Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 907 · 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.A drawer has lots of blue, green, black, white 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) 2 (b) 6 (c) 5 (d) 10
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 2/11 (b) 1/11 (c) 1/18 (d) 1/12
3. 3.In which quadrant does the point (−6, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
4. 4.What is the 29th term of the AP 6, 8, 10, 12, …? (a) 62 (b) 56 (c) 58 (d) 64
5. 5.What is the product of the roots of x² − 15x + 56 = 0? (a) 15 (b) 57 (c) 56 (d) 55
6. 6.What is the prime factorisation of 126? (a) 2 × 3² × 7 (b) 2² × 3² × 7 (c) 2³ × 3² × 7 (d) 2 × 3² × 7²
7. 7.A drawer has lots of black, red and yellow 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) 2 (c) 4 (d) 3
8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
9. 9.In a class of 34 children, 20 like cricket, 11 like football and 6 like both. How many like only cricket? (a) 20 (b) 23 (c) 14 (d) 5
10. 10.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 120 (d) 240
11. 11.What is the prime factorisation of 15? (a) 3² × 5 (b) 3 × 5² (c) 3 × 5 (d) 3³ × 5
12. 12.A bag has 6 green, 7 blue and 9 yellow balls. One ball is taken out without looking. What is the probability that it is blue? (a) 7/22 (b) 1/3 (c) 15/22 (d) 7/15
13. 13.Which is the correct factorisation of x² + 8x + 12? (a) (x + 1)(x + 7) (b) (x + 2)(x + 6) (c) (x − 2)(x − 6) (d) (x + 1)(x + 12)
14. 14.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
15. 15.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 30° (b) 150° (c) 300° (d) 120°
16. 16.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
17. 17.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 63 (c) 20 (d) 60
18. 18.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 110 (b) 121 (c) 55 (d) 22
19. 19.A bag has 9 blue balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 10 (b) 2 (c) 14 (d) 11
20. 20.Using (a + b)² = a² + 2ab + b², what is 32²? (a) 904 (b) 1034 (c) 784 (d) 1024
21. 21.What is the midpoint of the line joining (3, 14) and (5, 4)? (a) (9, 4) (b) (1, 5) (c) (8, 18) (d) (4, 9)
22. 22.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 105° (b) 75° (c) 130° (d) 125°
23. 23.What is the midpoint of the line joining (7, 6) and (9, 10)? (a) (9, 8) (b) (1, 2) (c) (8, 8) (d) (16, 16)
24. 24.A bag has 5 blue balls and 7 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 6 (b) 7 (c) 12 (d) 2
25. 25.A drawer has lots of 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) 5 (b) 4 (c) 3 (d) 2
26. 26.What is the midpoint of the line joining (7, 2) and (11, 12)? (a) (18, 14) (b) (9, 7) (c) (2, 5) (d) (7, 9)
27. 27.Using (a + b)² = a² + 2ab + b², what is 102²? (a) 10404 (b) 9604 (c) 10414 (d) 10004
28. 28.What is the sum of all the whole numbers from 1 to 86? (a) 3698 (b) 3741 (c) 3655 (d) 7482
29. 29.3 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 15 (b) 24 (c) 12 (d) 7
30. 30.A bag has 9 black balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 11 (b) 2 (c) 20 (d) 10
31. 31.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/6
32. 32.A bag has 12 red balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 18 (b) 13 (c) 14 (d) 2
33. 33.In a class of 30 children, 18 like dance, 17 like music and 4 like neither. How many like both? (a) 5 (b) 26 (c) 9 (d) 4
34. 34.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/6 (b) 1/5 (c) 5/6 (d) 1/3
35. 35.What is the prime factorisation of 20? (a) 2² × 5 (b) 2 × 5 (c) 2³ × 5 (d) 2 × 5²
36. 36.How many factors does 20 have? (a) 4 (b) 7 (c) 5 (d) 6
37. 37.A bag has 10 green balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 6 (c) 2 (d) 11
38. 38.What is the midpoint of the line joining (7, 3) and (11, 13)? (a) (9, 8) (b) (18, 16) (c) (2, 5) (d) (8, 9)
39. 39.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 130° (b) 65° (c) 25° (d) 155°
40. 40.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)

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