Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 248 · 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 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) 22 (b) 14 (c) 15 (d) 21
2. 2.How many factors does 27 have? (a) 4 (b) 3 (c) 2 (d) 5
3. 3.There are 7 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 28 (b) 11 (c) 56 (d) 35
4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 9 (d) 20
5. 5.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 22 (b) 121 (c) 110 (d) 55
6. 6.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 328 (c) 290 (d) 327
7. 7.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 136 (c) 31 (d) 272
8. 8.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 1/4 (c) 5/6 (d) 2/3
9. 9.In a class of 22 children, 11 like maths, 14 like science and 8 like both. How many like only maths? (a) 3 (b) 8 (c) 11 (d) 6
10. 10.Two straight lines cross. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 100° (b) 40° (c) 140° (d) 280°
11. 11.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 110 (b) 100 (c) 19 (d) 55
12. 12.In a class of 38 children, 18 like mangoes, 24 like bananas and 4 like neither. How many like both? (a) 4 (b) 8 (c) 9 (d) 34
13. 13.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 72 (c) 36 (d) 81
14. 14.What is the distance between the points (0, 4) and (3, 0)? (a) 7 (b) 25 (c) 5 (d) 6
15. 15.What is the mean of 13, 4, 13, 6, 5 and 13? (a) 8 (b) 9 (c) 11 (d) 10
16. 16.A bag has 5 green balls and 3 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 6 (c) 7 (d) 8
17. 17.In a class of 34 children, 23 like mangoes, 18 like bananas and 9 like both. How many like at least one of the two? (a) 34 (b) 41 (c) 32 (d) 23
18. 18.In a class of 29 children, 22 like dance, 13 like music and 7 like both. How many like at least one of the two? (a) 29 (b) 35 (c) 21 (d) 28
19. 19.What is the midpoint of the line joining (0, 5) and (2, 9)? (a) (2, 14) (b) (7, 1) (c) (1, 7) (d) (1, 2)
20. 20.Which is the correct factorisation of x² + 8x + 12? (a) (x − 2)(x − 6) (b) (x + 1)(x + 7) (c) (x + 2)(x + 6) (d) (x + 1)(x + 12)
21. 21.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 85° (b) 95° (c) 265° (d) 86°
22. 22.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/6 (d) 1/2
23. 23.In which quadrant does the point (−7, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
24. 24.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 6 (c) 9 (d) 3
25. 25.What is the distance between the points (9, 2) and (14, 14)? (a) 17 (b) 14 (c) 13 (d) 169
26. 26.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/3 (c) 1/2 (d) 1/4
27. 27.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 36 (b) 72 (c) 81 (d) 18
28. 28.Two angles of a triangle are 35° and 95°. What is the exterior angle at the third corner? (a) 145° (b) 50° (c) 85° (d) 130°
29. 29.What are the roots of x² − 11x + 30 = 0? (a) 2 and 15 (b) 1 and 30 (c) 1 and 10 (d) 5 and 6
30. 30.How many factors does 51 have? (a) 2 (b) 4 (c) 5 (d) 3
31. 31.In a class of 16 children, 11 like mangoes, 7 like bananas and 4 like both. How many like only mangoes? (a) 9 (b) 11 (c) 3 (d) 7
32. 32.In which quadrant does the point (6, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
33. 33.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 570 (c) 452 (d) 571
34. 34.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 64 times (b) 16 times (c) 8 times (d) 4 times
35. 35.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
36. 36.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 30 (c) 12 (d) 15
37. 37.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
38. 38.If a + b = 19 and ab = 84, what is a² + b²? (a) 361 (b) 193 (c) 277 (d) 529
39. 39.What is the mode of 9, 9, 8, 6, 6, 6 and 4? (a) 4 (b) 8 (c) 9 (d) 6
40. 40.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x − 8)(x − 9) (c) (x + 1)(x + 16) (d) (x + 8)(x + 9)

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