Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 427 · 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 area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
2. 2.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 50° (c) 40° (d) 100°
3. 3.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
4. 4.What is the median of 38, 17, 26, 13 and 35? (a) 17 (b) 26 (c) 27 (d) 35
5. 5.What is the median of 29, 23, 3, 12 and 7? (a) 7 (b) 23 (c) 3 (d) 12
6. 6.In which quadrant does the point (9, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
7. 7.8 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 48 (b) 80 (c) 40 (d) 13
8. 8.A bag has 9 green, 8 blue and 3 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 1/3 (b) 3/20 (c) 17/20 (d) 3/17
9. 9.A bag has 5 yellow balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 6 (b) 2 (c) 7 (d) 14
10. 10.What is the mean of 13, 20, 13 and 2? (a) 11 (b) 16 (c) 13 (d) 12
11. 11.How many factors does 52 have? (a) 4 (b) 6 (c) 5 (d) 7
12. 12.What is the mean of 9, 13, 15, 6, 8 and 9? (a) 9 (b) 11 (c) 12 (d) 10
13. 13.If a + b = 14 and ab = 40, what is a² + b²? (a) 276 (b) 156 (c) 116 (d) 196
14. 14.What is the mean of 5, 16, 10, 10 and 14? (a) 12 (b) 13 (c) 11 (d) 10
15. 15.What is the prime factorisation of 105? (a) 3 × 5 × 7² (b) 3² × 5 × 7 (c) 3 × 5 × 7 (d) 3³ × 5 × 7
16. 16.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 144 (c) 51 (d) 16
17. 17.A bag has 7 red balls and 8 black 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) 15 (c) 8 (d) 2
18. 18.What is the smallest prime factor of 253? (a) 23 (b) 11 (c) 1 (d) 2
19. 19.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) 25 (b) 36 (c) 37 (d) 24
20. 20.Two angles of a triangle are 45° and 75°. What is the exterior angle at the third corner? (a) 120° (b) 60° (c) 105° (d) 135°
21. 21.A drawer has lots of yellow, red 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) 4 (c) 3 (d) 6
22. 22.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) 14 (b) 7 (c) 8 (d) 15
23. 23.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/3 (c) 2/3 (d) 1/2
24. 24.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 150° (b) 130° (c) 80° (d) 100°
25. 25.Using (a + b)² = a² + 2ab + b², what is 72²? (a) 5194 (b) 4624 (c) 5184 (d) 4904
26. 26.A fair dice is rolled once. What is the probability of getting a number greater than 1? (a) 5/6 (b) 1/5 (c) 1/3 (d) 1/6
27. 27.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
28. 28.A bag has 2 red, 9 green and 2 blue balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 2/13 (c) 2/11 (d) 11/13
29. 29.What is the median of 5, 2, 7, 12 and 38? (a) 5 (b) 8 (c) 7 (d) 12
30. 30.What is the median of 22, 37, 12, 6, 25, 16 and 14? (a) 16 (b) 6 (c) 22 (d) 14
31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 8 (b) 5 (c) 6 (d) 7
32. 32.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) 42 (b) 21 (c) 24 (d) 10
33. 33.What is the 22nd term of the AP 7, 15, 23, 31, …? (a) 176 (b) 183 (c) 168 (d) 175
34. 34.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 110° (b) 20° (c) 70° (d) 55°
35. 35.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 300° (c) 150° (d) 120°
36. 36.Two straight lines cross. Two vertically opposite angles add up to 290°. What is each of the other two angles? (a) 36° (b) 70° (c) 145° (d) 35°
37. 37.The mean of 6 numbers is 16. When the number 44 is added to them, what is the new mean? (a) 30 (b) 21 (c) 20 (d) 16
38. 38.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/3 (c) 1/4 (d) 1/2
39. 39.What are the roots of x² − 17x + 72 = 0? (a) 1 and 72 (b) 2 and 36 (c) 8 and 9 (d) 1 and 16
40. 40.If a + b = 20 and ab = 96, what is (a − b)²? (a) 4 (b) 208 (c) 400 (d) 16

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