Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 722 · 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 prime factorisation of 336? (a) 2⁵ × 3 × 7 (b) 2³ × 3 × 7 (c) 2⁴ × 3 × 7 (d) 2 × 3 × 7⁴
2. 2.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 4 times (c) 8 times (d) 6 times
3. 3.A bag has 12 white balls and 12 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 24 (b) 14 (c) 13 (d) 2
4. 4.What is the midpoint of the line joining (3, 12) and (7, 0)? (a) (6, 5) (b) (2, 6) (c) (10, 12) (d) (5, 6)
5. 5.A bag has 3 white balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 11 (d) 4
6. 6.In a class of 29 children, 12 like cricket, 18 like football and 9 like both. How many like at least one of the two? (a) 12 (b) 29 (c) 21 (d) 30
7. 7.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 378 (d) 729
8. 8.What is the sum of the first 10 terms of the AP 7, 9, 11, …? (a) 160 (b) 170 (c) 320 (d) 25
9. 9.If a + b = 8 and ab = 12, what is a² + b²? (a) 64 (b) 40 (c) 52 (d) 88
10. 10.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 12 (c) 7 (d) 24
11. 11.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 308 sq cm (d) 616 sq cm
12. 12.A bag has 11 red balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 22 (c) 12 (d) 13
13. 13.What is the median of 8, 32, 25, 10, 12, 34 and 1? (a) 12 (b) 13 (c) 10 (d) 25
14. 14.How many prime numbers are there between 20 and 30? (a) 4 (b) 2 (c) 3 (d) 1
15. 15.In a class of 34 children, 20 like dance, 14 like music and 2 like neither. How many like both? (a) 2 (b) 1 (c) 32 (d) 3
16. 16.A cube has edges of 3 cm. What is its volume? (a) 27 cu cm (b) 9 cu cm (c) 54 cu cm (d) 36 cu cm
17. 17.A bag has 11 red balls and 3 white 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) 14 (c) 4 (d) 12
18. 18.What is the prime factorisation of 180? (a) 2 × 3² × 5² (b) 2 × 3² × 5 (c) 2³ × 3² × 5 (d) 2² × 3² × 5
19. 19.In a class of 37 children, 19 like tea, 28 like coffee and 11 like both. How many like only tea? (a) 17 (b) 19 (c) 8 (d) 9
20. 20.In a class of 40 children, 26 like cricket, 16 like football and 10 like both. How many like only cricket? (a) 16 (b) 26 (c) 24 (d) 6
21. 21.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/11 (d) 1/9
23. 23.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 90 (b) 55 (c) 45 (d) 100
24. 24.A drawer has lots of white, blue, red and yellow 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) 2 (d) 5
25. 25.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 12 (c) 16 (d) 48
26. 26.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
27. 27.A bag has 6 green balls and 11 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 7 (c) 2 (d) 12
28. 28.In a class of 41 children, 25 like tea, 22 like coffee and 7 like both. How many like at least one of the two? (a) 33 (b) 41 (c) 47 (d) 40
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 1/6 (b) 7/36 (c) 6/11 (d) 1/11
30. 30.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 64 (b) 28 (c) 16 (d) 56
31. 31.Which is the correct factorisation of x² + 13x + 42? (a) (x + 6)(x + 7) (b) (x − 6)(x − 7) (c) (x + 1)(x + 42) (d) (x + 1)(x + 12)
32. 32.The mean of 6 numbers is 39. When the number 67 is added to them, what is the new mean? (a) 39 (b) 44 (c) 53 (d) 43
33. 33.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 130° (b) 105° (c) 125° (d) 75°
34. 34.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
35. 35.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 220° (b) 41° (c) 140° (d) 40°
36. 36.A bag has 6 white, 3 green and 6 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 1/5 (b) 1/3 (c) 4/5 (d) 13/15
37. 37.In a class of 42 children, 22 like maths, 19 like science and 4 like both. How many like at least one of the two? (a) 37 (b) 41 (c) 42 (d) 33
38. 38.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/2 (c) 3/4 (d) 1/4
39. 39.Which term of the AP 19, 23, 27, 31, … is 63? (a) 12th (b) 11th (c) 13th (d) 14th
40. 40.A drawer has lots of blue, yellow, black 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) 8 (b) 4 (c) 5 (d) 2

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