Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 223 · 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.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 11 (c) 10 (d) 20
2. 2.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/3 (c) 1/2 (d) 3/4
3. 3.Which term of the AP 13, 22, 31, 40, … is 355? (a) 40th (b) 38th (c) 39th (d) 41st
4. 4.Two angles of a triangle are 55° and 25°. What is the exterior angle at the third corner? (a) 125° (b) 155° (c) 100° (d) 80°
5. 5.What is the midpoint of the line joining (0, 6) and (2, 16)? (a) (11, 1) (b) (1, 5) (c) (2, 22) (d) (1, 11)
6. 6.In a class of 19 children, 5 like cricket, 9 like football and 7 like neither. How many like both? (a) 3 (b) 2 (c) 12 (d) 7
7. 7.What is the mean of 2, 10, 17 and 11? (a) 8 (b) 9 (c) 10 (d) 11
8. 8.What is the mode of 17, 17, 2, 10, 2, 2 and 5? (a) 10 (b) 2 (c) 5 (d) 17
9. 9.Two angles of a triangle are 30° and 70°. What is the third angle? (a) 100° (b) 80° (c) 110° (d) 150°
10. 10.If a + b = 20 and ab = 99, what is (a − b)²? (a) 2 (b) 4 (c) 400 (d) 202
11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
12. 12.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 616 sq cm (d) 77 sq cm
13. 13.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
14. 14.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
15. 15.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 91° (b) 90° (c) 45° (d) 135°
16. 16.What are the roots of x² − 15x + 54 = 0? (a) 1 and 14 (b) 2 and 27 (c) 6 and 9 (d) 1 and 54
17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 15 (b) 14 (c) 13 (d) 3
18. 18.A drawer has lots of white, green, black, 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) 2 (b) 10 (c) 6 (d) 5
19. 19.In a class of 37 children, 20 like tea, 10 like coffee and 10 like neither. How many like both? (a) 10 (b) 4 (c) 3 (d) 27
20. 20.Two angles of a triangle are 65° and 35°. What is the third angle? (a) 145° (b) 80° (c) 100° (d) 115°
21. 21.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
22. 22.What is the missing term in the AP 3, 8, ?, 18, 23? (a) 13 (b) 18 (c) 12 (d) 14
23. 23.A bag has 4 black balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 6 (b) 2 (c) 5 (d) 7
24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
25. 25.What is the mean of 13, 18, 10, 7, 19 and 17? (a) 14 (b) 13 (c) 12 (d) 15
26. 26.In which quadrant does the point (1, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
27. 27.In a class of 26 children, 8 like mangoes, 12 like bananas and 4 like both. How many like neither? (a) 14 (b) 6 (c) 4 (d) 10
28. 28.What is the distance between the points (3, 2) and (6, 6)? (a) 6 (b) 7 (c) 5 (d) 25
29. 29.What is the median of 7, 23, 39, 6 and 29? (a) 29 (b) 39 (c) 7 (d) 23
30. 30.What is the sum of the first 11 terms of the AP 2, 6, 10, …? (a) 42 (b) 484 (c) 264 (d) 242
31. 31.A cuboid is 6 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 198 sq cm (b) 162 sq cm (c) 396 sq cm (d) 99 sq cm
32. 32.8 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) 11 (b) 24 (c) 32 (d) 48
33. 33.How many prime numbers are there between 90 and 120? (a) 8 (b) 6 (c) 5 (d) 7
34. 34.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 35 (c) 42 (d) 70
35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 1 (d) 2
36. 36.In a class of 32 children, 16 like tea, 19 like coffee and 4 like both. How many like at least one of the two? (a) 35 (b) 31 (c) 27 (d) 32
37. 37.A bag has 7 white balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 16 (d) 10
38. 38.How many prime numbers are there between 40 and 60? (a) 4 (b) 5 (c) 7 (d) 6
39. 39.What is the midpoint of the line joining (2, 10) and (10, 4)? (a) (7, 6) (b) (4, 3) (c) (6, 7) (d) (12, 14)
40. 40.In which quadrant does the point (−8, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant

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