Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 706 · 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.Two angles of a triangle are 60° and 55°. What is the third angle? (a) 120° (b) 115° (c) 125° (d) 65°
2. 2.A bag has 3 green, 9 white and 2 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 6/7 (b) 13/14 (c) 1/7 (d) 1/3
3. 3.There are 5 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 15 (c) 20 (d) 7
4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
5. 5.How many prime numbers are there between 40 and 70? (a) 8 (b) 9 (c) 6 (d) 7
6. 6.Which term of the AP 5, 10, 15, 20, … is 40? (a) 7th (b) 10th (c) 9th (d) 8th
7. 7.What is the mode of 4, 15, 8, 16, 4, 8 and 8? (a) 15 (b) 16 (c) 4 (d) 8
8. 8.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 24 (b) 37 (c) 36 (d) 25
9. 9.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) 5 (b) 2 (c) 3 (d) 4
10. 10.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 630 (c) 498 (d) 639
11. 11.What is the prime factorisation of 30? (a) 2² × 3 × 5 (b) 2 × 3 × 5² (c) 2³ × 3 × 5 (d) 2 × 3 × 5
12. 12.In a class of 34 children, 18 like dance, 16 like music and 9 like neither. How many like both? (a) 25 (b) 9 (c) 10 (d) 8
13. 13.Two angles of a triangle are 80° and 75°. What is the third angle? (a) 25° (b) 105° (c) 155° (d) 100°
14. 14.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) 4 times (c) 8 times (d) 5 times
15. 15.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
16. 16.The mean of 3 numbers is 40. When the number 32 is added to them, what is the new mean? (a) 39 (b) 40 (c) 36 (d) 38
17. 17.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 3/4 (c) 1/2 (d) 1/4
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/11 (b) 2/11 (c) 1/18 (d) 1/12
19. 19.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
20. 20.How many factors does 71 have? (a) 3 (b) 4 (c) 1 (d) 2
21. 21.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 1/11 (c) 4/11 (d) 1/9
23. 23.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 15 (b) 30 (c) 12 (d) 36
24. 24.In a class of 31 children, 16 like dance, 19 like music and 4 like neither. How many like both? (a) 9 (b) 27 (c) 8 (d) 4
25. 25.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
26. 26.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) 25 (c) 24 (d) 13
27. 27.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
28. 28.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 784 (b) 406 (c) 812 (d) 55
29. 29.What is the sum of the roots of x² − 13x + 42 = 0? (a) 42 (b) 12 (c) 14 (d) 13
30. 30.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 48 (d) 24
31. 31.The mean of 4 numbers is 26. When the number 31 is added to them, what is the new mean? (a) 26 (b) 28 (c) 27 (d) 29
32. 32.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 523 (b) 420 (c) 513 (d) 522
33. 33.What is the midpoint of the line joining (4, 0) and (16, 12)? (a) (20, 12) (b) (10, 6) (c) (6, 10) (d) (6, 6)
34. 34.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
35. 35.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 100 (b) 20 (c) 45 (d) 90
36. 36.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 5 (d) 14
37. 37.A bag has 6 black balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 15 (d) 7
38. 38.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 220 cm (d) 440 cm
39. 39.What is the product of the roots of x² − 12x + 27 = 0? (a) 27 (b) 26 (c) 12 (d) 28
40. 40.There are 7 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 49 (b) 56 (c) 98 (d) 14

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