Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 206 · 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.In how many different ways can the letters of the word FISH be arranged? (a) 24 (b) 12 (c) 16 (d) 48
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 4/11 (c) 1/9 (d) 1/11
3. 3.A drawer has lots of white, black, yellow, blue 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) 5 (b) 2 (c) 10 (d) 6
4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 9 (b) 7 (c) 6 (d) 8
5. 5.In a class of 32 children, 18 like cricket, 12 like football and 4 like neither. How many like both? (a) 4 (b) 28 (c) 2 (d) 3
6. 6.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 20 (c) 15 (d) 25
7. 7.What is the sum of all the whole numbers from 1 to 25? (a) 300 (b) 326 (c) 325 (d) 650
8. 8.In how many different ways can the letters of the word MANGO be arranged? (a) 240 (b) 25 (c) 20 (d) 120
9. 9.A captain and a vice-captain are to be chosen from 5 players. In how many ways can this be done? (a) 25 (b) 20 (c) 21 (d) 10
10. 10.Which is the correct factorisation of x² + 9x + 14? (a) (x − 2)(x − 7) (b) (x + 2)(x + 7) (c) (x + 1)(x + 8) (d) (x + 1)(x + 14)
11. 11.In a class of 41 children, 14 like cricket, 20 like football and 2 like both. How many like neither? (a) 11 (b) 9 (c) 2 (d) 7
12. 12.A bag has 3 yellow balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 5 (c) 4 (d) 6
13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 8 (d) 17
14. 14.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 490 (c) 628 (d) 627
15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 4 (b) 5 (c) 7 (d) 6
16. 16.How many factors does 19 have? (a) 3 (b) 1 (c) 4 (d) 2
17. 17.In which quadrant does the point (−8, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
18. 18.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) 8 times (d) 5 times
19. 19.Which is the correct factorisation of x² + 12x + 32? (a) (x + 1)(x + 11) (b) (x + 1)(x + 32) (c) (x + 4)(x + 8) (d) (x − 4)(x − 8)
20. 20.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 9025 (b) 11025 (c) 10025 (d) 11035
21. 21.In a league, 8 teams each play every other team once. How many matches are played? (a) 36 (b) 28 (c) 56 (d) 64
22. 22.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/2 (c) 3/4 (d) 1/3
23. 23.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 6 times (b) 9 times (c) 27 times (d) 3 times
24. 24.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 5544 sq cm
25. 25.What is the sum of all the whole numbers from 1 to 69? (a) 2416 (b) 2346 (c) 2415 (d) 4830
26. 26.What is the 38th term of the AP 16, 23, 30, 37, …? (a) 282 (b) 266 (c) 259 (d) 275
27. 27.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 105 (b) 120 (c) 225 (d) 210
28. 28.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 78 (b) 66 (c) 144 (d) 132
29. 29.Using (a + b)² = a² + 2ab + b², what is 71²? (a) 5051 (b) 4761 (c) 5041 (d) 4901
30. 30.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 12 (b) 36 (c) 15 (d) 30
31. 31.If a + b = 21 and ab = 108, what is (a − b)²? (a) 9 (b) 225 (c) 3 (d) 441
32. 32.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 64 (c) 16 (d) 56
33. 33.In a class of 53 children, 25 like dance, 31 like music and 11 like both. How many like only dance? (a) 22 (b) 20 (c) 25 (d) 14
34. 34.In how many different ways can the letters of the word TIGER be arranged? (a) 25 (b) 120 (c) 20 (d) 240
35. 35.What is the median of 2, 21, 38, 25 and 18? (a) 25 (b) 21 (c) 18 (d) 38
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 5/11 (c) 5/36 (d) 1/11
37. 37.In how many different ways can the letters of the word BOAT be arranged? (a) 48 (b) 16 (c) 12 (d) 24
38. 38.What is the median of 36, 5, 9, 38, 2, 27 and 22? (a) 38 (b) 22 (c) 27 (d) 9
39. 39.Two angles of a triangle are 75° and 25°. What is the third angle? (a) 105° (b) 100° (c) 80° (d) 155°
40. 40.A bag has 7 red balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 16 (b) 10 (c) 8 (d) 2

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