Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 153 · 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 distance between the points (9, 2) and (21, 18)? (a) 400 (b) 20 (c) 21 (d) 28
2. 2.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 37 (c) 36 (d) 25
3. 3.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 14 (c) 21 (d) 49
4. 4.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 25° (c) 26° (d) 155°
5. 5.What is the 27th term of the AP 17, 23, 29, 35, …? (a) 179 (b) 162 (c) 173 (d) 156
6. 6.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 642 (b) 500 (c) 643 (d) 633
7. 7.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 112 (c) 64 (d) 56
8. 8.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 2 (d) 3
9. 9.Which term of the AP 7, 15, 23, 31, … is 87? (a) 12th (b) 10th (c) 11th (d) 13th
10. 10.What is the prime factorisation of 24? (a) 2² × 3 (b) 2³ × 3 (c) 2⁴ × 3 (d) 2 × 3³
11. 11.Two angles of a triangle are 30° and 45°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 105° (d) 150°
12. 12.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
13. 13.What is the missing term in the AP 6, ?, 16, 21, 26? (a) 12 (b) 10 (c) 16 (d) 11
14. 14.There are 8 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 10 (c) 16 (d) 32
15. 15.A bag has 8 blue, 5 green and 9 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 1/3 (b) 13/22 (c) 9/22 (d) 9/13
16. 16.In a class of 29 children, 18 like tea, 16 like coffee and 6 like both. How many like at least one of the two? (a) 34 (b) 28 (c) 22 (d) 29
17. 17.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 44 sq cm (d) 77 sq cm
18. 18.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 63 (c) 20 (d) 60
19. 19.The mean of 7 numbers is 20. When the number 12 is added to them, what is the new mean? (a) 16 (b) 20 (c) 19 (d) 18
20. 20.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 91 (c) 78 (d) 156
21. 21.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 272 (b) 256 (c) 31 (d) 136
22. 22.A cube has edges of 11 cm. What is its volume? (a) 726 cu cm (b) 484 cu cm (c) 1331 cu cm (d) 33 cu cm
23. 23.How many factors does 12 have? (a) 4 (b) 7 (c) 5 (d) 6
24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
25. 25.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 2 times (c) 8 times (d) 4 times
26. 26.Two angles of a triangle are 40° and 40°. What is the third angle? (a) 100° (b) 80° (c) 280° (d) 140°
27. 27.In which quadrant does the point (−4, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
28. 28.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 24 (c) 12 (d) 16
29. 29.In which quadrant does the point (4, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
30. 30.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
31. 31.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 9 (c) 12 (d) 6
32. 32.In a class of 28 children, 13 like cricket, 12 like football and 7 like both. How many like neither? (a) 7 (b) 3 (c) 10 (d) 17
33. 33.In a class of 32 children, 19 like dance, 10 like music and 3 like both. How many like neither? (a) 6 (b) 7 (c) 3 (d) 9
34. 34.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 155 (b) 170 (c) 310 (d) 29
35. 35.What is the sum of all the whole numbers from 1 to 45? (a) 990 (b) 2070 (c) 1036 (d) 1035
36. 36.A bag has 4 white balls and 12 green 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) 5 (c) 13 (d) 2
37. 37.What are the roots of x² − 17x + 72 = 0? (a) 1 and 16 (b) 1 and 72 (c) 2 and 36 (d) 8 and 9
38. 38.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 1/4 (c) 3/5 (d) 5/8
39. 39.What is the median of 4, 36, 2, 8, 28, 17 and 24? (a) 18 (b) 17 (c) 24 (d) 8
40. 40.A bag has 11 green balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 2 (c) 5 (d) 12

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