Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 790 · 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 diameter 70 cm? (Use π = 22/7.) (a) 440 cm (b) 3850 cm (c) 110 cm (d) 220 cm
2. 2.If a + b = 21 and ab = 108, what is (a − b)²? (a) 9 (b) 225 (c) 441 (d) 3
3. 3.What is the sum of all the whole numbers from 1 to 68? (a) 2346 (b) 4692 (c) 2278 (d) 2312
4. 4.What is the distance between the points (1, 23) and (13, 7)? (a) 400 (b) 20 (c) 21 (d) 28
5. 5.There are 8 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) 11 (b) 48 (c) 24 (d) 32
6. 6.In how many different ways can the letters of the word FISH be arranged? (a) 12 (b) 16 (c) 48 (d) 24
7. 7.In which quadrant does the point (6, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
8. 8.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 12 (d) 30
9. 9.A drawer has lots of 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) 4 (b) 2 (c) 5 (d) 3
10. 10.In a class of 19 children, 14 like tea, 11 like coffee and 7 like both. How many like neither? (a) 8 (b) 2 (c) 7 (d) 1
11. 11.If a + b = 13 and ab = 30, what is (a − b)²? (a) 49 (b) 7 (c) 109 (d) 169
12. 12.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 144 (b) 78 (c) 132 (d) 66
13. 13.In a class of 38 children, 14 like mangoes, 22 like bananas and 10 like neither. How many like both? (a) 10 (b) 28 (c) 8 (d) 9
14. 14.What is the midpoint of the line joining (1, 3) and (7, 15)? (a) (9, 4) (b) (4, 9) (c) (8, 18) (d) (3, 6)
15. 15.How many factors does 32 have? (a) 4 (b) 6 (c) 5 (d) 7
16. 16.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 36 (c) 45 (d) 72
17. 17.A drawer has lots of yellow and green 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) 5 (c) 4 (d) 2
18. 18.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 9856 sq cm (d) 1232 sq cm
19. 19.Three coins are tossed together. What is the probability of getting exactly one head? (a) 5/8 (b) 1/4 (c) 3/5 (d) 3/8
20. 20.What is the distance between the points (0, 17) and (15, 9)? (a) 18 (b) 17 (c) 23 (d) 289
21. 21.Which is the correct factorisation of x² + 9x + 20? (a) (x + 1)(x + 20) (b) (x + 1)(x + 8) (c) (x + 4)(x + 5) (d) (x − 4)(x − 5)
22. 22.In a class of 19 children, 15 like tea, 6 like coffee and 3 like both. How many like only tea? (a) 12 (b) 15 (c) 3 (d) 13
23. 23.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 24 (c) 48 (d) 12
24. 24.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 6 times (b) 27 times (c) 9 times (d) 3 times
25. 25.Two angles of a triangle are 45° and 50°. What is the third angle? (a) 135° (b) 95° (c) 130° (d) 85°
26. 26.Two angles of a triangle are 70° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 30° (c) 110° (d) 150°
27. 27.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 1/2 (c) 1/3 (d) 2/3
28. 28.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 14) (b) (x − 7)(x − 8) (c) (x + 7)(x + 8) (d) (x + 1)(x + 56)
29. 29.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 4 times (b) 2 times (c) 5 times (d) 8 times
30. 30.A bag has 2 white, 4 yellow and 7 green balls. One ball is taken out without looking. What is the probability that it is not green? (a) 7/13 (b) 6/7 (c) 1/3 (d) 6/13
31. 31.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 12 (c) 36 (d) 15
32. 32.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 15 (d) 6
33. 33.In a class of 24 children, 9 like cricket, 10 like football and 4 like both. How many like neither? (a) 13 (b) 5 (c) 4 (d) 9
34. 34.If a + b = 11 and ab = 10, what is a² + b²? (a) 121 (b) 141 (c) 101 (d) 111
35. 35.In a class of 22 children, 7 like cricket, 16 like football and 2 like both. How many like at least one of the two? (a) 21 (b) 22 (c) 19 (d) 23
36. 36.In a class of 46 children, 23 like tea, 21 like coffee and 8 like both. How many like neither? (a) 18 (b) 10 (c) 8 (d) 2
37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
38. 38.The mean of 4 numbers is 28. When the number 48 is added to them, what is the new mean? (a) 32 (b) 33 (c) 38 (d) 28
39. 39.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
40. 40.In an isosceles triangle, the two equal angles are 60° each. What is the third angle? (a) 30° (b) 61° (c) 120° (d) 60°

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