Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 904 · 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 18 children, 10 like dance, 10 like music and 7 like both. How many like at least one of the two? (a) 20 (b) 6 (c) 18 (d) 13
2. 2.In how many different ways can the letters of the word PEN be arranged? (a) 3 (b) 12 (c) 9 (d) 6
3. 3.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/4 (c) 1/3 (d) 3/4
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 4/11 (c) 5/36 (d) 1/9
5. 5.In a class of 33 children, 14 like mangoes, 24 like bananas and 9 like both. How many like at least one of the two? (a) 33 (b) 38 (c) 20 (d) 29
6. 6.A cuboid is 4 cm long, 3 cm wide and 8 cm high. What is its volume? (a) 15 cu cm (b) 136 cu cm (c) 12 cu cm (d) 96 cu cm
7. 7.What is the mean of 18, 7, 16 and 3? (a) 10 (b) 12 (c) 11 (d) 13
8. 8.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 100° (d) 40°
9. 9.In a class of 18 children, 7 like cricket, 13 like football and 4 like both. How many like neither? (a) 2 (b) 3 (c) 4 (d) 6
10. 10.What is the 37th term of the AP 14, 17, 20, 23, …? (a) 125 (b) 108 (c) 122 (d) 111
11. 11.4 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) 6 (b) 12 (c) 16 (d) 8
12. 12.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
13. 13.What is the 38th term of the AP 4, 11, 18, 25, …? (a) 270 (b) 266 (c) 259 (d) 263
14. 14.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/2 (c) 3/4 (d) 1/4
15. 15.What is the 29th term of the AP 9, 18, 27, 36, …? (a) 261 (b) 270 (c) 262 (d) 252
16. 16.A canteen sells 5 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 7 (c) 10 (d) 20
17. 17.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 216 (c) 24 (d) 72
18. 18.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 274 (b) 264 (c) 254 (d) 273
19. 19.What is the mode of 1, 15, 4, 1, 15, 6 and 1? (a) 4 (b) 15 (c) 6 (d) 1
20. 20.What is the 13th term of the AP 10, 13, 16, 19, …? (a) 46 (b) 36 (c) 39 (d) 49
21. 21.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 121 (c) 22 (d) 55
22. 22.There are 8 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 56 (c) 14 (d) 96
23. 23.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 22 (d) 15
24. 24.What is the sum of the roots of x² − 11x + 24 = 0? (a) 10 (b) 11 (c) 12 (d) 24
25. 25.If a + b = 15 and ab = 36, what is (a − b)²? (a) 225 (b) 153 (c) 9 (d) 81
26. 26.What is the smallest prime factor of 91? (a) 2 (b) 1 (c) 7 (d) 13
27. 27.A cube has edges of 12 cm. What is its total surface area? (a) 864 sq cm (b) 576 sq cm (c) 144 sq cm (d) 1728 sq cm
28. 28.A bag has 11 blue balls and 3 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 4 (b) 12 (c) 14 (d) 2
29. 29.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 3/5 (c) 1/4 (d) 5/8
30. 30.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
31. 31.In a class of 38 children, 21 like cricket, 25 like football and 12 like both. How many like at least one of the two? (a) 38 (b) 22 (c) 34 (d) 46
32. 32.If a + b = 16 and ab = 63, what is a² + b²? (a) 193 (b) 256 (c) 130 (d) 382
33. 33.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 40° (c) 130° (d) 50°
34. 34.Two angles of a triangle are 45° and 50°. What is the exterior angle at the third corner? (a) 135° (b) 130° (c) 85° (d) 95°
35. 35.In a class of 34 children, 23 like maths, 14 like science and 4 like both. How many like only maths? (a) 10 (b) 19 (c) 23 (d) 20
36. 36.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
37. 37.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
38. 38.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
39. 39.What is the 19th term of the AP 14, 18, 22, 26, …? (a) 76 (b) 72 (c) 86 (d) 90
40. 40.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 66 (c) 78 (d) 132

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