Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 745 · 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.If a + b = 20 and ab = 96, what is (a − b)²? (a) 16 (b) 400 (c) 208 (d) 4
2. 2.In a class of 41 children, 31 like mangoes, 17 like bananas and 11 like both. How many like only mangoes? (a) 20 (b) 24 (c) 6 (d) 31
3. 3.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 5/6 (b) 2/3 (c) 1/3 (d) 1/4
4. 4.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 125 times (c) 10 times (d) 25 times
5. 5.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
6. 6.Which term of the AP 16, 19, 22, 25, … is 91? (a) 25th (b) 28th (c) 27th (d) 26th
7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
8. 8.A bag has 9 blue, 6 green and 4 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 9/19 (b) 9/10 (c) 1/3 (d) 10/19
9. 9.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/3 (b) 1/6 (c) 5/6 (d) 1/5
10. 10.A fair dice is rolled once. What is the probability of getting a number greater than 2? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
11. 11.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
12. 12.What is the product of the roots of x² − 15x + 56 = 0? (a) 55 (b) 15 (c) 57 (d) 56
13. 13.A drawer has lots of black, green, yellow, red 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) 6 (b) 5 (c) 10 (d) 2
14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
15. 15.What is the sum of the first 26 odd numbers (1 + 3 + 5 + …)? (a) 51 (b) 676 (c) 351 (d) 702
16. 16.In a class of 20 children, 9 like maths, 11 like science and 4 like neither. How many like both? (a) 16 (b) 3 (c) 4 (d) 5
17. 17.A bag has 6 green, 2 yellow and 7 white balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 2/15 (b) 1/3 (c) 13/15 (d) 2/13
18. 18.In which quadrant does the point (1, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
19. 19.Which is the correct factorisation of x² + 7x + 10? (a) (x + 2)(x + 5) (b) (x − 2)(x − 5) (c) (x + 1)(x + 6) (d) (x + 1)(x + 10)
20. 20.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 24 (c) 48 (d) 16
21. 21.What is the sum of the first 17 odd numbers (1 + 3 + 5 + …)? (a) 306 (b) 33 (c) 289 (d) 153
22. 22.In which quadrant does the point (6, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
23. 23.A bag has 2 yellow, 2 red and 7 blue balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 2/9 (b) 9/11 (c) 1/3 (d) 2/11
24. 24.What is the product of the roots of x² − 11x + 28 = 0? (a) 11 (b) 29 (c) 28 (d) 27
25. 25.If a + b = 11 and ab = 18, what is (a − b)²? (a) 121 (b) 7 (c) 85 (d) 49
26. 26.What is the median of 26, 6, 25, 2, 13, 33 and 32? (a) 13 (b) 26 (c) 25 (d) 2
27. 27.A canteen sells 7 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 10 (c) 21 (d) 28
28. 28.What is the mean of 20, 3, 7 and 14? (a) 12 (b) 13 (c) 10 (d) 11
29. 29.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 110 (c) 92 (d) 101
30. 30.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 30 (c) 36 (d) 12
31. 31.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 30° (c) 110° (d) 150°
32. 32.What is the distance between the points (5, 16) and (10, 4)? (a) 169 (b) 13 (c) 17 (d) 14
33. 33.In a class of 23 children, 8 like cricket, 12 like football and 8 like neither. How many like both? (a) 8 (b) 5 (c) 6 (d) 15
34. 34.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 10° (c) 80° (d) 20°
35. 35.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 8 times (c) 5 times (d) 4 times
36. 36.How many factors does 47 have? (a) 3 (b) 1 (c) 2 (d) 4
37. 37.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 121 (c) 22 (d) 55
38. 38.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 189 (c) 63 (d) 21
39. 39.A bag has 9 red, 2 white and 6 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 11/17 (c) 6/11 (d) 6/17
40. 40.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) 36 (b) 48 (c) 49 (d) 37

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