Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 719 · 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.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/5 (c) 1/4 (d) 3/8
2. 2.What is the distance between the points (2, 12) and (8, 4)? (a) 14 (b) 10 (c) 100 (d) 11
3. 3.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
4. 4.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 264 cm (c) 66 cm (d) 1386 cm
5. 5.What is the distance between the points (3, 13) and (9, 5)? (a) 100 (b) 10 (c) 14 (d) 11
6. 6.In a class of 25 children, 17 like dance, 16 like music and 3 like neither. How many like both? (a) 3 (b) 8 (c) 11 (d) 22
7. 7.What is the median of 27, 24, 3, 9, 13, 4 and 20? (a) 20 (b) 14 (c) 9 (d) 13
8. 8.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
9. 9.There are 3 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) 24 (b) 21 (c) 10 (d) 42
10. 10.What is the distance between the points (1, 9) and (7, 1)? (a) 100 (b) 10 (c) 11 (d) 14
11. 11.How many factors does 70 have? (a) 8 (b) 7 (c) 9 (d) 6
12. 12.A bag has 11 red balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 20 (b) 12 (c) 2 (d) 13
13. 13.Which term of the AP 16, 18, 20, 22, … is 42? (a) 15th (b) 13th (c) 21st (d) 14th
14. 14.How many factors does 15 have? (a) 4 (b) 2 (c) 3 (d) 5
15. 15.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 48 (c) 16 (d) 24
16. 16.How many prime numbers are there between 50 and 70? (a) 4 (b) 6 (c) 5 (d) 3
17. 17.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7 (c) 2 × 3 × 7² (d) 2² × 3 × 7
18. 18.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
19. 19.What is the distance between the points (1, 12) and (13, 3)? (a) 15 (b) 225 (c) 16 (d) 21
20. 20.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
21. 21.In a class of 28 children, 16 like dance, 18 like music and 6 like neither. How many like both? (a) 13 (b) 12 (c) 6 (d) 22
22. 22.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 70° (b) 160° (c) 20° (d) 80°
23. 23.In a class of 27 children, 14 like dance, 11 like music and 7 like both. How many like at least one of the two? (a) 25 (b) 11 (c) 27 (d) 18
24. 24.A drawer has lots of black, white, green, red and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 2 (c) 6 (d) 5
25. 25.What is the median of 1, 39, 32, 6, 24, 33 and 36? (a) 6 (b) 33 (c) 32 (d) 24
26. 26.Two angles of a triangle are 50° and 95°. What is the exterior angle at the third corner? (a) 35° (b) 85° (c) 145° (d) 130°
27. 27.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 552 (c) 561 (d) 446
28. 28.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
29. 29.In a class of 27 children, 12 like dance, 21 like music and 9 like both. How many like at least one of the two? (a) 27 (b) 33 (c) 24 (d) 15
30. 30.What is the sum of the first 7 terms of the AP 10, 11, 12, …? (a) 182 (b) 91 (c) 16 (d) 92
31. 31.How many factors does 43 have? (a) 2 (b) 3 (c) 1 (d) 4
32. 32.A drawer has lots of red, yellow, black, 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) 2 (b) 5 (c) 6 (d) 10
33. 33.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 130° (b) 110° (c) 160° (d) 70°
34. 34.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 121 (b) 55 (c) 66 (d) 110
35. 35.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 3/4 (c) 1/4 (d) 1/3
36. 36.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 3 (c) 12 (d) 6
37. 37.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) 15 (c) 21 (d) 14
38. 38.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 10° (d) 20°
39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 2 (b) 5 (c) 4 (d) 3
40. 40.What is the sum of all the whole numbers from 1 to 31? (a) 465 (b) 992 (c) 496 (d) 497

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