Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 97 · 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 bag has 5 red, 8 blue and 7 yellow balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 7/20 (b) 7/10 (c) 13/20 (d) 1/3
2. 2.In a class of 27 children, 16 like cricket, 21 like football and 11 like both. How many like at least one of the two? (a) 26 (b) 27 (c) 15 (d) 37
3. 3.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 16 (c) 48 (d) 12
4. 4.A bag has 3 white balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 4 (c) 5 (d) 7
5. 5.What is the mean of 8, 18, 3 and 11? (a) 8 (b) 11 (c) 10 (d) 9
6. 6.What is the 17th term of the AP 19, 28, 37, 46, …? (a) 172 (b) 153 (c) 144 (d) 163
7. 7.A bag has 4 blue balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 14 (b) 6 (c) 5 (d) 2
8. 8.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) 28 (b) 21 (c) 29 (d) 22
9. 9.In a class of 32 children, 15 like cricket, 23 like football and 9 like both. How many like at least one of the two? (a) 29 (b) 32 (c) 20 (d) 38
10. 10.Two angles of a triangle are 75° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 110° (c) 105° (d) 70°
11. 11.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 9) (b) (x − 4)(x − 6) (c) (x + 1)(x + 24) (d) (x + 4)(x + 6)
12. 12.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 16 (c) 56 (d) 64
13. 13.What is the mean of 14, 18, 15 and 17? (a) 17 (b) 16 (c) 18 (d) 15
14. 14.A bag has 6 black balls and 10 white 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) 16 (c) 2 (d) 11
15. 15.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 176 cm (d) 88 cm
17. 17.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 45 (c) 135 (d) 48
18. 18.Using (a − b)² = a² − 2ab + b², what is 48²? (a) 2314 (b) 2496 (c) 2704 (d) 2304
19. 19.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2⁴ × 3 × 5 (c) 2³ × 3 × 5 (d) 2⁵ × 3 × 5
20. 20.A cube has edges of 8 cm. What is its total surface area? (a) 64 sq cm (b) 512 sq cm (c) 256 sq cm (d) 384 sq cm
21. 21.A bag has 8 yellow balls and 5 black 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) 6 (c) 9 (d) 2
22. 22.What is the sum of the first 9 odd numbers (1 + 3 + 5 + …)? (a) 45 (b) 90 (c) 81 (d) 17
23. 23.What is the sum of all the whole numbers from 1 to 47? (a) 1081 (b) 1129 (c) 1128 (d) 2256
24. 24.Two angles of a triangle are 20° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 160° (c) 110° (d) 70°
25. 25.A bag has 8 blue balls and 3 green 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) 9 (d) 4
26. 26.How many prime numbers are there between 90 and 120? (a) 7 (b) 5 (c) 6 (d) 8
27. 27.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 150° (c) 135° (d) 105°
28. 28.What is the smallest prime factor of 217? (a) 1 (b) 7 (c) 31 (d) 2
29. 29.A bag has 3 green, 5 yellow and 7 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 7/8 (b) 1/3 (c) 7/15 (d) 8/15
30. 30.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 100° (c) 20° (d) 80°
31. 31.Using (a − b)² = a² − 2ab + b², what is 95²? (a) 9035 (b) 11025 (c) 9025 (d) 9975
32. 32.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
33. 33.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its total surface area? (a) 80 sq cm (b) 16 sq cm (c) 20 sq cm (d) 40 sq cm
34. 34.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
35. 35.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
36. 36.5 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 50 (c) 30 (d) 25
37. 37.A bag has 7 yellow, 6 blue and 5 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 11/18 (c) 7/18 (d) 7/11
38. 38.In a class of 26 children, 15 like mangoes, 11 like bananas and 3 like both. How many like at least one of the two? (a) 24 (b) 26 (c) 23 (d) 20
39. 39.What is the 27th term of the AP 3, 5, 7, 9, …? (a) 52 (b) 57 (c) 54 (d) 55
40. 40.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 6 (c) 12 (d) 3

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