Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 510 · 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 roots of x² − 15x + 54 = 0? (a) 14 (b) 54 (c) 16 (d) 15
2. 2.What is the mode of 15, 15, 8, 6, 11, 8 and 15? (a) 6 (b) 11 (c) 8 (d) 15
3. 3.In a class of 37 children, 27 like tea, 18 like coffee and 12 like both. How many like only tea? (a) 19 (b) 27 (c) 6 (d) 15
4. 4.In a class of 45 children, 18 like dance, 26 like music and 9 like neither. How many like both? (a) 8 (b) 7 (c) 9 (d) 36
5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 6 (b) 5 (c) 4 (d) 7
6. 6.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 4 times (c) 16 times (d) 64 times
7. 7.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
8. 8.In which quadrant does the point (7, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
9. 9.In a class of 38 children, 15 like cricket, 26 like football and 6 like both. How many like at least one of the two? (a) 35 (b) 38 (c) 41 (d) 29
10. 10.If a + b = 7 and ab = 12, what is (a − b)²? (a) 25 (b) 37 (c) 1 (d) 49
11. 11.What is the midpoint of the line joining (10, 1) and (16, 11)? (a) (6, 13) (b) (26, 12) (c) (13, 6) (d) (3, 5)
12. 12.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/4 (d) 3/8
13. 13.A drawer has lots of black 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) 4 (b) 5 (c) 2 (d) 3
14. 14.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 70° (b) 40° (c) 140° (d) 50°
15. 15.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 15 (c) 14 (d) 7
16. 16.How many factors does 33 have? (a) 2 (b) 5 (c) 3 (d) 4
17. 17.The mean of 4 numbers is 22. When the number 7 is added to them, what is the new mean? (a) 22 (b) 20 (c) 18 (d) 19
18. 18.In a class of 39 children, 15 like cricket, 25 like football and 8 like neither. How many like both? (a) 9 (b) 8 (c) 1 (d) 31
19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 3 (b) 1 (c) 2 (d) 4
20. 20.In how many different ways can the letters of the word TIGER be arranged? (a) 120 (b) 20 (c) 25 (d) 240
21. 21.What is the sum of the first 9 terms of the AP 8, 10, 12, …? (a) 24 (b) 153 (c) 144 (d) 288
22. 22.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 49 (b) 28 (c) 42 (d) 21
23. 23.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
24. 24.How many factors does 119 have? (a) 2 (b) 5 (c) 3 (d) 4
25. 25.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 132 sq cm (d) 5544 sq cm
26. 26.What is the smallest prime factor of 319? (a) 1 (b) 2 (c) 11 (d) 29
27. 27.What is the prime factorisation of 240? (a) 2³ × 3 × 5 (b) 2 × 3 × 5⁴ (c) 2⁴ × 3 × 5 (d) 2⁵ × 3 × 5
28. 28.The mean of 8 numbers is 34. When the number 61 is added to them, what is the new mean? (a) 37 (b) 34 (c) 36 (d) 38
29. 29.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
30. 30.A bag has 9 red balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 15 (b) 2 (c) 11 (d) 10
31. 31.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) 25 (c) 36 (d) 37
32. 32.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2² × 3⁴ (d) 2⁴ × 3²
33. 33.A drawer has lots of white, black, yellow 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) 8 (b) 5 (c) 2 (d) 4
34. 34.7 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 56 (b) 49 (c) 14 (d) 98
35. 35.How many prime numbers are there between 20 and 40? (a) 3 (b) 6 (c) 5 (d) 4
36. 36.What is the distance between the points (1, 2) and (6, 14)? (a) 169 (b) 13 (c) 17 (d) 14
37. 37.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 20 (c) 180 (d) 60
38. 38.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 54 (c) 18 (d) 162
39. 39.A bag has 6 red, 5 white and 6 blue balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/3 (b) 6/17 (c) 11/17 (d) 12/17
40. 40.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 285° (b) 15° (c) 75° (d) 105°

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