Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 89 · 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.A drawer has lots of yellow, white 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) 4 (c) 3 (d) 2
2. 2.Using (a − b)² = a² − 2ab + b², what is 95²? (a) 9035 (b) 9975 (c) 11025 (d) 9025
3. 3.If a + b = 3 and ab = 2, what is (a − b)²? (a) 1 (b) 7 (c) 9 (d) 5
4. 4.What is the mean of 8, 14, 6, 9 and 18? (a) 13 (b) 11 (c) 10 (d) 12
5. 5.Two straight lines cross. One of the angles is 170°. What is the angle next to it on the same straight line? (a) 170° (b) 11° (c) 10° (d) 190°
6. 6.Which term of the AP 6, 14, 22, 30, … is 230? (a) 28th (b) 31st (c) 29th (d) 30th
7. 7.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 15 (c) 21 (d) 30
8. 8.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
9. 9.How many prime numbers are there between 20 and 50? (a) 8 (b) 7 (c) 6 (d) 9
10. 10.A drawer has lots of white 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) 5 (c) 3 (d) 4
11. 11.A bag has 5 red, 4 blue and 6 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 11/15 (b) 1/3 (c) 4/15 (d) 4/5
12. 12.What is the prime factorisation of 144? (a) 2⁵ × 3² (b) 2³ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
13. 13.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
14. 14.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 5 times (b) 2 times (c) 4 times (d) 8 times
15. 15.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 155° (b) 140° (c) 65° (d) 115°
16. 16.8 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 32 (b) 24 (c) 16 (d) 10
17. 17.In a class of 42 children, 19 like maths, 21 like science and 7 like neither. How many like both? (a) 5 (b) 6 (c) 7 (d) 35
18. 18.What is the sum of the roots of x² − 17x + 72 = 0? (a) 72 (b) 16 (c) 17 (d) 18
19. 19.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 7 (b) 14 (c) 15 (d) 8
20. 20.Which term of the AP 11, 13, 15, 17, … is 75? (a) 35th (b) 33rd (c) 34th (d) 32nd
21. 21.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 12 (b) 24 (c) 25 (d) 13
22. 22.What is the prime factorisation of 90? (a) 2³ × 3² × 5 (b) 2 × 3² × 5² (c) 2² × 3² × 5 (d) 2 × 3² × 5
23. 23.A drawer has lots of blue, yellow, white 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
24. 24.Which is the correct factorisation of x² + 11x + 28? (a) (x + 4)(x + 7) (b) (x − 4)(x − 7) (c) (x + 1)(x + 10) (d) (x + 1)(x + 28)
25. 25.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 10° (b) 85° (c) 95° (d) 5°
26. 26.In a class of 17 children, 7 like tea, 12 like coffee and 3 like both. How many like at least one of the two? (a) 17 (b) 19 (c) 16 (d) 13
27. 27.What is the sum of the first 12 terms of the AP 7, 12, 17, …? (a) 62 (b) 444 (c) 828 (d) 414
28. 28.What is the 11th term of the AP 6, 15, 24, 33, …? (a) 105 (b) 90 (c) 99 (d) 96
29. 29.A bag has 5 black balls and 8 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 13 (c) 6 (d) 9
30. 30.A bag has 10 red balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 14 (b) 12 (c) 11 (d) 2
31. 31.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 220 cm (c) 3850 cm (d) 110 cm
32. 32.In a class of 26 children, 10 like dance, 11 like music and 4 like both. How many like at least one of the two? (a) 21 (b) 13 (c) 26 (d) 17
33. 33.A cuboid is 7 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 35 cu cm (b) 15 cu cm (c) 105 cu cm (d) 142 cu cm
34. 34.What is the 35th term of the AP 3, 6, 9, 12, …? (a) 106 (b) 105 (c) 108 (d) 102
35. 35.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
36. 36.What is the 27th term of the AP 1, 6, 11, 16, …? (a) 130 (b) 131 (c) 136 (d) 135
37. 37.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 50° (d) 140°
38. 38.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 50° (c) 40° (d) 130°
39. 39.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 86° (c) 95° (d) 170°
40. 40.In which quadrant does the point (2, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant

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