5. 5.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 86° (c) 170° (d) 95°
6. 6.How many prime numbers are there between 30 and 50? (a) 5 (b) 4 (c) 7 (d) 6
7. 7.What is the distance between the points (9, 15) and (15, 7)? (a) 14 (b) 10 (c) 100 (d) 11
8. 8.A bag has 5 blue balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 2 (c) 7 (d) 6
9. 9.What is the mode of 6, 11, 15, 9, 9, 11 and 11? (a) 15 (b) 11 (c) 6 (d) 9
10. 10.8 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 48 (b) 32 (c) 11 (d) 24
11. 11.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 125° (c) 100° (d) 55°
12. 12.How many prime numbers are there between 90 and 120? (a) 5 (b) 6 (c) 7 (d) 8
13. 13.In which quadrant does the point (1, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
14. 14.A bag has 10 white balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 4 (c) 2 (d) 13
15. 15.In a class of 34 children, 19 like mangoes, 18 like bananas and 7 like both. How many like neither? (a) 7 (b) 4 (c) 5 (d) 11
16. 16.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
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/9 (b) 1/11 (c) 4/11 (d) 5/36
18. 18.In a class of 49 children, 24 like cricket, 29 like football and 10 like both. How many like at least one of the two? (a) 33 (b) 43 (c) 49 (d) 53
19. 19.Two straight lines cross. Two vertically opposite angles add up to 50°. What is each of the other two angles? (a) 310° (b) 130° (c) 25° (d) 155°
20. 20.What is the 24th term of the AP 11, 19, 27, 35, …? (a) 192 (b) 184 (c) 203 (d) 195
21. 21.How many factors does 61 have? (a) 2 (b) 3 (c) 1 (d) 4
22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 19 (b) 20 (c) 9 (d) 18
23. 23.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
24. 24.What is the 17th term of the AP 11, 14, 17, 20, …? (a) 48 (b) 62 (c) 59 (d) 51
25. 25.What is the 35th term of the AP 6, 15, 24, 33, …? (a) 312 (b) 306 (c) 315 (d) 321
26. 26.In a class of 33 children, 13 like maths, 25 like science and 3 like neither. How many like both? (a) 5 (b) 8 (c) 3 (d) 30
27. 27.What is the median of 37, 6, 15, 36, 10, 1 and 25? (a) 15 (b) 10 (c) 25 (d) 36
28. 28.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 421 (c) 411 (d) 420
29. 29.Which term of the AP 10, 14, 18, 22, … is 138? (a) 35th (b) 33rd (c) 34th (d) 32nd
30. 30.In a class of 33 children, 22 like tea, 13 like coffee and 8 like both. How many like neither? (a) 7 (b) 6 (c) 14 (d) 8
31. 31.Two angles of a triangle are 65° and 75°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 105° (d) 115°
32. 32.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 13 (c) 24 (d) 25
33. 33.What is the distance between the points (0, 5) and (8, 11)? (a) 14 (b) 100 (c) 10 (d) 11
34. 34.What is the smallest prime factor of 187? (a) 11 (b) 17 (c) 2 (d) 1
35. 35.In a class of 32 children, 15 like mangoes, 19 like bananas and 7 like both. How many like at least one of the two? (a) 20 (b) 32 (c) 27 (d) 34
36. 36.In which quadrant does the point (3, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
37. 37.7 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) 28 (b) 21 (c) 9 (d) 14
38. 38.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/6
39. 39.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
40. 40.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 270° (c) 90° (d) 120°

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