Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 83 · 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 75° and 45°. What is the exterior angle at the third corner? (a) 60° (b) 105° (c) 120° (d) 135°
2. 2.If a + b = 10 and ab = 9, what is a² + b²? (a) 82 (b) 91 (c) 118 (d) 100
3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 5 (b) 3 (c) 6 (d) 4
4. 4.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) 21 (c) 22 (d) 15
5. 5.6 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) 18 (b) 24 (c) 12 (d) 8
6. 6.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 90 (c) 33 (d) 30
7. 7.A bag has 6 red balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 10 (c) 7 (d) 8
8. 8.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
9. 9.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 25° (b) 115° (c) 50° (d) 65°
10. 10.A bag has 2 yellow, 4 red and 2 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 1/4 (c) 3/8 (d) 3/4
11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 17 (d) 16
12. 12.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 240° (b) 60° (c) 120° (d) 121°
13. 13.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
14. 14.How many factors does 65 have? (a) 3 (b) 2 (c) 4 (d) 5
15. 15.In a class of 43 children, 18 like maths, 27 like science and 9 like both. How many like at least one of the two? (a) 36 (b) 43 (c) 45 (d) 27
16. 16.How many prime numbers are there between 30 and 60? (a) 9 (b) 6 (c) 7 (d) 8
17. 17.What is the midpoint of the line joining (8, 15) and (12, 9)? (a) (10, 12) (b) (2, 3) (c) (12, 10) (d) (20, 24)
18. 18.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 132 (d) 66
19. 19.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/8 (b) 1/7 (c) 7/8 (d) 1/4
20. 20.Which is the correct factorisation of x² + 9x + 18? (a) (x + 1)(x + 8) (b) (x − 3)(x − 6) (c) (x + 1)(x + 18) (d) (x + 3)(x + 6)
21. 21.In a class of 37 children, 18 like cricket, 14 like football and 8 like neither. How many like both? (a) 8 (b) 29 (c) 4 (d) 3
22. 22.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
23. 23.How many factors does 118 have? (a) 4 (b) 2 (c) 5 (d) 3
24. 24.What is the distance between the points (3, 0) and (12, 12)? (a) 225 (b) 21 (c) 15 (d) 16
25. 25.A drawer has lots of blue, yellow, green and white 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) 8 (c) 5 (d) 2
26. 26.A bag has 3 blue balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 4 (c) 5 (d) 11
27. 27.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 182 (c) 91 (d) 196
28. 28.A bag has 3 yellow, 8 red and 3 white balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 3/14 (b) 11/14 (c) 6/7 (d) 1/3
29. 29.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
30. 30.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 25 (c) 15 (d) 9
31. 31.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2 × 3 × 5 × 7² (d) 2³ × 3 × 5 × 7
32. 32.In a league, 5 teams each play every other team once. How many matches are played? (a) 25 (b) 20 (c) 15 (d) 10
33. 33.In which quadrant does the point (−3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
34. 34.What is the median of 34, 10, 2, 12 and 22? (a) 2 (b) 12 (c) 22 (d) 16
35. 35.A bag has 3 green balls and 4 red 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) 7 (c) 4 (d) 5
36. 36.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 176 (c) 175 (d) 184
37. 37.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 1/3 (c) 1/4 (d) 3/4
38. 38.What is the sum of the first 6 odd numbers (1 + 3 + 5 + …)? (a) 21 (b) 42 (c) 11 (d) 36
39. 39.A bag has 3 blue, 3 yellow and 2 green balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 3/8 (c) 5/8 (d) 3/5
40. 40.What are the roots of x² − 8x + 12 = 0? (a) 2 and 6 (b) 1 and 12 (c) 3 and 4 (d) 1 and 7

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