Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 538 · 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 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
2. 2.What is the mean of 17, 20, 9, 16 and 23? (a) 18 (b) 19 (c) 17 (d) 16
3. 3.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
4. 4.What is the sum of the roots of x² − 14x + 48 = 0? (a) 14 (b) 15 (c) 13 (d) 48
5. 5.8 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) 15 (b) 112 (c) 64 (d) 56
6. 6.What is the median of 5, 11, 13, 3 and 29? (a) 11 (b) 5 (c) 12 (d) 13
7. 7.If a + b = 20 and ab = 99, what is (a − b)²? (a) 202 (b) 2 (c) 4 (d) 400
8. 8.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 50° (b) 70° (c) 140° (d) 40°
9. 9.In which quadrant does the point (9, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
10. 10.A drawer has lots of yellow, white, black and green 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) 8 (c) 4 (d) 2
11. 11.A drawer has lots of yellow, green, blue and red 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) 4 (c) 5 (d) 8
12. 12.In a class of 21 children, 15 like cricket, 12 like football and 1 like neither. How many like both? (a) 7 (b) 20 (c) 1 (d) 6
13. 13.The mean of 5 numbers is 22. When the number 4 is added to them, what is the new mean? (a) 13 (b) 19 (c) 22 (d) 20
14. 14.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2 × 3 (c) 2² × 3 (d) 2 × 3²
15. 15.Using (a − b)² = a² − 2ab + b², what is 47²? (a) 2491 (b) 2809 (c) 2219 (d) 2209
16. 16.What is the mode of 3, 12, 19, 12, 12, 10 and 3? (a) 10 (b) 3 (c) 19 (d) 12
17. 17.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 396 (c) 397 (d) 387
18. 18.A drawer has lots of white, blue and black 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) 6 (c) 4 (d) 3
19. 19.The mean of 5 numbers is 30. When the number 6 is added to them, what is the new mean? (a) 18 (b) 27 (c) 26 (d) 30
20. 20.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 1/2 (c) 3/4 (d) 1/4
21. 21.How many prime numbers are there between 90 and 120? (a) 5 (b) 6 (c) 7 (d) 8
22. 22.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 50° (b) 10° (c) 100° (d) 80°
23. 23.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 110° (b) 70° (c) 20° (d) 40°
24. 24.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 30° (b) 16° (c) 15° (d) 165°
25. 25.What is the median of 7, 32, 40, 4, 10, 38 and 23? (a) 4 (b) 32 (c) 23 (d) 22
26. 26.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 55° (b) 145° (c) 325° (d) 35°
27. 27.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/3 (c) 1/2 (d) 2/3
28. 28.What is the smallest prime factor of 143? (a) 13 (b) 2 (c) 11 (d) 1
29. 29.What is the product of the roots of x² − 15x + 54 = 0? (a) 53 (b) 55 (c) 15 (d) 54
30. 30.A bag has 7 red balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 8 (c) 2 (d) 12
31. 31.What is the sum of the first 13 odd numbers (1 + 3 + 5 + …)? (a) 91 (b) 25 (c) 182 (d) 169
32. 32.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) 24 (b) 12 (c) 13 (d) 25
33. 33.What is the prime factorisation of 21? (a) 3 × 7² (b) 3³ × 7 (c) 3 × 7 (d) 3² × 7
34. 34.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
35. 35.A bag has 10 black balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 18 (c) 2 (d) 11
36. 36.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 22 cm (d) 154 cm
37. 37.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 10 times (c) 5 times (d) 125 times
38. 38.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 150° (c) 30° (d) 210°
39. 39.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 20 (c) 240 (d) 120
40. 40.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6084 (b) 6734 (c) 6724 (d) 6404

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