Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 687 · 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.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 11 (c) 36 (d) 99
2. 2.Which term of the AP 19, 23, 27, 31, … is 167? (a) 38th (b) 37th (c) 39th (d) 40th
3. 3.A cuboid is 10 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 17 cu cm (b) 40 cu cm (c) 164 cu cm (d) 120 cu cm
4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 7 (b) 17 (c) 19 (d) 18
5. 5.In a class of 35 children, 11 like tea, 21 like coffee and 6 like both. How many like neither? (a) 3 (b) 15 (c) 9 (d) 6
6. 6.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 8)(x + 9) (c) (x + 1)(x + 16) (d) (x − 8)(x − 9)
7. 7.What is the product of the roots of x² − 12x + 35 = 0? (a) 12 (b) 35 (c) 36 (d) 34
8. 8.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) 5 (b) 45 (c) 18 (d) 15
9. 9.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 155° (b) 25° (c) 100° (d) 105°
10. 10.What is the smallest prime factor of 91? (a) 13 (b) 1 (c) 2 (d) 7
11. 11.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 25 (b) 20 (c) 15 (d) 10
12. 12.What is the midpoint of the line joining (10, 16) and (18, 4)? (a) (10, 14) (b) (4, 6) (c) (14, 10) (d) (28, 20)
13. 13.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 55 (d) 121
14. 14.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) 12 (b) 24 (c) 13 (d) 25
15. 15.5 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 50 (b) 10 (c) 30 (d) 25
16. 16.What is the smallest prime factor of 299? (a) 13 (b) 23 (c) 2 (d) 1
17. 17.A bag has 6 yellow, 7 white and 9 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 9/22 (c) 9/13 (d) 13/22
18. 18.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 20 (b) 180 (c) 63 (d) 60
19. 19.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 121° (b) 120° (c) 60° (d) 240°
20. 20.What is the midpoint of the line joining (5, 0) and (15, 8)? (a) (20, 8) (b) (10, 4) (c) (5, 4) (d) (4, 10)
21. 21.In a class of 51 children, 25 like cricket, 23 like football and 5 like both. How many like only cricket? (a) 18 (b) 28 (c) 20 (d) 25
22. 22.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 49 (c) 42 (d) 28
23. 23.If a + b = 19 and ab = 88, what is a² + b²? (a) 361 (b) 273 (c) 185 (d) 537
24. 24.In a class of 25 children, 13 like dance, 13 like music and 8 like both. How many like neither? (a) 7 (b) 6 (c) 8 (d) 15
25. 25.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times
26. 26.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 2/11 (c) 1/12 (d) 1/18
27. 27.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
28. 28.What is the prime factorisation of 112? (a) 2⁴ × 7 (b) 2³ × 7 (c) 2 × 7⁴ (d) 2⁵ × 7
29. 29.A drawer has lots of 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) 5 (b) 4 (c) 3 (d) 2
30. 30.How many prime numbers are there between 50 and 80? (a) 9 (b) 6 (c) 7 (d) 8
31. 31.If a + b = 11 and ab = 10, what is (a − b)²? (a) 121 (b) 101 (c) 9 (d) 81
32. 32.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
33. 33.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 88 cm (d) 616 cm
34. 34.If a + b = 13 and ab = 12, what is (a − b)²? (a) 145 (b) 169 (c) 11 (d) 121
35. 35.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
36. 36.What is the sum of the first 10 terms of the AP 9, 11, 13, …? (a) 360 (b) 27 (c) 190 (d) 180
37. 37.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
38. 38.Which is the correct factorisation of x² + 12x + 27? (a) (x + 1)(x + 27) (b) (x − 3)(x − 9) (c) (x + 3)(x + 9) (d) (x + 1)(x + 11)
39. 39.A drawer has lots of green 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) 5 (b) 4 (c) 3 (d) 2
40. 40.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 45 (c) 36 (d) 72

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