Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 867 · 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.In a class of 47 children, 25 like maths, 21 like science and 7 like both. How many like at least one of the two? (a) 32 (b) 39 (c) 46 (d) 47
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 6/11 (b) 7/36 (c) 1/6 (d) 1/11
3. 3.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 165° (c) 16° (d) 15°
4. 4.In a class of 43 children, 26 like cricket, 19 like football and 10 like both. How many like only cricket? (a) 26 (b) 24 (c) 9 (d) 16
5. 5.In which quadrant does the point (−6, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
6. 6.What is the sum of the first 6 terms of the AP 5, 8, 11, …? (a) 75 (b) 20 (c) 150 (d) 84
7. 7.8 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 64 (b) 15 (c) 112 (d) 56
8. 8.Two angles of a triangle are 25° and 40°. What is the third angle? (a) 140° (b) 155° (c) 115° (d) 65°
9. 9.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 125° (b) 235° (c) 55° (d) 56°
10. 10.The mean of 7 numbers is 26. When the number 34 is added to them, what is the new mean? (a) 26 (b) 30 (c) 28 (d) 27
11. 11.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 1/7 (c) 1/4 (d) 7/8
12. 12.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6734 (b) 6404 (c) 6724 (d) 6084
13. 13.Two straight lines cross. One of the angles is 120°. What is the angle next to it on the same straight line? (a) 240° (b) 120° (c) 61° (d) 60°
14. 14.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 364 (c) 314 (d) 354
15. 15.What is the smallest prime factor of 115? (a) 5 (b) 23 (c) 2 (d) 1
16. 16.What is the smallest prime factor of 65? (a) 2 (b) 1 (c) 5 (d) 13
17. 17.What is the distance between the points (1, 3) and (5, 0)? (a) 5 (b) 7 (c) 6 (d) 25
18. 18.In which quadrant does the point (−5, 6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
19. 19.What is the distance between the points (2, 22) and (10, 7)? (a) 23 (b) 17 (c) 18 (d) 289
20. 20.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
21. 21.In a class of 23 children, 12 like cricket, 8 like football and 2 like both. How many like at least one of the two? (a) 16 (b) 20 (c) 23 (d) 18
22. 22.A bag has 3 red balls and 10 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) 4 (c) 13 (d) 11
23. 23.What is the sum of the first 9 terms of the AP 1, 7, 13, …? (a) 450 (b) 225 (c) 252 (d) 49
24. 24.In a class of 31 children, 25 like maths, 13 like science and 3 like neither. How many like both? (a) 10 (b) 28 (c) 7 (d) 3
25. 25.In a class of 28 children, 15 like maths, 17 like science and 5 like both. How many like only maths? (a) 15 (b) 11 (c) 10 (d) 12
26. 26.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 54 sq cm (c) 36 sq cm (d) 9 sq cm
27. 27.A bag has 12 white balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 13 (d) 20
28. 28.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 20 (c) 240 (d) 120
29. 29.Using (a + b)² = a² + 2ab + b², what is 41²? (a) 1601 (b) 1681 (c) 1521 (d) 1691
30. 30.A bag has 4 yellow, 6 green and 7 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 7/10 (b) 10/17 (c) 7/17 (d) 1/3
31. 31.A bag has 9 red balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 12 (c) 10 (d) 11
32. 32.What is the midpoint of the line joining (8, 11) and (20, 3)? (a) (14, 7) (b) (6, 4) (c) (28, 14) (d) (7, 14)
33. 33.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 105° (c) 285° (d) 75°
34. 34.A drawer has lots of yellow, red 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) 4 (b) 3 (c) 6 (d) 2
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
36. 36.What is the distance between the points (5, 19) and (17, 3)? (a) 400 (b) 21 (c) 20 (d) 28
37. 37.What is the smallest prime factor of 39? (a) 1 (b) 13 (c) 2 (d) 3
38. 38.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 100° (b) 160° (c) 80° (d) 81°
39. 39.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/3 (c) 1/4 (d) 3/4
40. 40.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 135° (b) 45° (c) 125° (d) 100°

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