Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 635 · 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 mean of 18, 13, 20, 6, 13 and 14? (a) 12 (b) 14 (c) 13 (d) 15
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) 22 (b) 14 (c) 21 (d) 15
3. 3.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
4. 4.A bag has 10 white balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 12 (b) 18 (c) 11 (d) 2
5. 5.In a class of 37 children, 16 like cricket, 30 like football and 12 like both. How many like neither? (a) 3 (b) 12 (c) 4 (d) 15
6. 6.Using (a + b)² = a² + 2ab + b², what is 34²? (a) 916 (b) 676 (c) 1166 (d) 1156
7. 7.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 499 (b) 498 (c) 404 (d) 489
8. 8.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 150° (b) 125° (c) 55° (d) 155°
9. 9.Two straight lines cross. One of the angles is 60°. What is the angle next to it on the same straight line? (a) 30° (b) 120° (c) 60° (d) 300°
10. 10.In which quadrant does the point (9, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
11. 11.A bag has 7 red, 5 white and 7 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 13/19 (b) 7/19 (c) 12/19 (d) 1/3
12. 12.What is the midpoint of the line joining (3, 8) and (13, 18)? (a) (16, 26) (b) (5, 5) (c) (13, 8) (d) (8, 13)
13. 13.In how many different ways can the letters of the word LAMP be arranged? (a) 12 (b) 16 (c) 48 (d) 24
14. 14.4 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 48 (c) 28 (d) 24
15. 15.8 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 64 (b) 56 (c) 112 (d) 15
16. 16.In a class of 21 children, 14 like dance, 8 like music and 2 like both. How many like only dance? (a) 13 (b) 6 (c) 12 (d) 14
17. 17.How many factors does 105 have? (a) 7 (b) 9 (c) 6 (d) 8
18. 18.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/3 (c) 1/4 (d) 2/3
19. 19.A cube has edges of 5 cm. What is its total surface area? (a) 125 sq cm (b) 100 sq cm (c) 150 sq cm (d) 25 sq cm
20. 20.A bag has 6 white balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 8 (b) 12 (c) 7 (d) 2
21. 21.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 5° (c) 10° (d) 95°
22. 22.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 25 (b) 36 (c) 37 (d) 24
23. 23.In a class of 35 children, 19 like cricket, 18 like football and 7 like both. How many like at least one of the two? (a) 30 (b) 35 (c) 23 (d) 37
24. 24.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 42 cu cm (b) 82 cu cm (c) 12 cu cm (d) 6 cu cm
25. 25.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) 6 (b) 21 (c) 54 (d) 18
26. 26.What is the mean of 18, 5, 6 and 15? (a) 13 (b) 10 (c) 12 (d) 11
27. 27.What is the distance between the points (7, 3) and (10, 7)? (a) 25 (b) 5 (c) 7 (d) 6
28. 28.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 2/11 (c) 1/11 (d) 1/12
29. 29.What is the distance between the points (7, 19) and (19, 3)? (a) 20 (b) 28 (c) 21 (d) 400
30. 30.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 15 (c) 30 (d) 12
31. 31.What is the prime factorisation of 280? (a) 2² × 5 × 7 (b) 2 × 5 × 7³ (c) 2³ × 5 × 7 (d) 2⁴ × 5 × 7
32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
33. 33.A drawer has lots of 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) 4 (b) 5 (c) 2 (d) 3
34. 34.What is the smallest prime factor of 91? (a) 7 (b) 1 (c) 2 (d) 13
35. 35.What is the median of 30, 8, 9, 27, 21, 20 and 7? (a) 20 (b) 9 (c) 21 (d) 27
36. 36.What is the sum of the first 6 terms of the AP 8, 13, 18, …? (a) 138 (b) 33 (c) 123 (d) 246
37. 37.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
38. 38.A drawer has lots of red, yellow, green, white and blue 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) 5 (c) 10 (d) 2
39. 39.What is the distance between the points (0, 2) and (12, 11)? (a) 21 (b) 15 (c) 225 (d) 16
40. 40.What is the missing term in the AP 14, ?, 32, 41, 50? (a) 24 (b) 32 (c) 23 (d) 22

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