Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 293 · 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 mean of 6, 18, 2, 15 and 14? (a) 12 (b) 13 (c) 11 (d) 10
2. 2.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 48 (d) 16
3. 3.What is the sum of the roots of x² − 14x + 48 = 0? (a) 14 (b) 13 (c) 15 (d) 48
4. 4.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 464 (c) 579 (d) 588
5. 5.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 2/3 (d) 1/3
6. 6.In which quadrant does the point (−1, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
7. 7.What is the missing term in the AP 11, 16, ?, 26, 31? (a) 22 (b) 20 (c) 26 (d) 21
8. 8.How many factors does 29 have? (a) 3 (b) 1 (c) 4 (d) 2
9. 9.In a class of 28 children, 17 like mangoes, 11 like bananas and 5 like both. How many like only mangoes? (a) 5 (b) 6 (c) 17 (d) 12
10. 10.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 21 (c) 30 (d) 36
11. 11.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) 21 (b) 14 (c) 15 (d) 22
12. 12.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 39 (c) 13 (d) 42
13. 13.A bag has 12 green balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 13 (b) 17 (c) 2 (d) 6
14. 14.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 30 (d) 15
15. 15.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 130° (b) 230° (c) 50° (d) 100°
16. 16.How many factors does 73 have? (a) 2 (b) 4 (c) 3 (d) 1
17. 17.What is the median of 2, 13, 8, 14, 31, 38 and 36? (a) 15 (b) 14 (c) 31 (d) 13
18. 18.In a class of 23 children, 12 like dance, 11 like music and 4 like both. How many like neither? (a) 5 (b) 8 (c) 0 (d) 4
19. 19.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 81 (b) 72 (c) 45 (d) 36
20. 20.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
21. 21.There are 4 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) 28 (b) 56 (c) 32 (d) 11
22. 22.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) 2 (b) 4 (c) 5 (d) 3
23. 23.What is the sum of the first 24 odd numbers (1 + 3 + 5 + …)? (a) 47 (b) 576 (c) 600 (d) 300
24. 24.What is the missing term in the AP 6, 11, ?, 21, 26? (a) 21 (b) 15 (c) 16 (d) 17
25. 25.A drawer has lots of yellow 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) 3 (b) 4 (c) 2 (d) 5
26. 26.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 69 (c) 66 (d) 198
27. 27.What is the product of the roots of x² − 16x + 63 = 0? (a) 64 (b) 63 (c) 16 (d) 62
28. 28.Two straight lines cross. One of the angles is 110°. What is the angle next to it on the same straight line? (a) 70° (b) 110° (c) 71° (d) 250°
29. 29.What is the midpoint of the line joining (4, 2) and (6, 4)? (a) (1, 1) (b) (5, 3) (c) (10, 6) (d) (3, 5)
30. 30.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
31. 31.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x − 8)(x − 9) (c) (x + 1)(x + 16) (d) (x + 1)(x + 72)
32. 32.In a class of 34 children, 8 like cricket, 23 like football and 4 like both. How many like at least one of the two? (a) 27 (b) 34 (c) 23 (d) 31
33. 33.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
34. 34.A bag has 6 yellow balls and 10 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 16 (b) 2 (c) 8 (d) 7
35. 35.A drawer has lots of blue, white 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) 6 (b) 3 (c) 4 (d) 2
36. 36.A canteen sells 3 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 15 (c) 18 (d) 30
37. 37.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 616 cm (c) 88 cm (d) 44 cm
38. 38.What is the 22nd term of the AP 12, 19, 26, 33, …? (a) 159 (b) 147 (c) 154 (d) 166
39. 39.If a + b = 20 and ab = 96, what is (a − b)²? (a) 400 (b) 4 (c) 16 (d) 208
40. 40.What is the mode of 1, 15, 1, 1, 6, 18 and 18? (a) 18 (b) 1 (c) 6 (d) 15

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