Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 664 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/11 (c) 1/12 (d) 1/18
2. 2.What is the mode of 11, 11, 11, 18, 18, 6 and 20? (a) 6 (b) 20 (c) 18 (d) 11
3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
4. 4.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 75° (c) 285° (d) 105°
5. 5.What is the product of the roots of x² − 11x + 28 = 0? (a) 28 (b) 27 (c) 29 (d) 11
6. 6.Two angles of a triangle are 30° and 60°. What is the third angle? (a) 270° (b) 150° (c) 120° (d) 90°
7. 7.In a class of 40 children, 16 like mangoes, 28 like bananas and 6 like neither. How many like both? (a) 6 (b) 4 (c) 10 (d) 34
8. 8.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 72 (b) 8 (c) 24 (d) 27
9. 9.What is the mode of 4, 3, 15, 1, 1, 1 and 3? (a) 1 (b) 3 (c) 15 (d) 4
10. 10.A bag has 6 yellow balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 7 (c) 8 (d) 11
11. 11.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 44 cm (d) 176 cm
12. 12.What is the midpoint of the line joining (3, 15) and (15, 9)? (a) (18, 24) (b) (9, 12) (c) (6, 3) (d) (12, 9)
13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 18 (b) 19 (c) 20 (d) 8
14. 14.In how many different ways can the letters of the word BOAT be arranged? (a) 12 (b) 48 (c) 16 (d) 24
15. 15.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 72 (c) 36 (d) 81
16. 16.What is the 13th term of the AP 19, 26, 33, 40, …? (a) 110 (b) 103 (c) 84 (d) 91
17. 17.A bag has 3 red, 7 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 3/4 (c) 1/12 (d) 1/4
18. 18.A drawer has lots of green, red 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) 4 (c) 2 (d) 3
19. 19.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 268 (c) 267 (d) 258
20. 20.The mean of 9 numbers is 11. When the number 21 is added to them, what is the new mean? (a) 12 (b) 11 (c) 13 (d) 16
21. 21.What is the midpoint of the line joining (2, 6) and (10, 12)? (a) (6, 9) (b) (4, 3) (c) (9, 6) (d) (12, 18)
22. 22.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/5 (b) 5/6 (c) 1/3 (d) 1/6
23. 23.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/3 (c) 2/3 (d) 1/2
24. 24.How many factors does 97 have? (a) 4 (b) 3 (c) 1 (d) 2
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/11 (b) 1/36 (c) 1/12 (d) 1/18
26. 26.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 2 (d) 3
27. 27.What is the sum of the first 5 terms of the AP 7, 8, 9, …? (a) 11 (b) 45 (c) 46 (d) 90
28. 28.What is the sum of the first 6 terms of the AP 1, 7, 13, …? (a) 114 (b) 31 (c) 96 (d) 192
29. 29.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
30. 30.In a class of 37 children, 23 like cricket, 15 like football and 3 like both. How many like only cricket? (a) 23 (b) 12 (c) 20 (d) 22
31. 31.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 36 (b) 72 (c) 18 (d) 81
32. 32.Two angles of a triangle are 55° and 40°. What is the third angle? (a) 140° (b) 85° (c) 125° (d) 95°
33. 33.What is the sum of the first 9 terms of the AP 2, 4, 6, …? (a) 99 (b) 18 (c) 180 (d) 90
34. 34.What is the 37th term of the AP 9, 13, 17, 21, …? (a) 144 (b) 157 (c) 153 (d) 148
35. 35.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 63) (b) (x − 7)(x − 9) (c) (x + 7)(x + 9) (d) (x + 1)(x + 15)
36. 36.What is the 32nd term of the AP 16, 22, 28, 34, …? (a) 192 (b) 208 (c) 186 (d) 202
37. 37.In which quadrant does the point (1, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
38. 38.What is the smallest prime factor of 121? (a) 11 (b) 2 (c) 3 (d) 1
39. 39.What is the mean of 18, 12, 18, 6, 10 and 14? (a) 14 (b) 13 (c) 12 (d) 15
40. 40.In a class of 44 children, 19 like tea, 20 like coffee and 3 like both. How many like only tea? (a) 16 (b) 17 (c) 19 (d) 24

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