Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 55 · 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.A canteen sells 4 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 40 (b) 20 (c) 9 (d) 24
2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 7 (d) 5
3. 3.A drawer has lots of black, blue 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) 2 (c) 4 (d) 3
4. 4.What is the sum of all the whole numbers from 1 to 78? (a) 6162 (b) 3042 (c) 3081 (d) 3003
5. 5.In a class of 28 children, 11 like mangoes, 13 like bananas and 10 like neither. How many like both? (a) 10 (b) 18 (c) 6 (d) 7
6. 6.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 1/4 (c) 3/8 (d) 7/8
7. 7.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) 12 (b) 13 (c) 25 (d) 24
8. 8.What is the 14th term of the AP 4, 8, 12, 16, …? (a) 60 (b) 57 (c) 52 (d) 56
9. 9.In a league, 13 teams each play every other team once. How many matches are played? (a) 78 (b) 91 (c) 156 (d) 169
10. 10.The mean of 5 numbers is 34. When the number 40 is added to them, what is the new mean? (a) 34 (b) 36 (c) 35 (d) 37
11. 11.In a class of 25 children, 13 like dance, 15 like music and 6 like both. How many like neither? (a) 9 (b) 6 (c) 4 (d) 3
12. 12.Two angles of a triangle are 80° and 20°. What is the third angle? (a) 80° (b) 160° (c) 260° (d) 100°
13. 13.What is the mode of 12, 19, 2, 13, 19, 13 and 19? (a) 13 (b) 2 (c) 19 (d) 12
14. 14.How many prime numbers are there between 90 and 100? (a) 1 (b) 2 (c) 3 (d) 0
15. 15.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 27 (c) 81 (d) 30
16. 16.In a class of 26 children, 15 like mangoes, 16 like bananas and 6 like both. How many like at least one of the two? (a) 26 (b) 31 (c) 19 (d) 25
17. 17.A canteen sells 8 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 32 (c) 24 (d) 48
18. 18.Which is the correct factorisation of x² + 11x + 18? (a) (x − 2)(x − 9) (b) (x + 2)(x + 9) (c) (x + 1)(x + 10) (d) (x + 1)(x + 18)
19. 19.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/9 (b) 1/11 (c) 3/11 (d) 1/12
20. 20.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 172 (c) 163 (d) 164
21. 21.How many factors does 41 have? (a) 1 (b) 3 (c) 4 (d) 2
22. 22.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 155° (b) 85° (c) 110° (d) 95°
23. 23.In which quadrant does the point (2, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
24. 24.Two angles of a triangle are 45° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 135° (d) 85°
25. 25.What is the median of 5, 37, 23, 7 and 17? (a) 7 (b) 18 (c) 17 (d) 23
26. 26.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 495 (c) 496 (d) 402
27. 27.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x − 7)(x − 8) (c) (x + 1)(x + 14) (d) (x + 7)(x + 8)
28. 28.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 8 times (d) 5 times
29. 29.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 12 (c) 108 (d) 39
30. 30.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 70° (c) 140° (d) 110°
31. 31.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 15° (d) 75°
32. 32.Which term of the AP 2, 6, 10, 14, … is 150? (a) 37th (b) 40th (c) 39th (d) 38th
33. 33.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
34. 34.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 145° (b) 155° (c) 35° (d) 60°
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 3/11 (d) 1/11
36. 36.A bag has 3 white balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 14 (c) 2 (d) 4
37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
38. 38.Which is the correct factorisation of x² + 10x + 21? (a) (x − 3)(x − 7) (b) (x + 3)(x + 7) (c) (x + 1)(x + 21) (d) (x + 1)(x + 9)
39. 39.A bag has 3 black balls and 12 blue 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) 2 (c) 15 (d) 4
40. 40.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 3 (d) 6

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