Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 395 · 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.In a class of 27 children, 7 like cricket, 18 like football and 4 like neither. How many like both? (a) 23 (b) 2 (c) 3 (d) 4
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 day of the week? (a) 15 (b) 14 (c) 22 (d) 21
3. 3.In a class of 19 children, 10 like maths, 5 like science and 2 like both. How many like only maths? (a) 10 (b) 14 (c) 3 (d) 8
4. 4.What is the midpoint of the line joining (5, 7) and (13, 19)? (a) (13, 9) (b) (18, 26) (c) (4, 6) (d) (9, 13)
5. 5.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
6. 6.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 30° (c) 40° (d) 60°
7. 7.What is the sum of the first 12 terms of the AP 7, 11, 15, …? (a) 372 (b) 348 (c) 51 (d) 696
8. 8.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/6 (c) 2/3 (d) 1/3
9. 9.What is the smallest prime factor of 119? (a) 2 (b) 7 (c) 17 (d) 1
10. 10.A bag has 9 white balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 11 (c) 14 (d) 10
11. 11.A bag has 7 yellow balls and 6 white 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) 8 (c) 13 (d) 2
12. 12.A drawer has lots of red, white, green and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 4 (c) 2 (d) 5
13. 13.Two angles of a triangle are 50° and 85°. What is the third angle? (a) 95° (b) 130° (c) 45° (d) 135°
14. 14.Two angles of a triangle are 65° and 20°. What is the exterior angle at the third corner? (a) 95° (b) 85° (c) 160° (d) 115°
15. 15.What is the distance between the points (7, 9) and (19, 0)? (a) 225 (b) 21 (c) 15 (d) 16
16. 16.What is the smallest prime factor of 169? (a) 2 (b) 13 (c) 1 (d) 3
17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/11 (b) 1/36 (c) 1/18 (d) 1/12
18. 18.What is the mean of 3, 5, 4, 13 and 5? (a) 8 (b) 5 (c) 6 (d) 7
19. 19.What is the 29th term of the AP 20, 29, 38, 47, …? (a) 281 (b) 261 (c) 252 (d) 272
20. 20.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
21. 21.6 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 36 (b) 60 (c) 11 (d) 30
22. 22.A drawer has lots of green, blue, black 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) 2 (b) 4 (c) 5 (d) 8
23. 23.What is the distance between the points (2, 8) and (14, 3)? (a) 13 (b) 14 (c) 169 (d) 17
24. 24.What is the smallest prime factor of 377? (a) 13 (b) 29 (c) 2 (d) 1
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
26. 26.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 72 (c) 216 (d) 75
27. 27.What is the median of 8, 5, 20, 24 and 9? (a) 10 (b) 20 (c) 8 (d) 9
28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 17 (b) 15 (c) 16 (d) 5
29. 29.A bag has 7 yellow, 2 blue and 5 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 9/14 (b) 5/14 (c) 1/3 (d) 5/9
30. 30.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x + 7)(x + 8) (c) (x + 1)(x + 14) (d) (x − 7)(x − 8)
31. 31.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
32. 32.What is the 33rd term of the AP 9, 18, 27, 36, …? (a) 306 (b) 288 (c) 298 (d) 297
33. 33.Two angles of a triangle are 40° and 90°. What is the exterior angle at the third corner? (a) 130° (b) 140° (c) 50° (d) 90°
34. 34.In which quadrant does the point (2, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
35. 35.If a + b = 6 and ab = 8, what is (a − b)²? (a) 4 (b) 20 (c) 2 (d) 36
36. 36.In a class of 39 children, 28 like cricket, 22 like football and 12 like both. How many like neither? (a) 12 (b) 13 (c) 1 (d) 2
37. 37.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 88 sq cm (d) 2464 sq cm
38. 38.What is the sum of the first 5 terms of the AP 4, 6, 8, …? (a) 12 (b) 40 (c) 45 (d) 80
39. 39.What is the mode of 14, 12, 10, 12, 10, 17 and 10? (a) 10 (b) 14 (c) 12 (d) 17
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/12 (c) 3/11 (d) 1/9

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