Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 500 · 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 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) 3 (b) 5 (c) 4 (d) 2
2. 2.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 144 sq cm (c) 1728 sq cm (d) 864 sq cm
3. 3.What is the prime factorisation of 84? (a) 2 × 3 × 7² (b) 2³ × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7
4. 4.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 300 (b) 47 (c) 576 (d) 600
5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 18 (b) 17 (c) 7 (d) 19
6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
7. 7.What is the prime factorisation of 21? (a) 3 × 7 (b) 3³ × 7 (c) 3² × 7 (d) 3 × 7²
8. 8.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 49 (c) 42 (d) 21
9. 9.A cube has edges of 3 cm. What is its total surface area? (a) 27 sq cm (b) 36 sq cm (c) 54 sq cm (d) 9 sq cm
10. 10.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 30 (b) 21 (c) 15 (d) 36
11. 11.Which is the correct factorisation of x² + 13x + 42? (a) (x − 6)(x − 7) (b) (x + 1)(x + 42) (c) (x + 1)(x + 12) (d) (x + 6)(x + 7)
12. 12.A drawer has lots of white, green and black 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) 2 (c) 3 (d) 4
13. 13.A drawer has lots of blue, yellow, white, red and black 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) 2 (c) 5 (d) 6
14. 14.A drawer has lots of red, blue, green and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 4 (c) 5 (d) 2
15. 15.Two angles of a triangle are 60° and 90°. What is the exterior angle at the third corner? (a) 90° (b) 120° (c) 30° (d) 150°
16. 16.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
17. 17.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 171 (b) 35 (c) 342 (d) 324
18. 18.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) 24 (b) 37 (c) 25 (d) 36
19. 19.What is the distance between the points (7, 7) and (19, 16)? (a) 225 (b) 16 (c) 15 (d) 21
20. 20.In a class of 38 children, 17 like cricket, 19 like football and 4 like both. How many like only cricket? (a) 19 (b) 15 (c) 13 (d) 17
21. 21.What is the midpoint of the line joining (6, 10) and (12, 2)? (a) (18, 12) (b) (6, 9) (c) (9, 6) (d) (3, 4)
22. 22.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 30 (b) 15 (c) 25 (d) 9
23. 23.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 115° (b) 65° (c) 145° (d) 150°
24. 24.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 5 (c) 18 (d) 15
25. 25.What is the 37th term of the AP 20, 27, 34, 41, …? (a) 259 (b) 252 (c) 279 (d) 272
26. 26.What is the sum of the first 10 terms of the AP 9, 12, 15, …? (a) 450 (b) 225 (c) 240 (d) 36
27. 27.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 1386 sq cm (d) 5544 sq cm
28. 28.A drawer has lots of blue, green, white, red and black 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) 6 (d) 2
29. 29.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) 15 (b) 7 (c) 14 (d) 8
30. 30.A canteen sells 5 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 35 (b) 40 (c) 12 (d) 70
31. 31.A bag has 5 blue balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 14 (b) 6 (c) 7 (d) 2
32. 32.A drawer has lots of red 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) 5 (b) 4 (c) 3 (d) 2
33. 33.In a class of 31 children, 15 like tea, 19 like coffee and 10 like both. How many like at least one of the two? (a) 31 (b) 34 (c) 14 (d) 24
34. 34.What is the sum of the roots of x² − 13x + 42 = 0? (a) 42 (b) 12 (c) 13 (d) 14
35. 35.A bag has 8 red, 7 yellow and 9 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 17/24 (b) 1/3 (c) 1/24 (d) 2/3
36. 36.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 75° (b) 285° (c) 105° (d) 15°
37. 37.Which is the correct factorisation of x² + 8x + 15? (a) (x − 3)(x − 5) (b) (x + 1)(x + 15) (c) (x + 1)(x + 7) (d) (x + 3)(x + 5)
38. 38.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 28 (b) 56 (c) 16 (d) 64
39. 39.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
40. 40.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25

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