Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 453 · 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 fair dice is rolled once. What is the probability of getting a prime number? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
2. 2.A canteen sells 6 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 42 (c) 36 (d) 72
3. 3.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) 15 (b) 21 (c) 14 (d) 22
4. 4.What is the sum of the roots of x² − 8x + 12 = 0? (a) 9 (b) 7 (c) 8 (d) 12
5. 5.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) 14 (b) 7 (c) 15 (d) 8
6. 6.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 45 (c) 14 (d) 126
7. 7.In a class of 36 children, 20 like maths, 21 like science and 9 like both. How many like only maths? (a) 11 (b) 15 (c) 20 (d) 12
8. 8.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 36 (c) 64 (d) 56
9. 9.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 12) (b) (x − 6)(x − 7) (c) (x + 6)(x + 7) (d) (x + 1)(x + 42)
10. 10.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) 13 (c) 25 (d) 24
11. 11.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/4 (c) 1/3 (d) 1/2
12. 12.Using (a + b)² = a² + 2ab + b², what is 24²? (a) 586 (b) 576 (c) 256 (d) 416
13. 13.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
14. 14.A cuboid is 5 cm long, 2 cm wide and 8 cm high. What is its total surface area? (a) 66 sq cm (b) 264 sq cm (c) 132 sq cm (d) 80 sq cm
15. 15.A drawer has lots of white, blue, black, 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) 2 (b) 6 (c) 10 (d) 5
16. 16.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 4 times (b) 2 times (c) 8 times (d) 6 times
17. 17.In a class of 37 children, 22 like maths, 19 like science and 12 like both. How many like only maths? (a) 7 (b) 10 (c) 18 (d) 22
18. 18.In a class of 23 children, 18 like dance, 15 like music and 11 like both. How many like neither? (a) 2 (b) 1 (c) 12 (d) 11
19. 19.What is the prime factorisation of 36? (a) 2³ × 3² (b) 2 × 3² (c) 2² × 3³ (d) 2² × 3²
20. 20.What is the product of the roots of x² − 9x + 14 = 0? (a) 13 (b) 9 (c) 15 (d) 14
21. 21.What is the sum of the roots of x² − 11x + 18 = 0? (a) 12 (b) 10 (c) 18 (d) 11
22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 4 (d) 2
23. 23.If a + b = 12 and ab = 11, what is a² + b²? (a) 133 (b) 144 (c) 122 (d) 166
24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 2 (d) 3
25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 5/11 (c) 1/11 (d) 1/6
26. 26.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
27. 27.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 70° (b) 45° (c) 35° (d) 110°
28. 28.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
29. 29.What is the mode of 9, 11, 9, 2, 11, 13 and 9? (a) 2 (b) 13 (c) 11 (d) 9
30. 30.What is the median of 27, 34, 19, 22 and 32? (a) 22 (b) 27 (c) 32 (d) 19
31. 31.What is the missing term in the AP 5, ?, 11, 14, 17? (a) 9 (b) 7 (c) 8 (d) 11
32. 32.What is the mean of 10, 20, 15, 12, 13 and 20? (a) 15 (b) 14 (c) 18 (d) 16
33. 33.Which is the correct factorisation of x² + 11x + 30? (a) (x + 5)(x + 6) (b) (x + 1)(x + 30) (c) (x − 5)(x − 6) (d) (x + 1)(x + 10)
34. 34.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
35. 35.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 28 (c) 64 (d) 56
36. 36.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
37. 37.What is the sum of all the whole numbers from 1 to 25? (a) 325 (b) 326 (c) 650 (d) 300
38. 38.In a class of 32 children, 9 like maths, 19 like science and 4 like both. How many like at least one of the two? (a) 32 (b) 28 (c) 20 (d) 24
39. 39.In which quadrant does the point (5, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
40. 40.A drawer has lots of green, black 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) 2 (b) 3 (c) 4 (d) 6

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