Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 324 · 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 circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
2. 2.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 27 cu cm (d) 54 cu cm
3. 3.In how many different ways can the letters of the word SUN be arranged? (a) 3 (b) 6 (c) 12 (d) 9
4. 4.How many prime numbers are there between 10 and 20? (a) 6 (b) 5 (c) 3 (d) 4
5. 5.In a class of 43 children, 23 like cricket, 28 like football and 12 like both. How many like at least one of the two? (a) 43 (b) 27 (c) 39 (d) 51
6. 6.What is the 31st term of the AP 19, 25, 31, 37, …? (a) 186 (b) 180 (c) 205 (d) 199
7. 7.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 37 (b) 24 (c) 25 (d) 36
8. 8.There are 5 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 8 (c) 20 (d) 15
9. 9.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 225 (b) 120 (c) 240 (d) 29
10. 10.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) 14 (b) 8 (c) 7 (d) 15
11. 11.What is the 28th term of the AP 6, 14, 22, 30, …? (a) 224 (b) 216 (c) 230 (d) 222
12. 12.In which quadrant does the point (−3, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
13. 13.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 155° (b) 70° (c) 110° (d) 135°
14. 14.A bag has 3 yellow balls and 4 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 4 (b) 5 (c) 7 (d) 2
15. 15.What is the smallest prime factor of 57? (a) 1 (b) 19 (c) 3 (d) 2
16. 16.The mean of 6 numbers is 15. When the number 36 is added to them, what is the new mean? (a) 19 (b) 17 (c) 15 (d) 18
17. 17.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/8 (c) 7/8 (d) 1/7
18. 18.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 616 cm (c) 176 cm (d) 88 cm
19. 19.In a class of 47 children, 27 like maths, 25 like science and 8 like both. How many like at least one of the two? (a) 44 (b) 52 (c) 36 (d) 47
20. 20.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
21. 21.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 5 times (c) 4 times (d) 2 times
22. 22.If a + b = 17 and ab = 72, what is a² + b²? (a) 289 (b) 145 (c) 217 (d) 433
23. 23.A drawer has lots of green, black, yellow, blue 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) 10 (b) 5 (c) 2 (d) 6
24. 24.What is the 34th term of the AP 7, 11, 15, 19, …? (a) 139 (b) 136 (c) 143 (d) 132
25. 25.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 64 (c) 28 (d) 56
26. 26.How many factors does 51 have? (a) 2 (b) 3 (c) 4 (d) 5
27. 27.A bag has 9 yellow, 2 white and 6 red balls. One ball is taken out without looking. What is the probability that it is not yellow? (a) 9/17 (b) 8/17 (c) 8/9 (d) 1/3
28. 28.What is the median of 4, 12, 21, 24, 15, 7 and 39? (a) 12 (b) 21 (c) 15 (d) 24
29. 29.What is the 20th term of the AP 15, 21, 27, 33, …? (a) 129 (b) 114 (c) 120 (d) 135
30. 30.If a + b = 19 and ab = 84, what is a² + b²? (a) 361 (b) 193 (c) 277 (d) 529
31. 31.In which quadrant does the point (−7, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
32. 32.How many prime numbers are there between 40 and 50? (a) 4 (b) 5 (c) 2 (d) 3
33. 33.Two angles of a triangle are 65° and 60°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 115° (d) 120°
34. 34.What is the sum of the first 10 terms of the AP 4, 8, 12, …? (a) 40 (b) 240 (c) 440 (d) 220
35. 35.In a class of 39 children, 17 like tea, 23 like coffee and 3 like both. How many like only tea? (a) 14 (b) 17 (c) 20 (d) 16
36. 36.In a class of 20 children, 11 like mangoes, 10 like bananas and 5 like both. How many like at least one of the two? (a) 16 (b) 11 (c) 21 (d) 20
37. 37.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 619 (c) 484 (d) 618
38. 38.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 154 cm (c) 44 cm (d) 22 cm
39. 39.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
40. 40.What is the midpoint of the line joining (7, 7) and (13, 1)? (a) (20, 8) (b) (10, 4) (c) (3, 3) (d) (4, 10)

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