Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 547 · 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.A canteen sells 6 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 60 (c) 30 (d) 36
2. 2.Two angles of a triangle are 25° and 120°. What is the exterior angle at the third corner? (a) 60° (b) 155° (c) 145° (d) 35°
3. 3.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
4. 4.What is the 13th term of the AP 19, 26, 33, 40, …? (a) 110 (b) 103 (c) 91 (d) 84
5. 5.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 105° (c) 75° (d) 285°
6. 6.What is the product of the roots of x² − 15x + 54 = 0? (a) 53 (b) 15 (c) 55 (d) 54
7. 7.Two straight lines cross. One of the angles is 165°. What is the angle next to it on the same straight line? (a) 195° (b) 165° (c) 15° (d) 16°
8. 8.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 45 (b) 276 (c) 300 (d) 552
9. 9.What is the missing term in the AP 13, 20, 27, ?, 41? (a) 34 (b) 33 (c) 41 (d) 35
10. 10.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 49 (c) 14 (d) 42
11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
12. 12.What is the mean of 16, 12, 19, 4, 12 and 15? (a) 14 (b) 12 (c) 15 (d) 13
13. 13.In which quadrant does the point (−9, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
14. 14.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 10 times (c) 25 times (d) 125 times
15. 15.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 55° (b) 115° (c) 120° (d) 125°
16. 16.A bag has 4 white balls and 9 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 10 (c) 2 (d) 13
17. 17.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
18. 18.What is the mode of 17, 6, 6, 17, 6, 1 and 15? (a) 15 (b) 6 (c) 1 (d) 17
19. 19.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) 12 (b) 13 (c) 24 (d) 25
20. 20.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 105° (b) 145° (c) 140° (d) 75°
21. 21.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
22. 22.What is the missing term in the AP 5, 13, 21, ?, 37? (a) 37 (b) 28 (c) 29 (d) 30
23. 23.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
24. 24.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 48 (c) 24 (d) 12
25. 25.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) 16 (c) 51 (d) 144
26. 26.What is the mean of 7, 19, 12 and 18? (a) 15 (b) 14 (c) 13 (d) 16
27. 27.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 176 sq cm (c) 9856 sq cm (d) 1232 sq cm
28. 28.What is the smallest prime factor of 91? (a) 7 (b) 2 (c) 1 (d) 13
29. 29.In a class of 29 children, 20 like mangoes, 9 like bananas and 2 like both. How many like only mangoes? (a) 20 (b) 2 (c) 7 (d) 18
30. 30.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 80° (d) 160°
31. 31.A bag has 6 green, 4 blue and 2 yellow balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 5/6 (b) 1/3 (c) 1/6 (d) 1/5
32. 32.How many factors does 50 have? (a) 4 (b) 7 (c) 6 (d) 5
33. 33.Two angles of a triangle are 40° and 105°. What is the third angle? (a) 35° (b) 140° (c) 75° (d) 145°
34. 34.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 120 (c) 240 (d) 20
35. 35.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 69 (c) 70 (d) 78
36. 36.A captain and a vice-captain are to be chosen from 7 players. In how many ways can this be done? (a) 42 (b) 21 (c) 49 (d) 14
37. 37.What is the median of 16, 21, 15, 3, 12, 9 and 20? (a) 3 (b) 12 (c) 15 (d) 16
38. 38.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
39. 39.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 215° (b) 35° (c) 36° (d) 145°
40. 40.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 261 (b) 271 (c) 270 (d) 252

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