Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 188 · 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.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 16) (c) (x + 1)(x + 72) (d) (x + 8)(x + 9)
2. 2.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 28 (b) 21 (c) 22 (d) 29
3. 3.In a class of 42 children, 13 like mangoes, 26 like bananas and 7 like both. How many like at least one of the two? (a) 32 (b) 25 (c) 42 (d) 39
4. 4.In a class of 19 children, 12 like mangoes, 6 like bananas and 3 like neither. How many like both? (a) 1 (b) 2 (c) 3 (d) 16
5. 5.How many factors does 58 have? (a) 3 (b) 2 (c) 5 (d) 4
6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 40? (a) 4 (b) 13 (c) 15 (d) 14
7. 7.In a class of 37 children, 15 like cricket, 31 like football and 12 like both. How many like neither? (a) 4 (b) 3 (c) 15 (d) 12
8. 8.In how many different ways can the letters of the word FISH be arranged? (a) 16 (b) 24 (c) 12 (d) 48
9. 9.Two angles of a triangle are 70° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 235° (c) 110° (d) 55°
10. 10.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 7/8 (b) 1/7 (c) 1/8 (d) 1/4
11. 11.A bag has 8 yellow balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 9 (b) 2 (c) 11 (d) 10
12. 12.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
13. 13.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 86° (b) 85° (c) 170° (d) 95°
14. 14.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) 7 (c) 15 (d) 8
15. 15.What is the smallest prime factor of 161? (a) 1 (b) 7 (c) 2 (d) 23
16. 16.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
17. 17.What is the median of 36, 14, 27, 35, 39, 5 and 34? (a) 35 (b) 27 (c) 34 (d) 33
18. 18.What is the mode of 6, 10, 5, 15, 15, 15 and 10? (a) 5 (b) 6 (c) 15 (d) 10
19. 19.Using (a − b)² = a² − 2ab + b², what is 78²? (a) 6724 (b) 6094 (c) 6396 (d) 6084
20. 20.In which quadrant does the point (3, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
21. 21.What is the sum of the first 11 terms of the AP 9, 11, 13, …? (a) 29 (b) 220 (c) 418 (d) 209
22. 22.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
23. 23.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 10 (c) 21 (d) 20
24. 24.What is the 17th term of the AP 9, 14, 19, 24, …? (a) 80 (b) 94 (c) 85 (d) 89
25. 25.Two angles of a triangle are 80° and 45°. What is the exterior angle at the third corner? (a) 55° (b) 125° (c) 135° (d) 100°
26. 26.There are 3 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) 12 (b) 6 (c) 9 (d) 18
27. 27.A drawer has lots of red, blue, green, black and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 10 (c) 2 (d) 5
28. 28.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 91 (c) 182 (d) 196
29. 29.A canteen sells 7 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 49 (b) 98 (c) 56 (d) 14
30. 30.What is the distance between the points (6, 14) and (18, 5)? (a) 15 (b) 225 (c) 21 (d) 16
31. 31.What is the median of 29, 5, 13, 6, 11, 27 and 1? (a) 6 (b) 12 (c) 13 (d) 11
32. 32.A bag has 9 white, 4 blue and 8 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 3/7 (b) 1/3 (c) 4/7 (d) 13/21
33. 33.What is the missing term in the AP 5, ?, 9, 11, 13? (a) 6 (b) 7 (c) 8 (d) 9
34. 34.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/12 (c) 1/11 (d) 1/18
35. 35.A bag has 9 blue, 5 red and 2 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 5/8 (b) 7/16 (c) 1/3 (d) 9/16
36. 36.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 35° (b) 55° (c) 145° (d) 110°
37. 37.Two angles of a triangle are 30° and 85°. What is the exterior angle at the third corner? (a) 65° (b) 150° (c) 115° (d) 95°
38. 38.The mean of 4 numbers is 15. When the number 30 is added to them, what is the new mean? (a) 19 (b) 15 (c) 17 (d) 18
39. 39.A cube has edges of 5 cm. What is its volume? (a) 100 cu cm (b) 15 cu cm (c) 150 cu cm (d) 125 cu cm
40. 40.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 1/4 (c) 5/8 (d) 3/5

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad