Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 326 · 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 three of them were born in the same day of the week? (a) 22 (b) 15 (c) 14 (d) 21
2. 2.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 42 (c) 45 (d) 14
3. 3.In a class of 29 children, 14 like dance, 11 like music and 8 like neither. How many like both? (a) 8 (b) 5 (c) 21 (d) 4
4. 4.Which is the correct factorisation of x² + 8x + 12? (a) (x − 2)(x − 6) (b) (x + 1)(x + 7) (c) (x + 1)(x + 12) (d) (x + 2)(x + 6)
5. 5.What is the median of 5, 16, 13, 33 and 22? (a) 17 (b) 22 (c) 16 (d) 13
6. 6.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) 15 (b) 14 (c) 7 (d) 8
7. 7.A bag has 10 blue balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 11 (c) 13 (d) 12
8. 8.In a class of 26 children, 8 like cricket, 18 like football and 5 like both. How many like at least one of the two? (a) 21 (b) 16 (c) 22 (d) 26
9. 9.What is the smallest prime factor of 377? (a) 29 (b) 13 (c) 1 (d) 2
10. 10.What is the distance between the points (0, 15) and (8, 9)? (a) 11 (b) 14 (c) 100 (d) 10
11. 11.If a + b = 19 and ab = 84, what is (a − b)²? (a) 25 (b) 361 (c) 5 (d) 193
12. 12.Two angles of a triangle are 20° and 25°. What is the exterior angle at the third corner? (a) 160° (b) 45° (c) 135° (d) 155°
13. 13.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 46° (b) 55° (c) 45° (d) 90°
14. 14.A cuboid is 11 cm long, 2 cm wide and 7 cm high. What is its volume? (a) 226 cu cm (b) 20 cu cm (c) 22 cu cm (d) 154 cu cm
15. 15.Using (a + b)² = a² + 2ab + b², what is 34²? (a) 1166 (b) 1156 (c) 916 (d) 676
16. 16.Which is the correct factorisation of x² + 10x + 16? (a) (x + 1)(x + 16) (b) (x + 2)(x + 8) (c) (x + 1)(x + 9) (d) (x − 2)(x − 8)
17. 17.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
18. 18.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 22 (b) 110 (c) 55 (d) 121
19. 19.In a class of 18 children, 12 like cricket, 6 like football and 3 like both. How many like at least one of the two? (a) 16 (b) 12 (c) 18 (d) 15
20. 20.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 4 times (c) 8 times (d) 16 times
21. 21.A bag has 5 green, 4 yellow and 5 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 5/9 (b) 5/14 (c) 1/3 (d) 9/14
22. 22.What is the 12th term of the AP 19, 21, 23, 25, …? (a) 24 (b) 41 (c) 22 (d) 43
23. 23.How many factors does 97 have? (a) 4 (b) 3 (c) 2 (d) 1
24. 24.In which quadrant does the point (−1, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
25. 25.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 12 (d) 15
26. 26.What is the sum of all the whole numbers from 1 to 14? (a) 98 (b) 91 (c) 105 (d) 210
27. 27.Using (a − b)² = a² − 2ab + b², what is 46²? (a) 2116 (b) 2126 (c) 2484 (d) 2916
28. 28.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 36 (c) 30 (d) 15
29. 29.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
30. 30.What is the distance between the points (1, 9) and (6, 21)? (a) 17 (b) 14 (c) 169 (d) 13
31. 31.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/3 (b) 2/3 (c) 5/6 (d) 1/4
32. 32.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/2 (c) 1/3 (d) 2/3
33. 33.In a class of 33 children, 12 like tea, 28 like coffee and 9 like both. How many like neither? (a) 2 (b) 9 (c) 11 (d) 3
34. 34.In a class of 51 children, 25 like maths, 27 like science and 7 like both. How many like at least one of the two? (a) 45 (b) 38 (c) 52 (d) 51
35. 35.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 50° (b) 140° (c) 40° (d) 100°
36. 36.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 150° (b) 120° (c) 270° (d) 90°
37. 37.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 115° (b) 100° (c) 65° (d) 145°
38. 38.A bag has 4 white, 2 red and 2 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 3/4 (c) 1/4 (d) 7/8
39. 39.Two angles of a triangle are 35° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 70° (c) 290° (d) 110°
40. 40.What is the smallest prime factor of 143? (a) 2 (b) 13 (c) 11 (d) 1

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