Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 71 · 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.In a class of 19 children, 13 like maths, 13 like science and 9 like both. How many like at least one of the two? (a) 26 (b) 8 (c) 19 (d) 17
2. 2.What is the median of 3, 38, 28, 29, 31, 37 and 25? (a) 30 (b) 29 (c) 31 (d) 28
3. 3.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 4/11 (c) 1/9 (d) 1/11
5. 5.In a class of 34 children, 18 like dance, 16 like music and 4 like both. How many like neither? (a) 5 (b) 4 (c) 0 (d) 8
6. 6.A bag has 4 white balls and 7 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 5 (c) 6 (d) 11
7. 7.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 66 cm (d) 1386 cm
8. 8.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
9. 9.What is the prime factorisation of 45? (a) 3³ × 5 (b) 3 × 5² (c) 3² × 5 (d) 3 × 5
10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 16 (b) 17 (c) 7 (d) 18
11. 11.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
12. 12.If a + b = 18 and ab = 72, what is (a − b)²? (a) 6 (b) 36 (c) 324 (d) 180
13. 13.How many factors does 95 have? (a) 4 (b) 3 (c) 2 (d) 5
14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 4 (b) 3 (c) 5 (d) 2
15. 15.In a class of 35 children, 22 like tea, 13 like coffee and 10 like both. How many like only tea? (a) 10 (b) 3 (c) 22 (d) 12
16. 16.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 88 cm (d) 22 cm
17. 17.What is the smallest prime factor of 221? (a) 2 (b) 1 (c) 13 (d) 17
18. 18.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 28 (b) 56 (c) 64 (d) 36
19. 19.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 30) (b) (x + 1)(x + 10) (c) (x + 5)(x + 6) (d) (x − 5)(x − 6)
20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
21. 21.What is the sum of the roots of x² − 14x + 48 = 0? (a) 48 (b) 13 (c) 14 (d) 15
22. 22.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 24 (d) 12
23. 23.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 9 (d) 7
24. 24.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 613 (c) 480 (d) 603
25. 25.There are 5 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 25 (b) 30 (c) 10 (d) 50
26. 26.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) 14 (b) 21 (c) 22 (d) 15
27. 27.Two angles of a triangle are 35° and 115°. What is the third angle? (a) 30° (b) 145° (c) 65° (d) 150°
28. 28.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 95° (b) 85° (c) 86° (d) 265°
29. 29.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 5/6 (b) 1/4 (c) 2/3 (d) 1/3
30. 30.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 77 sq cm (d) 154 sq cm
31. 31.In a class of 28 children, 21 like maths, 9 like science and 4 like both. How many like only maths? (a) 19 (b) 21 (c) 17 (d) 5
32. 32.What is the median of 3, 35, 8, 29 and 24? (a) 29 (b) 8 (c) 25 (d) 24
33. 33.Using (a − b)² = a² − 2ab + b², what is 35²? (a) 1235 (b) 1575 (c) 1225 (d) 2025
34. 34.A bag has 5 red balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 7 (c) 17 (d) 6
35. 35.How many factors does 55 have? (a) 4 (b) 2 (c) 3 (d) 5
36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 52? (a) 15 (b) 14 (c) 16 (d) 5
37. 37.What is the midpoint of the line joining (8, 3) and (20, 5)? (a) (6, 1) (b) (4, 14) (c) (14, 4) (d) (28, 8)
38. 38.What is the median of 8, 23, 3, 11 and 28? (a) 11 (b) 3 (c) 23 (d) 8
39. 39.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 14 (b) 21 (c) 28 (d) 9
40. 40.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 240 (c) 20 (d) 120

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