Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 826 · 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.What are the roots of x² − 15x + 54 = 0? (a) 2 and 27 (b) 6 and 9 (c) 1 and 14 (d) 1 and 54
2. 2.What is the 33rd term of the AP 5, 8, 11, 14, …? (a) 99 (b) 101 (c) 96 (d) 104
3. 3.What is the sum of all the whole numbers from 1 to 58? (a) 3422 (b) 1653 (c) 1711 (d) 1682
4. 4.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
5. 5.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 55 (b) 22 (c) 110 (d) 121
6. 6.How many factors does 40 have? (a) 8 (b) 7 (c) 9 (d) 6
7. 7.In a class of 18 children, 12 like mangoes, 7 like bananas and 2 like both. How many like neither? (a) 3 (b) 0 (c) 2 (d) 1
8. 8.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 10 (b) 25 (c) 11 (d) 20
9. 9.A drawer has lots of blue, yellow, black, 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) 10 (b) 6 (c) 2 (d) 5
10. 10.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
11. 11.In a class of 43 children, 23 like tea, 17 like coffee and 6 like both. How many like at least one of the two? (a) 40 (b) 34 (c) 28 (d) 43
12. 12.In a class of 21 children, 14 like dance, 7 like music and 2 like both. How many like at least one of the two? (a) 19 (b) 21 (c) 20 (d) 17
13. 13.3 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 21 (c) 36 (d) 18
14. 14.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
15. 15.In which quadrant does the point (−1, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 44 sq cm (d) 616 sq cm
17. 17.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
18. 18.What is the 12th term of the AP 11, 13, 15, 17, …? (a) 33 (b) 22 (c) 35 (d) 24
19. 19.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 28 (c) 21 (d) 42
20. 20.A cuboid is 12 cm long, 4 cm wide and 6 cm high. What is its total surface area? (a) 288 sq cm (b) 144 sq cm (c) 289 sq cm (d) 576 sq cm
21. 21.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
22. 22.Using (a − b)² = a² − 2ab + b², what is 58²? (a) 3596 (b) 3364 (c) 3844 (d) 3374
23. 23.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 48 (c) 36 (d) 37
24. 24.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 78 (b) 156 (c) 144 (d) 23
25. 25.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 30 (c) 9 (d) 81
26. 26.A bag has 8 red, 4 green and 9 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 4/21 (b) 4/17 (c) 17/21 (d) 1/3
27. 27.A bag has 8 blue 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) 14 (b) 7 (c) 9 (d) 2
28. 28.What is the mode of 5, 5, 7, 5, 3, 1 and 1? (a) 5 (b) 1 (c) 3 (d) 7
29. 29.Two angles of a triangle are 60° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 160° (c) 100° (d) 120°
30. 30.What is the sum of all the whole numbers from 1 to 94? (a) 4371 (b) 4418 (c) 8930 (d) 4465
31. 31.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
32. 32.A drawer has lots of green, red, yellow, blue 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) 6 (b) 10 (c) 2 (d) 5
33. 33.Two angles of a triangle are 20° and 40°. What is the exterior angle at the third corner? (a) 120° (b) 160° (c) 60° (d) 140°
34. 34.What is the distance between the points (3, 12) and (19, 0)? (a) 28 (b) 21 (c) 400 (d) 20
35. 35.What is the median of 32, 21, 2, 20, 35, 24 and 30? (a) 20 (b) 21 (c) 24 (d) 30
36. 36.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 18 (b) 15 (c) 14 (d) 13
37. 37.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 48 (d) 16
38. 38.What is the 38th term of the AP 15, 21, 27, 33, …? (a) 228 (b) 243 (c) 222 (d) 237
39. 39.If a + b = 13 and ab = 40, what is (a − b)²? (a) 3 (b) 89 (c) 9 (d) 169
40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 9 (b) 18 (c) 19 (d) 20

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