Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 520 · 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 angles of a triangle are 30° and 95°. What is the third angle? (a) 125° (b) 85° (c) 150° (d) 55°
2. 2.In a class of 41 children, 26 like maths, 18 like science and 8 like both. How many like neither? (a) 5 (b) 8 (c) 6 (d) 13
3. 3.In a class of 26 children, 7 like mangoes, 12 like bananas and 9 like neither. How many like both? (a) 9 (b) 17 (c) 2 (d) 3
4. 4.The mean of 6 numbers is 23. When the number 9 is added to them, what is the new mean? (a) 22 (b) 23 (c) 21 (d) 16
5. 5.What is the smallest prime factor of 377? (a) 1 (b) 13 (c) 29 (d) 2
6. 6.Which term of the AP 12, 20, 28, 36, … is 276? (a) 35th (b) 34th (c) 33rd (d) 36th
7. 7.In a class of 31 children, 20 like dance, 18 like music and 11 like both. How many like neither? (a) 5 (b) 15 (c) 4 (d) 11
8. 8.If a + b = 13 and ab = 40, what is (a − b)²? (a) 3 (b) 89 (c) 169 (d) 9
9. 9.A bag has 8 white balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 9 (c) 17 (d) 10
10. 10.In which quadrant does the point (−8, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
11. 11.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
12. 12.A drawer has lots of blue, green, white, yellow and red 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) 6 (c) 2 (d) 10
13. 13.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
14. 14.In a class of 33 children, 14 like mangoes, 21 like bananas and 10 like both. How many like neither? (a) 10 (b) 9 (c) 8 (d) 18
15. 15.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 3/8 (d) 5/8
16. 16.How many prime numbers are there between 30 and 40? (a) 1 (b) 3 (c) 4 (d) 2
17. 17.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) 108 (b) 36 (c) 12 (d) 39
18. 18.What is the distance between the points (5, 4) and (14, 16)? (a) 15 (b) 16 (c) 21 (d) 225
19. 19.In a class of 33 children, 18 like cricket, 19 like football and 6 like neither. How many like both? (a) 6 (b) 4 (c) 27 (d) 10
20. 20.What is the mean of 20, 20, 10, 13 and 7? (a) 14 (b) 13 (c) 16 (d) 15
21. 21.A cube has edges of 2 cm. What is its total surface area? (a) 16 sq cm (b) 8 sq cm (c) 24 sq cm (d) 4 sq cm
22. 22.What is the mode of 17, 9, 17, 8, 9, 4 and 17? (a) 17 (b) 9 (c) 8 (d) 4
23. 23.In a class of 22 children, 15 like mangoes, 11 like bananas and 7 like both. How many like at least one of the two? (a) 22 (b) 12 (c) 19 (d) 26
24. 24.What is the median of 3, 6, 37, 20, 39, 13 and 38? (a) 37 (b) 20 (c) 21 (d) 13
25. 25.Which is the correct factorisation of x² + 14x + 45? (a) (x + 1)(x + 45) (b) (x − 5)(x − 9) (c) (x + 5)(x + 9) (d) (x + 1)(x + 13)
26. 26.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 135° (b) 115° (c) 70° (d) 110°
27. 27.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) 15 (c) 22 (d) 21
28. 28.How many factors does 28 have? (a) 7 (b) 6 (c) 5 (d) 4
29. 29.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
30. 30.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
31. 31.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/18 (c) 1/12 (d) 2/11
33. 33.If a + b = 15 and ab = 44, what is a² + b²? (a) 181 (b) 225 (c) 313 (d) 137
34. 34.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 250° (d) 71°
35. 35.How many prime numbers are there between 60 and 90? (a) 8 (b) 9 (c) 7 (d) 6
36. 36.What is the mode of 6, 14, 5, 16, 6, 14 and 6? (a) 5 (b) 6 (c) 16 (d) 14
37. 37.Two straight lines cross. Two vertically opposite angles add up to 170°. What is each of the other two angles? (a) 10° (b) 190° (c) 85° (d) 95°
38. 38.In which quadrant does the point (7, −1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
39. 39.What is the product of the roots of x² − 10x + 24 = 0? (a) 25 (b) 23 (c) 10 (d) 24
40. 40.A bag has 10 red balls and 5 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) 6 (c) 15 (d) 2

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