Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 837 · 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 fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/3 (b) 1/6 (c) 5/6 (d) 1/5
2. 2.A bag has 5 blue balls and 4 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 9 (b) 2 (c) 7 (d) 6
3. 3.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
4. 4.What is the missing term in the AP 2, ?, 20, 29, 38? (a) 10 (b) 20 (c) 11 (d) 12
5. 5.What is the smallest prime factor of 155? (a) 2 (b) 5 (c) 1 (d) 31
6. 6.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 91 (d) 156
7. 7.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 11035 (b) 9025 (c) 10025 (d) 11025
8. 8.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 2/3
9. 9.Which term of the AP 7, 10, 13, 16, … is 100? (a) 31st (b) 32nd (c) 33rd (d) 34th
10. 10.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 145° (b) 60° (c) 155° (d) 25°
11. 11.In a class of 44 children, 18 like cricket, 31 like football and 12 like both. How many like neither? (a) 8 (b) 7 (c) 12 (d) 19
12. 12.A bag has 12 black balls and 13 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 25 (c) 2 (d) 14
13. 13.A drawer has lots of red, yellow 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) 2 (b) 6 (c) 4 (d) 3
14. 14.Two angles of a triangle are 40° and 95°. What is the third angle? (a) 45° (b) 140° (c) 135° (d) 85°
15. 15.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 90 (b) 33 (c) 10 (d) 30
16. 16.A bag has 11 white balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 12 (c) 17 (d) 2
17. 17.A bag has 10 green balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 14 (b) 11 (c) 2 (d) 5
18. 18.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 14 (b) 21 (c) 28 (d) 9
19. 19.Which is the correct factorisation of x² + 9x + 14? (a) (x − 2)(x − 7) (b) (x + 1)(x + 14) (c) (x + 1)(x + 8) (d) (x + 2)(x + 7)
20. 20.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 22 (b) 29 (c) 28 (d) 21
21. 21.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 110 (c) 55 (d) 22
22. 22.In which quadrant does the point (−8, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
23. 23.How many prime numbers are there between 50 and 80? (a) 8 (b) 6 (c) 7 (d) 9
24. 24.What is the distance between the points (2, 9) and (10, 3)? (a) 11 (b) 10 (c) 14 (d) 100
25. 25.A cube has edges of 11 cm. What is its volume? (a) 484 cu cm (b) 726 cu cm (c) 1331 cu cm (d) 33 cu cm
26. 26.Two angles of a triangle are 40° and 80°. What is the exterior angle at the third corner? (a) 60° (b) 120° (c) 100° (d) 140°
27. 27.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 16° (c) 15° (d) 165°
28. 28.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/4 (c) 1/3 (d) 5/6
29. 29.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 165° (b) 110° (c) 85° (d) 15°
30. 30.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 130° (c) 50° (d) 51°
31. 31.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
32. 32.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
33. 33.6 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 24 (b) 10 (c) 48 (d) 30
34. 34.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 20 (c) 25 (d) 240
35. 35.A bag has 7 red, 5 white and 4 green balls. One ball is taken out without looking. What is the probability that it is red? (a) 7/9 (b) 1/3 (c) 9/16 (d) 7/16
36. 36.A bag has 8 blue balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 4 (d) 11
37. 37.5 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 40 (b) 35 (c) 12 (d) 70
38. 38.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 51 (c) 60 (d) 42
39. 39.Two angles of a triangle are 35° and 90°. What is the third angle? (a) 90° (b) 145° (c) 125° (d) 55°
40. 40.A drawer has lots of black, yellow, blue and green 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) 5 (c) 4 (d) 8

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