Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 186 · 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 straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 76° (b) 150° (c) 75° (d) 105°
2. 2.A bag has 5 red balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 9 (c) 6 (d) 5
3. 3.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 150 (b) 85 (c) 23 (d) 75
4. 4.What is the mode of 9, 10, 7, 7, 10, 10 and 5? (a) 9 (b) 10 (c) 7 (d) 5
5. 5.A bag has 4 green, 3 blue and 7 white balls. One ball is taken out without looking. What is the probability that it is blue? (a) 3/14 (b) 3/11 (c) 11/14 (d) 1/3
6. 6.Two angles of a triangle are 30° and 40°. What is the third angle? (a) 150° (b) 110° (c) 140° (d) 70°
7. 7.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 25° (d) 155°
8. 8.Using (a + b)² = a² + 2ab + b², what is 95²? (a) 9025 (b) 8125 (c) 7225 (d) 9035
9. 9.How many prime numbers are there between 90 and 120? (a) 5 (b) 7 (c) 6 (d) 8
10. 10.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) 51 (b) 17 (c) 54 (d) 153
11. 11.How many factors does 12 have? (a) 6 (b) 5 (c) 4 (d) 7
12. 12.What is the smallest prime factor of 253? (a) 1 (b) 23 (c) 11 (d) 2
13. 13.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 4 times (d) 2 times
14. 14.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 48 (c) 24 (d) 12
15. 15.What is the sum of the roots of x² − 17x + 72 = 0? (a) 16 (b) 17 (c) 72 (d) 18
16. 16.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 12 (c) 9 (d) 6
17. 17.How many factors does 43 have? (a) 1 (b) 3 (c) 4 (d) 2
18. 18.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 121 (b) 66 (c) 132 (d) 21
19. 19.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 90 (c) 45 (d) 55
20. 20.There are 7 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 14 (b) 28 (c) 21 (d) 9
21. 21.In a class of 40 children, 17 like mangoes, 23 like bananas and 9 like both. How many like at least one of the two? (a) 40 (b) 32 (c) 31 (d) 22
22. 22.In which quadrant does the point (3, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
23. 23.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
24. 24.What are the roots of x² − 12x + 27 = 0? (a) 1 and 11 (b) 3 and 9 (c) 1 and 27 (d) 2 and 10
25. 25.What is the sum of the first 6 terms of the AP 8, 12, 16, …? (a) 120 (b) 28 (c) 216 (d) 108
26. 26.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 9 times (b) 3 times (c) 27 times (d) 6 times
27. 27.Two dice are rolled together. What is the probability that the two numbers add up to 6? (a) 5/11 (b) 1/6 (c) 1/11 (d) 5/36
28. 28.How many prime numbers are there between 10 and 30? (a) 8 (b) 5 (c) 6 (d) 7
29. 29.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 4/11 (c) 1/9 (d) 5/36
30. 30.In a class of 30 children, 16 like mangoes, 10 like bananas and 10 like neither. How many like both? (a) 7 (b) 20 (c) 6 (d) 10
31. 31.A bag has 8 red balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 9 (c) 17 (d) 10
32. 32.Two angles of a triangle are 40° and 90°. What is the third angle? (a) 90° (b) 130° (c) 50° (d) 140°
33. 33.What is the missing term in the AP 4, 7, 10, ?, 16? (a) 14 (b) 16 (c) 12 (d) 13
34. 34.There are 4 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 48 (b) 10 (c) 28 (d) 24
35. 35.A drawer has lots of blue, black, yellow, white 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) 5 (b) 2 (c) 6 (d) 10
36. 36.A drawer has lots of green 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) 3 (b) 2 (c) 5 (d) 4
37. 37.A bag has 8 yellow, 6 blue and 3 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 3/14 (b) 3/17 (c) 1/3 (d) 14/17
38. 38.In how many different ways can the letters of the word PLANT be arranged? (a) 240 (b) 25 (c) 120 (d) 20
39. 39.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 20° (b) 110° (c) 70° (d) 55°
40. 40.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 10 (b) 32 (c) 16 (d) 24

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