Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 252 · 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 class of 27 children, 5 like maths, 19 like science and 5 like neither. How many like both? (a) 22 (b) 2 (c) 5 (d) 3
2. 2.What is the prime factorisation of 36? (a) 2² × 3³ (b) 2² × 3² (c) 2 × 3² (d) 2³ × 3²
3. 3.What is the mode of 16, 11, 11, 16, 18, 16 and 10? (a) 10 (b) 16 (c) 11 (d) 18
4. 4.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 20 (b) 63 (c) 180 (d) 60
5. 5.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 726 cu cm (d) 484 cu cm
6. 6.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 25 (b) 24 (c) 13 (d) 12
7. 7.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 99 (c) 11 (d) 33
8. 8.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
9. 9.In a class of 31 children, 20 like tea, 7 like coffee and 2 like both. How many like at least one of the two? (a) 27 (b) 23 (c) 31 (d) 25
10. 10.What is the 24th term of the AP 18, 21, 24, 27, …? (a) 69 (b) 72 (c) 90 (d) 87
11. 11.In a class of 44 children, 24 like maths, 21 like science and 8 like both. How many like at least one of the two? (a) 45 (b) 37 (c) 44 (d) 29
12. 12.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
13. 13.A cube has edges of 8 cm. What is its total surface area? (a) 256 sq cm (b) 384 sq cm (c) 512 sq cm (d) 64 sq cm
14. 14.Using (a − b)² = a² − 2ab + b², what is 46²? (a) 2126 (b) 2484 (c) 2116 (d) 2916
15. 15.What is the distance between the points (6, 17) and (18, 8)? (a) 225 (b) 21 (c) 16 (d) 15
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 176 cm (d) 44 cm
17. 17.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 64 (c) 28 (d) 16
18. 18.A bag has 2 yellow, 6 red and 4 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/6 (b) 5/6 (c) 1/3 (d) 1/5
19. 19.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 3/4 (c) 1/4 (d) 1/3
20. 20.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 125° (c) 45° (d) 135°
21. 21.In a league, 7 teams each play every other team once. How many matches are played? (a) 49 (b) 21 (c) 42 (d) 28
22. 22.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 60 (b) 36 (c) 11 (d) 30
23. 23.What is the 31st term of the AP 8, 11, 14, 17, …? (a) 101 (b) 93 (c) 90 (d) 98
24. 24.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 80° (c) 160° (d) 20°
25. 25.A bag has 4 yellow balls and 7 white 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) 8 (c) 5 (d) 2
26. 26.In a class of 42 children, 17 like tea, 28 like coffee and 12 like both. How many like neither? (a) 21 (b) 10 (c) 9 (d) 12
27. 27.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 270° (d) 90°
28. 28.Using (a − b)² = a² − 2ab + b², what is 95²? (a) 9975 (b) 9025 (c) 9035 (d) 11025
29. 29.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
30. 30.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 16 times (c) 4 times (d) 8 times
31. 31.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
32. 32.A bag has 3 white, 4 yellow and 3 red balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 7/10 (b) 2/5 (c) 3/5 (d) 1/3
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 4/11 (b) 1/11 (c) 5/36 (d) 1/9
34. 34.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 120° (d) 105°
35. 35.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 2464 sq cm (d) 616 sq cm
36. 36.How many factors does 83 have? (a) 3 (b) 2 (c) 1 (d) 4
37. 37.What is the mean of 20, 7, 8 and 9? (a) 10 (b) 13 (c) 12 (d) 11
38. 38.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/2 (c) 1/4 (d) 2/3
39. 39.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
40. 40.4 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) 7 (b) 16 (c) 12 (d) 24

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