Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 310 · 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 angles of a triangle are 80° and 50°. What is the third angle? (a) 100° (b) 230° (c) 130° (d) 50°
2. 2.How many factors does 21 have? (a) 5 (b) 3 (c) 4 (d) 2
3. 3.What is the 10th term of the AP 11, 19, 27, 35, …? (a) 72 (b) 80 (c) 83 (d) 91
4. 4.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 616 sq cm (c) 308 sq cm (d) 88 sq cm
5. 5.How many factors does 20 have? (a) 6 (b) 4 (c) 7 (d) 5
6. 6.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 48 (c) 28 (d) 10
7. 7.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 12 (c) 3 (d) 6
8. 8.What is the mean of 3, 6, 4, 5 and 12? (a) 8 (b) 7 (c) 6 (d) 5
9. 9.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 110 cm (d) 440 cm
10. 10.How many factors does 61 have? (a) 3 (b) 1 (c) 4 (d) 2
11. 11.The mean of 3 numbers is 23. When the number 39 is added to them, what is the new mean? (a) 23 (b) 28 (c) 31 (d) 27
12. 12.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 21 (b) 10 (c) 20 (d) 25
13. 13.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 145° (c) 35° (d) 125°
14. 14.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 354 (c) 414 (d) 423
15. 15.5 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) 30 (b) 15 (c) 8 (d) 20
16. 16.In a class of 31 children, 14 like tea, 22 like coffee and 6 like neither. How many like both? (a) 6 (b) 25 (c) 5 (d) 11
17. 17.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/2 (d) 1/3
18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 14 (b) 4 (c) 16 (d) 15
19. 19.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
20. 20.A bag has 9 yellow, 3 green and 9 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 19/21 (b) 1/3 (c) 6/7 (d) 1/7
21. 21.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2³ × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2 × 3 × 5 × 7
22. 22.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times
23. 23.A bag has 9 green balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 10 (b) 16 (c) 2 (d) 11
24. 24.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2³ × 3² (c) 2² × 3² (d) 2 × 3²
25. 25.A bag has 2 white, 2 yellow and 5 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 2/3 (c) 5/9 (d) 4/9
26. 26.What is the mode of 4, 16, 19, 4, 12, 19 and 4? (a) 12 (b) 19 (c) 16 (d) 4
27. 27.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 140° (b) 70° (c) 40° (d) 50°
28. 28.A drawer has lots of blue, yellow, green 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) 8 (b) 5 (c) 4 (d) 2
29. 29.In a class of 31 children, 19 like cricket, 12 like football and 2 like both. How many like neither? (a) 3 (b) 4 (c) 0 (d) 2
30. 30.What is the sum of the first 9 terms of the AP 7, 13, 19, …? (a) 55 (b) 558 (c) 279 (d) 306
31. 31.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/3 (c) 2/3 (d) 1/4
32. 32.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 76° (b) 255° (c) 75° (d) 105°
33. 33.In a class of 62 children, 32 like mangoes, 32 like bananas and 12 like both. How many like neither? (a) 11 (b) 10 (c) 12 (d) 22
34. 34.Two angles of a triangle are 40° and 35°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 75° (d) 140°
35. 35.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
36. 36.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 15 (c) 30 (d) 12
37. 37.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 20° (c) 110° (d) 55°
38. 38.Which is the correct factorisation of x² + 10x + 16? (a) (x − 2)(x − 8) (b) (x + 1)(x + 16) (c) (x + 1)(x + 9) (d) (x + 2)(x + 8)
39. 39.What is the mean of 13, 4, 2 and 5? (a) 7 (b) 5 (c) 8 (d) 6
40. 40.Two angles of a triangle are 35° and 60°. What is the exterior angle at the third corner? (a) 95° (b) 120° (c) 85° (d) 145°

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