Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 734 · 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 smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 28 (c) 29 (d) 22
2. 2.In a class of 48 children, 26 like tea, 20 like coffee and 8 like neither. How many like both? (a) 40 (b) 6 (c) 8 (d) 7
3. 3.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 100° (c) 140° (d) 40°
4. 4.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
5. 5.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 95° (b) 5° (c) 10° (d) 85°
6. 6.What is the product of the roots of x² − 12x + 35 = 0? (a) 34 (b) 12 (c) 35 (d) 36
7. 7.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 100° (c) 20° (d) 10°
8. 8.In a class of 46 children, 18 like cricket, 21 like football and 3 like both. How many like at least one of the two? (a) 39 (b) 33 (c) 36 (d) 46
9. 9.What is the mean of 5, 5, 4, 18 and 18? (a) 12 (b) 11 (c) 9 (d) 10
10. 10.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 80° (b) 130° (c) 40° (d) 50°
11. 11.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) 189 (b) 63 (c) 66 (d) 21
12. 12.If a + b = 14 and ab = 40, what is (a − b)²? (a) 6 (b) 116 (c) 196 (d) 36
13. 13.In which quadrant does the point (3, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
14. 14.Two angles of a triangle are 30° and 25°. What is the third angle? (a) 155° (b) 125° (c) 55° (d) 150°
15. 15.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 130° (c) 65° (d) 50°
16. 16.What is the sum of all the whole numbers from 1 to 64? (a) 2016 (b) 4160 (c) 2048 (d) 2080
17. 17.How many factors does 15 have? (a) 5 (b) 2 (c) 3 (d) 4
18. 18.What is the mode of 7, 2, 16, 16, 7, 5 and 16? (a) 16 (b) 7 (c) 2 (d) 5
19. 19.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 3/8 (c) 3/5 (d) 1/4
20. 20.The mean of 4 numbers is 35. When the number 50 is added to them, what is the new mean? (a) 38 (b) 39 (c) 37 (d) 35
21. 21.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 15 (d) 12
22. 22.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
23. 23.What is the distance between the points (2, 13) and (11, 1)? (a) 15 (b) 225 (c) 21 (d) 16
24. 24.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 16 times (b) 8 times (c) 64 times (d) 4 times
25. 25.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 54 (c) 17 (d) 51
26. 26.What is the median of 13, 15, 33, 12, 24, 3 and 2? (a) 15 (b) 13 (c) 12 (d) 14
27. 27.In a class of 26 children, 17 like maths, 11 like science and 3 like neither. How many like both? (a) 2 (b) 23 (c) 3 (d) 5
28. 28.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
29. 29.A bag has 7 red balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 14 (b) 2 (c) 8 (d) 9
30. 30.In an isosceles triangle, the two equal angles are 70° each. What is the third angle? (a) 70° (b) 110° (c) 40° (d) 20°
31. 31.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
32. 32.A team of 2 players is to be chosen from 5 players. How many different teams are possible? (a) 25 (b) 20 (c) 10 (d) 11
33. 33.A bag has 12 white balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 13 (b) 2 (c) 14 (d) 23
34. 34.A canteen sells 4 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 7 (b) 16 (c) 12 (d) 24
35. 35.The mean of 6 numbers is 38. When the number 31 is added to them, what is the new mean? (a) 37 (b) 36 (c) 38 (d) 39
36. 36.What is the prime factorisation of 360? (a) 2² × 3² × 5 (b) 2⁴ × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5³
37. 37.What is the sum of the first 7 odd numbers (1 + 3 + 5 + …)? (a) 13 (b) 49 (c) 28 (d) 56
38. 38.In a class of 35 children, 21 like tea, 21 like coffee and 11 like both. How many like at least one of the two? (a) 42 (b) 31 (c) 35 (d) 20
39. 39.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 56 (c) 16 (d) 28
40. 40.If a + b = 10 and ab = 9, what is a² + b²? (a) 118 (b) 82 (c) 91 (d) 100

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