Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 317 · 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.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
2. 2.What is the mean of 4, 15, 4, 14, 5 and 6? (a) 10 (b) 9 (c) 7 (d) 8
3. 3.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2⁴ × 3 × 5 (c) 2³ × 3 × 5 (d) 2⁵ × 3 × 5
4. 4.What is the distance between the points (3, 2) and (27, 9)? (a) 625 (b) 25 (c) 26 (d) 31
5. 5.In a class of 38 children, 23 like cricket, 16 like football and 8 like both. How many like only cricket? (a) 15 (b) 22 (c) 8 (d) 23
6. 6.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 144 (c) 24 (d) 66
7. 7.A cube has edges of 8 cm. What is its total surface area? (a) 384 sq cm (b) 256 sq cm (c) 512 sq cm (d) 64 sq cm
8. 8.Two angles of a triangle are 50° and 75°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 125° (d) 55°
9. 9.How many prime numbers are there between 60 and 70? (a) 4 (b) 1 (c) 2 (d) 3
10. 10.In a class of 41 children, 19 like maths, 22 like science and 4 like both. How many like only maths? (a) 19 (b) 18 (c) 4 (d) 15
11. 11.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 1)(x + 72) (c) (x − 8)(x − 9) (d) (x + 8)(x + 9)
12. 12.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 6 (d) 9
13. 13.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 129 (c) 120 (d) 130
14. 14.A bag has 4 green balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 8 (b) 2 (c) 5 (d) 6
15. 15.What is the sum of the roots of x² − 17x + 72 = 0? (a) 18 (b) 17 (c) 72 (d) 16
16. 16.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 3/4 (c) 1/2 (d) 1/4
17. 17.What is the mode of 14, 18, 19, 18, 18, 3 and 19? (a) 3 (b) 19 (c) 14 (d) 18
18. 18.In how many different ways can the letters of the word PEN be arranged? (a) 6 (b) 3 (c) 12 (d) 9
19. 19.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5 (c) 3³ × 5 (d) 3 × 5²
20. 20.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) 8 times (c) 64 times (d) 16 times
21. 21.A bag has 4 yellow balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 7 (b) 6 (c) 5 (d) 2
22. 22.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 5/8 (c) 1/4 (d) 3/8
23. 23.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 150° (b) 110° (c) 140° (d) 70°
24. 24.What is the mean of 3, 17, 10 and 22? (a) 15 (b) 12 (c) 14 (d) 13
25. 25.A drawer has lots of green, black, red 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) 2 (b) 5 (c) 8 (d) 4
26. 26.What is the midpoint of the line joining (5, 8) and (15, 14)? (a) (20, 22) (b) (5, 3) (c) (11, 10) (d) (10, 11)
27. 27.What is the missing term in the AP 15, 20, 25, ?, 35? (a) 30 (b) 29 (c) 31 (d) 35
28. 28.A drawer has lots of black, green, yellow, red 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) 2 (b) 6 (c) 5 (d) 10
29. 29.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 22 cm (c) 44 cm (d) 88 cm
30. 30.What is the midpoint of the line joining (5, 10) and (9, 6)? (a) (14, 16) (b) (8, 7) (c) (7, 8) (d) (2, 2)
31. 31.A bag has 12 black balls and 6 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 18 (b) 14 (c) 2 (d) 13
32. 32.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
33. 33.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
34. 34.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) 13 (b) 12 (c) 24 (d) 25
35. 35.A bag has 4 blue balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 6 (b) 2 (c) 7 (d) 5
36. 36.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 10 times (d) 125 times
37. 37.In a class of 41 children, 22 like cricket, 19 like football and 3 like both. How many like at least one of the two? (a) 39 (b) 38 (c) 41 (d) 35
38. 38.What is the midpoint of the line joining (10, 4) and (16, 8)? (a) (3, 2) (b) (6, 13) (c) (13, 6) (d) (26, 12)
39. 39.A drawer has lots of 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) 2 (b) 5 (c) 4 (d) 3
40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 3/11 (c) 1/11 (d) 1/12

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