Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 582 · 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 27th term of the AP 5, 12, 19, 26, …? (a) 189 (b) 194 (c) 187 (d) 182
2. 2.What is the smallest prime factor of 187? (a) 2 (b) 17 (c) 1 (d) 11
3. 3.How many prime numbers are there between 80 and 110? (a) 8 (b) 7 (c) 9 (d) 6
4. 4.A bag has 5 yellow balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 11 (c) 6 (d) 2
5. 5.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 20 (d) 240
6. 6.A drawer has lots of blue, yellow 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) 6 (c) 4 (d) 2
7. 7.What is the missing term in the AP 3, ?, 19, 27, 35? (a) 12 (b) 19 (c) 11 (d) 10
8. 8.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) 7 (b) 8 (c) 15 (d) 14
9. 9.Two angles of a triangle are 45° and 30°. What is the exterior angle at the third corner? (a) 75° (b) 135° (c) 105° (d) 150°
10. 10.Which term of the AP 18, 22, 26, 30, … is 86? (a) 19th (b) 20th (c) 18th (d) 17th
11. 11.There are 6 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) 36 (b) 42 (c) 12 (d) 72
12. 12.Two angles of a triangle are 55° and 80°. What is the third angle? (a) 135° (b) 125° (c) 45° (d) 100°
13. 13.In a class of 45 children, 25 like cricket, 20 like football and 8 like both. How many like neither? (a) 16 (b) 9 (c) 0 (d) 8
14. 14.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 440 cm (c) 220 cm (d) 3850 cm
15. 15.A bag has 5 blue balls and 4 yellow 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) 5 (c) 6 (d) 2
16. 16.The mean of 6 numbers is 15. When the number 8 is added to them, what is the new mean? (a) 16 (b) 15 (c) 14 (d) 13
17. 17.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 66 (c) 198 (d) 22
18. 18.What is the midpoint of the line joining (1, 8) and (13, 20)? (a) (6, 6) (b) (7, 14) (c) (14, 28) (d) (14, 7)
19. 19.In a class of 31 children, 21 like dance, 18 like music and 9 like both. How many like neither? (a) 10 (b) 9 (c) 1 (d) 2
20. 20.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 3 (c) 12 (d) 9
21. 21.What is the distance between the points (1, 5) and (9, 11)? (a) 14 (b) 100 (c) 11 (d) 10
22. 22.What is the missing term in the AP 3, ?, 17, 24, 31? (a) 9 (b) 17 (c) 10 (d) 11
23. 23.A canteen sells 7 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 12 (c) 70 (d) 35
24. 24.In which quadrant does the point (8, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
25. 25.What is the smallest prime factor of 49? (a) 3 (b) 1 (c) 2 (d) 7
26. 26.What is the median of 37, 28, 19, 10, 13, 17 and 24? (a) 17 (b) 10 (c) 19 (d) 24
27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 5 (b) 6 (c) 4 (d) 3
28. 28.A team of 2 players is to be chosen from 12 players. How many different teams are possible? (a) 132 (b) 24 (c) 66 (d) 144
29. 29.Two angles of a triangle are 80° and 85°. What is the third angle? (a) 95° (b) 15° (c) 165° (d) 100°
30. 30.In a class of 28 children, 15 like mangoes, 19 like bananas and 6 like neither. How many like both? (a) 22 (b) 13 (c) 6 (d) 12
31. 31.Two angles of a triangle are 55° and 90°. What is the exterior angle at the third corner? (a) 125° (b) 35° (c) 145° (d) 90°
32. 32.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
33. 33.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) 24 (c) 25 (d) 13
34. 34.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 140° (b) 41° (c) 220° (d) 40°
35. 35.What is the sum of the first 16 odd numbers (1 + 3 + 5 + …)? (a) 256 (b) 136 (c) 272 (d) 31
36. 36.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 280° (c) 10° (d) 100°
37. 37.A bag has 6 blue balls and 10 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 16 (b) 2 (c) 7 (d) 8
38. 38.In which quadrant does the point (−7, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
39. 39.A bag has 7 white balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 14 (b) 8 (c) 2 (d) 9
40. 40.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 48 (d) 16

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