Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 870 · 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 league, 12 teams each play every other team once. How many matches are played? (a) 66 (b) 78 (c) 144 (d) 132
2. 2.What is the prime factorisation of 168? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7³ (d) 2⁴ × 3 × 7
3. 3.How many factors does 52 have? (a) 7 (b) 6 (c) 4 (d) 5
4. 4.Two straight lines cross. Two vertically opposite angles add up to 200°. What is each of the other two angles? (a) 160° (b) 80° (c) 81° (d) 100°
5. 5.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 217 sq cm (c) 216 sq cm (d) 36 sq cm
6. 6.Which term of the AP 9, 14, 19, 24, … is 109? (a) 20th (b) 21st (c) 22nd (d) 23rd
7. 7.A cuboid is 6 cm long, 5 cm wide and 7 cm high. What is its total surface area? (a) 210 sq cm (b) 214 sq cm (c) 107 sq cm (d) 428 sq cm
8. 8.How many factors does 96 have? (a) 13 (b) 10 (c) 11 (d) 12
9. 9.If a + b = 11 and ab = 30, what is a² + b²? (a) 91 (b) 61 (c) 121 (d) 181
10. 10.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/2
11. 11.What is the mean of 4, 11, 4 and 9? (a) 8 (b) 7 (c) 6 (d) 9
12. 12.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 502 (c) 492 (d) 501
13. 13.A drawer has lots of red, white and black 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) 2 (c) 6 (d) 4
14. 14.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 50° (b) 130° (c) 160° (d) 70°
15. 15.What is the product of the roots of x² − 9x + 18 = 0? (a) 19 (b) 17 (c) 18 (d) 9
16. 16.In a class of 38 children, 23 like maths, 17 like science and 5 like both. How many like only maths? (a) 21 (b) 18 (c) 12 (d) 23
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/11 (c) 1/36 (d) 1/18
18. 18.In a class of 31 children, 17 like mangoes, 24 like bananas and 11 like both. How many like neither? (a) 1 (b) 12 (c) 2 (d) 11
19. 19.In a class of 34 children, 28 like dance, 14 like music and 9 like both. How many like at least one of the two? (a) 34 (b) 33 (c) 42 (d) 24
20. 20.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
21. 21.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 45° (b) 46° (c) 55° (d) 90°
22. 22.Two angles of a triangle are 35° and 130°. What is the third angle? (a) 15° (b) 50° (c) 165° (d) 145°
23. 23.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
24. 24.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 380 (c) 190 (d) 191
25. 25.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
26. 26.What is the 22nd term of the AP 12, 19, 26, 33, …? (a) 166 (b) 154 (c) 147 (d) 159
27. 27.What is the sum of the roots of x² − 7x + 10 = 0? (a) 7 (b) 6 (c) 10 (d) 8
28. 28.A bag has 6 green, 5 yellow and 8 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 8/19 (b) 1/3 (c) 11/19 (d) 8/11
29. 29.In a class of 50 children, 30 like mangoes, 25 like bananas and 12 like both. How many like neither? (a) 12 (b) 7 (c) 19 (d) 8
30. 30.How many factors does 101 have? (a) 2 (b) 1 (c) 4 (d) 3
31. 31.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 150° (b) 330° (c) 30° (d) 60°
32. 32.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 1/4 (d) 3/8
33. 33.In a league, 8 teams each play every other team once. How many matches are played? (a) 28 (b) 64 (c) 56 (d) 36
34. 34.Two straight lines cross. Two vertically opposite angles add up to 130°. What is each of the other two angles? (a) 65° (b) 230° (c) 115° (d) 50°
35. 35.In a class of 36 children, 15 like dance, 18 like music and 7 like both. How many like only dance? (a) 18 (b) 8 (c) 11 (d) 15
36. 36.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
37. 37.A bag has 10 blue balls and 9 yellow 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) 2 (c) 10 (d) 19
38. 38.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 20 (c) 240 (d) 120
39. 39.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 55 (c) 121 (d) 110
40. 40.In a class of 34 children, 16 like tea, 21 like coffee and 8 like both. How many like only tea? (a) 13 (b) 16 (c) 8 (d) 9

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