Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 484 · 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 the first 7 terms of the AP 8, 12, 16, …? (a) 154 (b) 32 (c) 140 (d) 280
2. 2.What is the midpoint of the line joining (2, 4) and (4, 6)? (a) (6, 10) (b) (3, 5) (c) (5, 3) (d) (1, 1)
3. 3.What is the smallest prime factor of 169? (a) 2 (b) 1 (c) 13 (d) 3
4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 14 (b) 4 (c) 16 (d) 15
5. 5.Two angles of a triangle are 30° and 55°. What is the exterior angle at the third corner? (a) 150° (b) 95° (c) 85° (d) 125°
6. 6.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 65° (c) 40° (d) 50°
7. 7.What is the median of 21, 33, 25, 15, 30, 10 and 5? (a) 25 (b) 22 (c) 15 (d) 21
8. 8.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 35 (b) 171 (c) 324 (d) 342
9. 9.What is the median of 27, 26, 24, 19 and 34? (a) 24 (b) 27 (c) 25 (d) 26
10. 10.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 21 (c) 22 (d) 29
11. 11.A cube has edges of 7 cm. What is its volume? (a) 196 cu cm (b) 21 cu cm (c) 343 cu cm (d) 294 cu cm
12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 46? (a) 3 (b) 5 (c) 2 (d) 4
13. 13.What is the mean of 10, 13, 18, 9, 16 and 24? (a) 15 (b) 18 (c) 14 (d) 16
14. 14.A bag has 7 white, 9 yellow and 5 blue balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 4/7 (b) 13/21 (c) 1/3 (d) 3/7
15. 15.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 88 cm (c) 176 cm (d) 44 cm
16. 16.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 24) (b) (x − 4)(x − 6) (c) (x + 1)(x + 9) (d) (x + 4)(x + 6)
17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
18. 18.In how many different ways can the letters of the word PLANT be arranged? (a) 20 (b) 120 (c) 240 (d) 25
19. 19.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 36 (c) 15 (d) 30
20. 20.A drawer has lots of red, yellow, blue 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) 2 (b) 5 (c) 8 (d) 4
21. 21.How many prime numbers are there between 40 and 50? (a) 3 (b) 5 (c) 4 (d) 2
22. 22.A bag has 7 black balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 8 (b) 2 (c) 11 (d) 5
23. 23.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) 30 (d) 18
24. 24.In a class of 39 children, 18 like tea, 16 like coffee and 4 like both. How many like at least one of the two? (a) 26 (b) 34 (c) 30 (d) 39
25. 25.Two straight lines cross. One of the angles is 30°. What is the angle next to it on the same straight line? (a) 330° (b) 30° (c) 150° (d) 60°
26. 26.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 cm (b) 1386 cm (c) 264 cm (d) 66 cm
27. 27.What is the distance between the points (3, 9) and (10, 33)? (a) 26 (b) 625 (c) 31 (d) 25
28. 28.How many factors does 42 have? (a) 9 (b) 6 (c) 7 (d) 8
29. 29.In a class of 46 children, 25 like dance, 24 like music and 9 like both. How many like at least one of the two? (a) 40 (b) 49 (c) 46 (d) 31
30. 30.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 110° (b) 85° (c) 165° (d) 15°
31. 31.The mean of 5 numbers is 23. When the number 47 is added to them, what is the new mean? (a) 27 (b) 23 (c) 28 (d) 35
32. 32.The mean of 4 numbers is 16. When the number 1 is added to them, what is the new mean? (a) 13 (b) 16 (c) 14 (d) 12
33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 15 (b) 13 (c) 4 (d) 14
34. 34.In a class of 39 children, 19 like dance, 28 like music and 9 like both. How many like neither? (a) 2 (b) 9 (c) 1 (d) 10
35. 35.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 110 (c) 55 (d) 22
36. 36.A bag has 9 yellow 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) 2 (b) 13 (c) 21 (d) 10
37. 37.A drawer has lots of blue, red and black 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) 6 (c) 3 (d) 2
38. 38.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 20 (c) 25 (d) 240
39. 39.A bag has 3 white balls and 4 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 7 (c) 5 (d) 4
40. 40.How many factors does 85 have? (a) 4 (b) 3 (c) 2 (d) 5

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