Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 435 · 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.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
2. 2.A cube has edges of 2 cm. What is its total surface area? (a) 8 sq cm (b) 4 sq cm (c) 24 sq cm (d) 16 sq cm
3. 3.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
4. 4.Which term of the AP 12, 21, 30, 39, … is 165? (a) 17th (b) 19th (c) 20th (d) 18th
5. 5.How many prime numbers are there between 70 and 100? (a) 7 (b) 6 (c) 8 (d) 5
6. 6.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
7. 7.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
8. 8.In a class of 39 children, 18 like dance, 21 like music and 9 like neither. How many like both? (a) 8 (b) 30 (c) 10 (d) 9
9. 9.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
10. 10.How many prime numbers are there between 50 and 80? (a) 7 (b) 6 (c) 8 (d) 9
11. 11.What is the distance between the points (4, 3) and (28, 10)? (a) 26 (b) 25 (c) 625 (d) 31
12. 12.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 50° (c) 80° (d) 130°
13. 13.In a class of 21 children, 16 like tea, 13 like coffee and 10 like both. How many like neither? (a) 2 (b) 10 (c) 3 (d) 12
14. 14.Two angles of a triangle are 30° and 130°. What is the third angle? (a) 50° (b) 20° (c) 160° (d) 150°
15. 15.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
16. 16.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 441 (b) 462 (c) 41 (d) 231
17. 17.A drawer has lots of yellow, white and red socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 4 (c) 2 (d) 6
18. 18.Two straight lines cross. One of the angles is 50°. What is the angle next to it on the same straight line? (a) 40° (b) 310° (c) 50° (d) 130°
19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/11 (b) 7/36 (c) 6/11 (d) 1/6
20. 20.What is the 11th term of the AP 18, 23, 28, 33, …? (a) 50 (b) 68 (c) 73 (d) 55
21. 21.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/8 (c) 7/8 (d) 1/8
22. 22.What is the prime factorisation of 28? (a) 2³ × 7 (b) 2² × 7 (c) 2 × 7 (d) 2 × 7²
23. 23.What is the sum of the first 11 terms of the AP 1, 4, 7, …? (a) 179 (b) 31 (c) 352 (d) 176
24. 24.What is the distance between the points (2, 4) and (10, 10)? (a) 10 (b) 11 (c) 100 (d) 14
25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 15 (b) 6 (c) 16 (d) 17
26. 26.In a class of 24 children, 14 like cricket, 14 like football and 8 like both. How many like at least one of the two? (a) 20 (b) 28 (c) 12 (d) 24
27. 27.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 253 (c) 276 (d) 277
28. 28.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2 × 5 × 7² (c) 2² × 5 × 7 (d) 2³ × 5 × 7
29. 29.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 352 cm (c) 176 cm (d) 88 cm
30. 30.What is the midpoint of the line joining (0, 10) and (2, 16)? (a) (2, 26) (b) (1, 3) (c) (1, 13) (d) (13, 1)
31. 31.What is the mean of 6, 2, 18, 4, 7 and 11? (a) 7 (b) 10 (c) 8 (d) 9
32. 32.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 36 (c) 81 (d) 72
33. 33.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
34. 34.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 30° (c) 150° (d) 60°
35. 35.A bag has 7 blue balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 9 (c) 13 (d) 2
36. 36.Two straight lines cross. One of the angles is 65°. What is the angle next to it on the same straight line? (a) 295° (b) 25° (c) 115° (d) 65°
37. 37.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
38. 38.A bag has 5 black balls and 9 white 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) 6 (c) 14 (d) 10
39. 39.What is the distance between the points (2, 0) and (5, 4)? (a) 7 (b) 6 (c) 5 (d) 25
40. 40.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 110° (c) 150° (d) 80°

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