Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 785 · 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.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
2. 2.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
3. 3.In a class of 37 children, 21 like cricket, 12 like football and 8 like neither. How many like both? (a) 8 (b) 4 (c) 29 (d) 5
4. 4.A drawer has lots of yellow, white, black and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 8 (d) 5
5. 5.If a + b = 15 and ab = 54, what is (a − b)²? (a) 9 (b) 117 (c) 3 (d) 225
6. 6.How many prime numbers are there between 20 and 40? (a) 4 (b) 3 (c) 5 (d) 6
7. 7.Two angles of a triangle are 30° and 85°. What is the third angle? (a) 150° (b) 115° (c) 65° (d) 95°
8. 8.What is the 32nd term of the AP 5, 10, 15, 20, …? (a) 155 (b) 165 (c) 160 (d) 161
9. 9.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 2/3 (c) 1/2 (d) 1/3
10. 10.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 9 (c) 3 (d) 6
11. 11.What is the mean of 3, 6, 13 and 6? (a) 9 (b) 7 (c) 6 (d) 8
12. 12.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 404 (b) 498 (c) 489 (d) 499
13. 13.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) 2 times (d) 4 times
14. 14.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 65° (c) 115° (d) 140°
15. 15.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 171 (c) 57 (d) 60
16. 16.What is the missing term in the AP 13, 17, ?, 25, 29? (a) 22 (b) 25 (c) 21 (d) 20
17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 18 (d) 19
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/18 (c) 1/12 (d) 1/11
19. 19.What is the mode of 5, 13, 12, 17, 12, 5 and 5? (a) 12 (b) 13 (c) 5 (d) 17
20. 20.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 8125 (b) 9035 (c) 7225 (d) 9025
21. 21.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 cm (b) 22 cm (c) 154 cm (d) 88 cm
22. 22.How many factors does 108 have? (a) 10 (b) 11 (c) 12 (d) 13
23. 23.In a class of 41 children, 28 like cricket, 23 like football and 1 like neither. How many like both? (a) 11 (b) 1 (c) 40 (d) 10
24. 24.What is the sum of the first 11 terms of the AP 5, 6, 7, …? (a) 220 (b) 110 (c) 15 (d) 111
25. 25.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 145° (b) 55° (c) 325° (d) 35°
26. 26.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
27. 27.A bag has 8 blue balls and 6 yellow 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) 14 (c) 9 (d) 2
28. 28.What is the distance between the points (6, 1) and (21, 9)? (a) 18 (b) 23 (c) 289 (d) 17
29. 29.How many factors does 48 have? (a) 9 (b) 10 (c) 8 (d) 11
30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
31. 31.A drawer has lots of red, blue, yellow, green and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 6 (d) 10
32. 32.A bag has 11 red balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 12 (c) 2 (d) 8
33. 33.What is the smallest prime factor of 145? (a) 1 (b) 29 (c) 5 (d) 2
34. 34.What is the median of 22, 12, 6, 21, 11, 17 and 1? (a) 17 (b) 21 (c) 11 (d) 12
35. 35.Two angles of a triangle are 30° and 75°. What is the exterior angle at the third corner? (a) 255° (b) 105° (c) 150° (d) 75°
36. 36.What is the product of the roots of x² − 17x + 72 = 0? (a) 17 (b) 71 (c) 73 (d) 72
37. 37.In a class of 21 children, 8 like tea, 10 like coffee and 3 like both. How many like at least one of the two? (a) 21 (b) 12 (c) 18 (d) 15
38. 38.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) 29 (c) 21 (d) 22
39. 39.What is the mean of 15, 9, 4, 13 and 4? (a) 11 (b) 9 (c) 10 (d) 8
40. 40.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

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