Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 696 · 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 8? (a) 1/6 (b) 5/36 (c) 1/11 (d) 5/11
2. 2.What is the mean of 8, 14, 5, 5, 15 and 7? (a) 10 (b) 11 (c) 8 (d) 9
3. 3.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
4. 4.Two angles of a triangle are 55° and 45°. What is the third angle? (a) 135° (b) 125° (c) 80° (d) 100°
5. 5.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 484 cu cm (c) 726 cu cm (d) 33 cu cm
6. 6.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 30 (c) 15 (d) 21
7. 7.A cuboid is 8 cm long, 6 cm wide and 4 cm high. What is its total surface area? (a) 416 sq cm (b) 104 sq cm (c) 192 sq cm (d) 208 sq cm
8. 8.In which quadrant does the point (−4, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
9. 9.There are 5 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) 25 (b) 9 (c) 20 (d) 40
10. 10.What is the prime factorisation of 28? (a) 2 × 7 (b) 2 × 7² (c) 2³ × 7 (d) 2² × 7
11. 11.What is the mean of 4, 14, 2 and 20? (a) 9 (b) 10 (c) 11 (d) 8
12. 12.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
13. 13.What is the mean of 20, 6, 16, 10 and 8? (a) 12 (b) 10 (c) 13 (d) 15
14. 14.What is the prime factorisation of 360? (a) 2 × 3² × 5³ (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2⁴ × 3² × 5
15. 15.What is the sum of the first 12 terms of the AP 6, 8, 10, …? (a) 216 (b) 204 (c) 28 (d) 408
16. 16.What is the 36th term of the AP 6, 11, 16, 21, …? (a) 175 (b) 181 (c) 180 (d) 186
17. 17.What is the median of 11, 25, 29, 27 and 34? (a) 27 (b) 25 (c) 28 (d) 29
18. 18.A canteen sells 5 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 20 (b) 40 (c) 9 (d) 25
19. 19.What is the missing term in the AP 7, ?, 11, 13, 15? (a) 8 (b) 9 (c) 11 (d) 10
20. 20.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 5/6 (d) 2/3
21. 21.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 35° (b) 65° (c) 150° (d) 145°
22. 22.How many factors does 26 have? (a) 5 (b) 3 (c) 4 (d) 2
23. 23.Two angles of a triangle are 65° and 45°. What is the exterior angle at the third corner? (a) 135° (b) 70° (c) 110° (d) 115°
24. 24.A bag has 8 yellow, 9 blue and 3 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 9/20 (b) 1/3 (c) 11/20 (d) 3/5
25. 25.In a class of 41 children, 19 like tea, 22 like coffee and 5 like both. How many like only tea? (a) 5 (b) 14 (c) 19 (d) 17
26. 26.What is the distance between the points (8, 7) and (12, 10)? (a) 6 (b) 7 (c) 25 (d) 5
27. 27.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 156 (c) 169 (d) 78
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/11 (c) 4/11 (d) 1/9
29. 29.A cuboid is 10 cm long, 8 cm wide and 7 cm high. What is its total surface area? (a) 206 sq cm (b) 824 sq cm (c) 412 sq cm (d) 560 sq cm
30. 30.If a + b = 8 and ab = 7, what is a² + b²? (a) 78 (b) 50 (c) 64 (d) 57
31. 31.A cube has edges of 2 cm. What is its volume? (a) 16 cu cm (b) 6 cu cm (c) 8 cu cm (d) 24 cu cm
32. 32.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
33. 33.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 22 (b) 21 (c) 15 (d) 14
34. 34.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 150° (b) 60° (c) 120° (d) 30°
35. 35.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
36. 36.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 24 (c) 16 (d) 12
37. 37.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 9 (c) 6 (d) 12
38. 38.A drawer has lots of blue, black, red, yellow and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 2 (d) 5
39. 39.What is the smallest prime factor of 51? (a) 3 (b) 1 (c) 2 (d) 17
40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 7 (b) 6 (c) 8 (d) 5

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