Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 165 · 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 missing term in the AP 6, 13, ?, 27, 34? (a) 27 (b) 19 (c) 20 (d) 21
2. 2.If a + b = 12 and ab = 11, what is a² + b²? (a) 144 (b) 166 (c) 122 (d) 133
3. 3.In a class of 39 children, 25 like dance, 12 like music and 5 like both. How many like at least one of the two? (a) 27 (b) 37 (c) 39 (d) 32
4. 4.In a class of 39 children, 16 like mangoes, 19 like bananas and 5 like both. How many like at least one of the two? (a) 39 (b) 35 (c) 25 (d) 30
5. 5.There are 4 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) 24 (b) 28 (c) 10 (d) 48
6. 6.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/8 (b) 1/4 (c) 3/4 (d) 1/8
7. 7.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 12 (c) 16 (d) 24
8. 8.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 45 (b) 81 (c) 36 (d) 72
9. 9.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 5/8 (d) 3/8
10. 10.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 100° (c) 20° (d) 10°
11. 11.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
12. 12.Two angles of a triangle are 35° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 125° (c) 55° (d) 145°
13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/11 (d) 1/9
14. 14.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) 15 (d) 22
15. 15.What is the median of 21, 28, 19, 5, 1, 18 and 24? (a) 5 (b) 21 (c) 19 (d) 18
16. 16.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 409 (b) 529 (c) 289 (d) 539
17. 17.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 104 (b) 19 (c) 192 (d) 96
18. 18.How many factors does 49 have? (a) 2 (b) 3 (c) 4 (d) 1
19. 19.A bag has 9 blue balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 17 (c) 2 (d) 10
20. 20.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 961 (b) 841 (c) 851 (d) 899
21. 21.The mean of 6 numbers is 23. When the number 37 is added to them, what is the new mean? (a) 26 (b) 25 (c) 23 (d) 30
22. 22.The mean of 3 numbers is 34. When the number 38 is added to them, what is the new mean? (a) 34 (b) 35 (c) 37 (d) 36
23. 23.A drawer has lots of red, black, yellow, blue 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) 6 (b) 10 (c) 5 (d) 2
24. 24.What is the sum of the first 5 terms of the AP 6, 7, 8, …? (a) 80 (b) 41 (c) 40 (d) 10
25. 25.In a class of 19 children, 6 like maths, 8 like science and 7 like neither. How many like both? (a) 12 (b) 3 (c) 2 (d) 7
26. 26.In which quadrant does the point (−4, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 1 (b) 3 (c) 2 (d) 4
28. 28.Two straight lines cross. One of the angles is 25°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 335° (d) 65°
29. 29.A bag has 8 white, 5 red and 9 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 9/22 (b) 9/13 (c) 13/22 (d) 1/3
30. 30.In a class of 26 children, 9 like dance, 16 like music and 3 like both. How many like at least one of the two? (a) 26 (b) 25 (c) 19 (d) 22
31. 31.What is the median of 34, 32, 10, 23 and 15? (a) 23 (b) 32 (c) 15 (d) 10
32. 32.What is the midpoint of the line joining (3, 10) and (9, 2)? (a) (3, 4) (b) (12, 12) (c) (6, 6) (d) (7, 6)
33. 33.Two angles of a triangle are 55° and 50°. What is the exterior angle at the third corner? (a) 125° (b) 75° (c) 105° (d) 130°
34. 34.How many factors does 45 have? (a) 6 (b) 7 (c) 5 (d) 4
35. 35.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 8 times (c) 4 times (d) 16 times
36. 36.A bag has 2 red, 3 blue and 8 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 5/8 (b) 8/13 (c) 5/13 (d) 1/3
37. 37.What is the distance between the points (7, 10) and (22, 2)? (a) 23 (b) 18 (c) 17 (d) 289
38. 38.Two angles of a triangle are 50° and 35°. What is the third angle? (a) 145° (b) 85° (c) 95° (d) 130°
39. 39.A bag has 5 white, 2 yellow and 5 green balls. One ball is taken out without looking. What is the probability that it is white? (a) 5/7 (b) 7/12 (c) 5/12 (d) 1/3
40. 40.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3

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