Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 705 · 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.How many prime numbers are there between 90 and 120? (a) 8 (b) 5 (c) 6 (d) 7
2. 2.In a class of 17 children, 8 like dance, 13 like music and 5 like both. How many like at least one of the two? (a) 11 (b) 21 (c) 17 (d) 16
3. 3.If every edge of a cube is made 5 times as long, how many times as big does its surface area become? (a) 10 times (b) 5 times (c) 125 times (d) 25 times
4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/36 (b) 1/18 (c) 1/11 (d) 1/12
5. 5.How many factors does 104 have? (a) 9 (b) 6 (c) 8 (d) 7
6. 6.What is the distance between the points (8, 13) and (17, 1)? (a) 21 (b) 16 (c) 225 (d) 15
7. 7.What is the prime factorisation of 21? (a) 3 × 7² (b) 3³ × 7 (c) 3 × 7 (d) 3² × 7
8. 8.A bag has 8 blue, 3 white and 9 red balls. One ball is taken out without looking. What is the probability that it is not red? (a) 9/20 (b) 11/20 (c) 3/5 (d) 1/3
9. 9.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 66 (c) 189 (d) 63
10. 10.In a class of 33 children, 25 like tea, 17 like coffee and 10 like both. How many like neither? (a) 2 (b) 10 (c) 1 (d) 11
11. 11.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
12. 12.A drawer has lots of 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) 5 (b) 4 (c) 2 (d) 3
13. 13.What is the median of 6, 10, 31, 18 and 4? (a) 18 (b) 31 (c) 10 (d) 6
14. 14.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm
15. 15.A bag has 5 white, 7 red and 9 blue balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 16/21 (c) 5/21 (d) 5/16
16. 16.Which is the correct factorisation of x² + 16x + 63? (a) (x + 1)(x + 15) (b) (x − 7)(x − 9) (c) (x + 7)(x + 9) (d) (x + 1)(x + 63)
17. 17.In a class of 33 children, 11 like cricket, 22 like football and 4 like neither. How many like both? (a) 3 (b) 5 (c) 4 (d) 29
18. 18.In a class of 39 children, 12 like tea, 25 like coffee and 5 like both. How many like neither? (a) 2 (b) 7 (c) 12 (d) 5
19. 19.In a class of 18 children, 13 like cricket, 6 like football and 3 like both. How many like only cricket? (a) 3 (b) 10 (c) 12 (d) 13
20. 20.A bag has 4 blue 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) 15 (c) 6 (d) 2
21. 21.What is the 31st term of the AP 10, 18, 26, 34, …? (a) 240 (b) 248 (c) 250 (d) 258
22. 22.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 120° (b) 60° (c) 115° (d) 125°
23. 23.In which quadrant does the point (2, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
24. 24.In which quadrant does the point (3, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
25. 25.Using (a + b)² = a² + 2ab + b², what is 74²? (a) 4916 (b) 5486 (c) 5476 (d) 4356
26. 26.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 3 times (d) 27 times
27. 27.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 64 cu cm (d) 65 cu cm
28. 28.Two angles of a triangle are 80° and 40°. What is the third angle? (a) 60° (b) 100° (c) 140° (d) 120°
29. 29.What is the prime factorisation of 24? (a) 2³ × 3 (b) 2² × 3 (c) 2 × 3³ (d) 2⁴ × 3
30. 30.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
31. 31.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 14 (b) 21 (c) 49 (d) 42
32. 32.Two straight lines cross. One of the angles is 55°. What is the angle next to it on the same straight line? (a) 125° (b) 55° (c) 305° (d) 35°
33. 33.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 42 (b) 49 (c) 21 (d) 28
34. 34.What is the sum of the first 11 terms of the AP 6, 12, 18, …? (a) 396 (b) 66 (c) 792 (d) 429
35. 35.What is the mean of 12, 5, 6, 19 and 18? (a) 10 (b) 15 (c) 12 (d) 13
36. 36.There are 4 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 16 (b) 7 (c) 24 (d) 12
37. 37.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 56 (c) 66 (d) 65
38. 38.What is the sum of the first 7 terms of the AP 1, 5, 9, …? (a) 105 (b) 182 (c) 25 (d) 91
39. 39.What is the 17th term of the AP 9, 16, 23, 30, …? (a) 128 (b) 119 (c) 112 (d) 121
40. 40.What is the sum of all the whole numbers from 1 to 90? (a) 4095 (b) 8190 (c) 4005 (d) 4050

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