Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 905 · 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 sum of all the whole numbers from 1 to 46? (a) 1058 (b) 1035 (c) 2162 (d) 1081
2. 2.What is the midpoint of the line joining (1, 7) and (7, 9)? (a) (3, 1) (b) (8, 16) (c) (4, 8) (d) (8, 4)
3. 3.In a class of 36 children, 30 like maths, 15 like science and 12 like both. How many like only maths? (a) 18 (b) 21 (c) 30 (d) 3
4. 4.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
5. 5.If a + b = 12 and ab = 11, what is a² + b²? (a) 144 (b) 122 (c) 133 (d) 166
6. 6.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
7. 7.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
8. 8.In a class of 46 children, 23 like cricket, 30 like football and 12 like both. How many like neither? (a) 5 (b) 6 (c) 12 (d) 17
9. 9.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 1/8 (c) 1/4 (d) 7/8
10. 10.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 693 sq cm
11. 11.In a class of 33 children, 17 like cricket, 18 like football and 7 like both. How many like neither? (a) 5 (b) 12 (c) 6 (d) 7
12. 12.What is the distance between the points (1, 13) and (7, 5)? (a) 10 (b) 100 (c) 11 (d) 14
13. 13.What is the smallest prime factor of 55? (a) 5 (b) 1 (c) 2 (d) 11
14. 14.What is the 13th term of the AP 3, 7, 11, 15, …? (a) 55 (b) 48 (c) 52 (d) 51
15. 15.The mean of 6 numbers is 28. When the number 35 is added to them, what is the new mean? (a) 31 (b) 30 (c) 29 (d) 28
16. 16.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
17. 17.A drawer has lots of white 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) 4 (b) 2 (c) 5 (d) 3
18. 18.In a class of 39 children, 16 like dance, 19 like music and 6 like both. How many like neither? (a) 16 (b) 4 (c) 6 (d) 10
19. 19.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 57 (c) 48 (d) 58
20. 20.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
21. 21.What is the sum of all the whole numbers from 1 to 98? (a) 4851 (b) 9702 (c) 4753 (d) 4802
22. 22.In a class of 43 children, 18 like maths, 19 like science and 8 like neither. How many like both? (a) 2 (b) 8 (c) 3 (d) 35
23. 23.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 45° (b) 155° (c) 160° (d) 20°
24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 18 (d) 20
25. 25.What is the 10th term of the AP 16, 22, 28, 34, …? (a) 60 (b) 54 (c) 76 (d) 70
26. 26.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) 36 (c) 49 (d) 37
27. 27.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 300° (c) 150° (d) 120°
28. 28.Two angles of a triangle are 75° and 70°. What is the third angle? (a) 105° (b) 35° (c) 110° (d) 145°
29. 29.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 40) (b) (x + 1)(x + 12) (c) (x − 5)(x − 8) (d) (x + 5)(x + 8)
30. 30.A bag has 10 white balls and 6 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 11 (d) 16
31. 31.What is the mean of 3, 10, 15, 17 and 5? (a) 11 (b) 9 (c) 12 (d) 10
32. 32.How many prime numbers are there between 40 and 60? (a) 4 (b) 6 (c) 7 (d) 5
33. 33.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/4 (d) 3/8
34. 34.What is the distance between the points (0, 3) and (7, 27)? (a) 26 (b) 25 (c) 31 (d) 625
35. 35.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 484 (c) 483 (d) 394
36. 36.In a class of 25 children, 14 like mangoes, 18 like bananas and 11 like both. How many like at least one of the two? (a) 21 (b) 10 (c) 25 (d) 32
37. 37.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
38. 38.Two angles of a triangle are 75° and 40°. What is the exterior angle at the third corner? (a) 115° (b) 140° (c) 65° (d) 105°
39. 39.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
40. 40.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm

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