Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 791 · 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.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 1
2. 2.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
3. 3.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 324 (c) 35 (d) 171
4. 4.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 1/6 (b) 1/3 (c) 5/6 (d) 1/5
5. 5.In a class of 30 children, 11 like tea, 20 like coffee and 8 like both. How many like at least one of the two? (a) 23 (b) 15 (c) 31 (d) 30
6. 6.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 140° (b) 41° (c) 40° (d) 220°
7. 7.In a class of 35 children, 11 like mangoes, 22 like bananas and 8 like neither. How many like both? (a) 7 (b) 6 (c) 27 (d) 8
8. 8.What are the roots of x² − 8x + 15 = 0? (a) 3 and 5 (b) 1 and 15 (c) 2 and 6 (d) 1 and 7
9. 9.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 108 (c) 36 (d) 39
10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 16 (b) 14 (c) 15 (d) 4
11. 11.A canteen sells 4 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 48 (b) 10 (c) 24 (d) 28
12. 12.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 78 (c) 91 (d) 169
13. 13.What is the 20th term of the AP 15, 18, 21, 24, …? (a) 57 (b) 60 (c) 75 (d) 72
14. 14.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
15. 15.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 50° (c) 25° (d) 115°
16. 16.What is the mean of 8, 18, 16, 17 and 21? (a) 20 (b) 17 (c) 15 (d) 16
17. 17.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
18. 18.If a + b = 15 and ab = 50, what is (a − b)²? (a) 125 (b) 25 (c) 225 (d) 5
19. 19.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 100 (c) 45 (d) 55
20. 20.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 81 (d) 36
21. 21.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 498 (c) 499 (d) 404
22. 22.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
23. 23.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 208 (c) 205 (d) 204
24. 24.A cuboid is 12 cm long, 11 cm wide and 4 cm high. What is its volume? (a) 448 cu cm (b) 27 cu cm (c) 528 cu cm (d) 132 cu cm
25. 25.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
26. 26.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 182 (b) 91 (c) 92 (d) 16
27. 27.A bag has 6 red balls and 10 blue 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) 7 (c) 16 (d) 2
28. 28.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 48 (d) 16
29. 29.A bag has 6 yellow, 6 red and 6 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/3 (b) 2/3 (c) 1/18 (d) 13/18
30. 30.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 48 (c) 16 (d) 12
31. 31.What is the distance between the points (7, 13) and (15, 7)? (a) 11 (b) 14 (c) 10 (d) 100
32. 32.Using (a + b)² = a² + 2ab + b², what is 54²? (a) 2516 (b) 2116 (c) 2926 (d) 2916
33. 33.What is the midpoint of the line joining (5, 0) and (13, 12)? (a) (6, 9) (b) (9, 6) (c) (18, 12) (d) (4, 6)
34. 34.In a class of 28 children, 22 like maths, 10 like science and 6 like both. How many like only maths? (a) 18 (b) 4 (c) 22 (d) 16
35. 35.A bag has 4 green balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 13 (c) 5 (d) 2
36. 36.Which is the correct factorisation of x² + 8x + 12? (a) (x + 2)(x + 6) (b) (x − 2)(x − 6) (c) (x + 1)(x + 7) (d) (x + 1)(x + 12)
37. 37.Two angles of a triangle are 20° and 105°. What is the third angle? (a) 55° (b) 160° (c) 125° (d) 75°
38. 38.In a class of 39 children, 13 like cricket, 26 like football and 7 like both. How many like at least one of the two? (a) 32 (b) 39 (c) 25 (d) 33
39. 39.What is the missing term in the AP 17, 22, 27, ?, 37? (a) 33 (b) 31 (c) 37 (d) 32
40. 40.In a class of 30 children, 10 like cricket, 20 like football and 6 like both. How many like only cricket? (a) 14 (b) 4 (c) 6 (d) 10

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