Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 952 · 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 area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
2. 2.What is the sum of the first 12 terms of the AP 5, 6, 7, …? (a) 252 (b) 126 (c) 132 (d) 16
3. 3.What is the mode of 9, 14, 11, 11, 14, 18 and 11? (a) 9 (b) 11 (c) 14 (d) 18
4. 4.What is the distance between the points (3, 15) and (18, 7)? (a) 289 (b) 17 (c) 23 (d) 18
5. 5.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 11 (d) 10
6. 6.Using (a + b)² = a² + 2ab + b², what is 101²? (a) 10211 (b) 9801 (c) 10201 (d) 10001
7. 7.The mean of 7 numbers is 36. When the number 4 is added to them, what is the new mean? (a) 33 (b) 36 (c) 32 (d) 20
8. 8.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 49 (b) 42 (c) 21 (d) 14
9. 9.In a class of 43 children, 22 like mangoes, 27 like bananas and 7 like both. How many like neither? (a) 1 (b) 2 (c) 8 (d) 7
10. 10.What is the midpoint of the line joining (2, 12) and (12, 0)? (a) (6, 7) (b) (14, 12) (c) (5, 6) (d) (7, 6)
11. 11.A bag has 12 green balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 14 (c) 13 (d) 20
12. 12.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 340° (c) 70° (d) 20°
13. 13.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x − 8)(x − 9) (c) (x + 8)(x + 9) (d) (x + 1)(x + 16)
14. 14.A drawer has lots of black, red, blue, yellow 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) 10 (b) 5 (c) 2 (d) 6
15. 15.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 54 cu cm (c) 36 cu cm (d) 9 cu cm
16. 16.What is the product of the roots of x² − 11x + 28 = 0? (a) 27 (b) 11 (c) 29 (d) 28
17. 17.A bag has 3 green, 7 blue and 8 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 5/6 (b) 8/9 (c) 1/3 (d) 1/6
18. 18.In an isosceles triangle, the angle between the two equal sides is 160°. What is each of the other two angles? (a) 10° (b) 160° (c) 20° (d) 11°
19. 19.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 1/4 (c) 2/3 (d) 5/6
20. 20.8 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 32 (c) 40 (d) 64
21. 21.A bag has 9 green balls and 8 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 11 (b) 17 (c) 10 (d) 2
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/11 (b) 1/9 (c) 1/12 (d) 3/11
23. 23.If a + b = 15 and ab = 36, what is a² + b²? (a) 189 (b) 153 (c) 225 (d) 297
24. 24.A bag has 12 yellow balls and 8 red 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) 2 (c) 13 (d) 20
25. 25.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
26. 26.How many prime numbers are there between 20 and 50? (a) 8 (b) 6 (c) 9 (d) 7
27. 27.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 18 (c) 6 (d) 21
28. 28.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 5544 sq cm (c) 693 sq cm (d) 1386 sq cm
29. 29.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 422 (c) 516 (d) 525
30. 30.What is the mode of 19, 19, 17, 19, 10, 3 and 17? (a) 3 (b) 19 (c) 10 (d) 17
31. 31.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 50° (c) 25° (d) 65°
32. 32.What is the mode of 9, 3, 2, 12, 2, 2 and 12? (a) 9 (b) 2 (c) 12 (d) 3
33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 1/6 (b) 5/11 (c) 1/11 (d) 5/36
34. 34.What is the sum of the roots of x² − 9x + 20 = 0? (a) 10 (b) 20 (c) 8 (d) 9
35. 35.A drawer has lots of yellow, blue, red, 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) 2 (b) 10 (c) 6 (d) 5
36. 36.How many prime numbers are there between 60 and 70? (a) 3 (b) 2 (c) 1 (d) 4
37. 37.What is the smallest prime factor of 187? (a) 1 (b) 2 (c) 11 (d) 17
38. 38.What is the mean of 7, 19, 11, 6, 15 and 20? (a) 15 (b) 14 (c) 12 (d) 13
39. 39.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 176 cm (c) 352 cm (d) 88 cm
40. 40.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 125° (d) 105°

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