Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 703 · 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.In a class of 21 children, 13 like mangoes, 13 like bananas and 7 like both. How many like only mangoes? (a) 6 (b) 13 (c) 8 (d) 7
2. 2.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
3. 3.A drawer has lots of yellow, red, green, blue 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) 2 (b) 10 (c) 5 (d) 6
4. 4.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
5. 5.In a class of 39 children, 24 like mangoes, 20 like bananas and 12 like both. How many like at least one of the two? (a) 44 (b) 20 (c) 32 (d) 39
6. 6.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 4 (d) 5
8. 8.In a class of 41 children, 24 like maths, 22 like science and 6 like both. How many like neither? (a) 2 (b) 6 (c) 1 (d) 7
9. 9.Two angles of a triangle are 30° and 115°. What is the third angle? (a) 150° (b) 65° (c) 145° (d) 35°
10. 10.A cube has edges of 5 cm. What is its volume? (a) 125 cu cm (b) 15 cu cm (c) 150 cu cm (d) 100 cu cm
11. 11.What is the 17th term of the AP 14, 20, 26, 32, …? (a) 110 (b) 96 (c) 102 (d) 116
12. 12.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 35° (b) 145° (c) 70° (d) 36°
13. 13.In a class of 41 children, 21 like dance, 24 like music and 9 like both. How many like only dance? (a) 17 (b) 12 (c) 15 (d) 21
14. 14.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 45° (c) 125° (d) 135°
15. 15.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 162 (c) 54 (d) 18
16. 16.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/2 (c) 2/3 (d) 1/3
17. 17.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) 8 (c) 15 (d) 7
18. 18.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 8 times (d) 4 times
19. 19.What is the median of 3, 2, 15, 32 and 23? (a) 15 (b) 16 (c) 23 (d) 3
20. 20.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 37 (b) 36 (c) 49 (d) 48
21. 21.In a class of 24 children, 8 like maths, 17 like science and 4 like both. How many like at least one of the two? (a) 24 (b) 21 (c) 17 (d) 25
22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 19 (d) 18
23. 23.A bag has 11 white balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 16 (b) 13 (c) 12 (d) 2
24. 24.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
25. 25.A drawer has lots of black, blue 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) 2 (b) 4 (c) 6 (d) 3
26. 26.If a + b = 19 and ab = 90, what is a² + b²? (a) 271 (b) 541 (c) 181 (d) 361
27. 27.A drawer has lots of green, white, blue, yellow and red 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) 6 (c) 5 (d) 2
28. 28.What is the missing term in the AP 6, ?, 20, 27, 34? (a) 12 (b) 13 (c) 20 (d) 14
29. 29.In a class of 26 children, 17 like cricket, 13 like football and 7 like both. How many like neither? (a) 7 (b) 3 (c) 4 (d) 10
30. 30.What is the mode of 4, 15, 15, 20, 20, 16 and 15? (a) 16 (b) 15 (c) 20 (d) 4
31. 31.If a + b = 6 and ab = 8, what is (a − b)²? (a) 20 (b) 2 (c) 4 (d) 36
32. 32.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 23 (c) 69 (d) 72
33. 33.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 400 (b) 210 (c) 420 (d) 39
34. 34.What is the mode of 8, 6, 6, 15, 8, 8 and 1? (a) 15 (b) 6 (c) 1 (d) 8
35. 35.Two straight lines cross. One of the angles is 115°. What is the angle next to it on the same straight line? (a) 245° (b) 65° (c) 66° (d) 115°
36. 36.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 56° (b) 125° (c) 235° (d) 55°
37. 37.The mean of 8 numbers is 34. When the number 52 is added to them, what is the new mean? (a) 36 (b) 34 (c) 43 (d) 37
38. 38.In a league, 9 teams each play every other team once. How many matches are played? (a) 72 (b) 45 (c) 36 (d) 81
39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 4/11 (b) 1/11 (c) 1/9 (d) 5/36
40. 40.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 16) (b) (x + 1)(x + 9) (c) (x − 2)(x − 8) (d) (x + 2)(x + 8)

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