Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 945 · 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 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 18 (c) 6 (d) 21
2. 2.What is the mode of 15, 1, 15, 14, 14, 4 and 14? (a) 1 (b) 15 (c) 14 (d) 4
3. 3.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
4. 4.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 36 (c) 81 (d) 72
5. 5.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
6. 6.In a class of 29 children, 20 like dance, 9 like music and 5 like neither. How many like both? (a) 24 (b) 6 (c) 4 (d) 5
7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/18 (b) 2/11 (c) 1/12 (d) 1/11
8. 8.If a + b = 19 and ab = 90, what is a² + b²? (a) 361 (b) 271 (c) 541 (d) 181
9. 9.How many factors does 59 have? (a) 3 (b) 4 (c) 2 (d) 1
10. 10.How many factors does 56 have? (a) 9 (b) 8 (c) 7 (d) 6
11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
12. 12.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 16) (b) (x + 1)(x + 72) (c) (x + 8)(x + 9) (d) (x − 8)(x − 9)
13. 13.What is the median of 13, 4, 12, 18, 16, 7 and 40? (a) 12 (b) 13 (c) 16 (d) 18
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) 25 (b) 24 (c) 13 (d) 12
15. 15.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) 37 (b) 24 (c) 25 (d) 36
16. 16.A drawer has lots of 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) 2 (b) 3 (c) 5 (d) 4
17. 17.How many prime numbers are there between 70 and 100? (a) 5 (b) 8 (c) 7 (d) 6
18. 18.The mean of 8 numbers is 30. When the number 3 is added to them, what is the new mean? (a) 26 (b) 28 (c) 27 (d) 30
19. 19.A bag has 10 yellow balls and 3 green 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) 11 (c) 4 (d) 13
20. 20.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
21. 21.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 156 (b) 169 (c) 78 (d) 91
22. 22.In how many different ways can the letters of the word BOAT be arranged? (a) 24 (b) 12 (c) 16 (d) 48
23. 23.What is the mean of 20, 9, 12, 10 and 9? (a) 15 (b) 12 (c) 13 (d) 10
24. 24.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) 48 (b) 37 (c) 49 (d) 36
25. 25.There are 5 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 70 (b) 12 (c) 35 (d) 40
26. 26.In which quadrant does the point (3, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
27. 27.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
28. 28.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 440 cm (b) 110 cm (c) 220 cm (d) 3850 cm
29. 29.In a class of 24 children, 16 like maths, 18 like science and 12 like both. How many like at least one of the two? (a) 22 (b) 10 (c) 24 (d) 34
30. 30.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 81 (d) 36
31. 31.The mean of 5 numbers is 11. When the number 23 is added to them, what is the new mean? (a) 11 (b) 13 (c) 14 (d) 17
32. 32.Two angles of a triangle are 40° and 110°. What is the third angle? (a) 140° (b) 30° (c) 70° (d) 150°
33. 33.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
34. 34.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 6 times (b) 8 times (c) 4 times (d) 2 times
35. 35.How many prime numbers are there between 80 and 90? (a) 1 (b) 2 (c) 3 (d) 4
36. 36.Two straight lines cross. Two vertically opposite angles add up to 150°. What is each of the other two angles? (a) 210° (b) 75° (c) 105° (d) 30°
37. 37.How many factors does 112 have? (a) 9 (b) 11 (c) 8 (d) 10
38. 38.In a class of 41 children, 23 like cricket, 11 like football and 3 like both. How many like only cricket? (a) 30 (b) 23 (c) 8 (d) 20
39. 39.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 406 (b) 812 (c) 784 (d) 55
40. 40.A bag has 7 yellow balls and 6 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) 7 (c) 13 (d) 8

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