Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 970 · 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 STAR be arranged? (a) 16 (b) 24 (c) 12 (d) 48
2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 7 (b) 6 (c) 5 (d) 4
3. 3.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
4. 4.Using (a − b)² = a² − 2ab + b², what is 75²? (a) 5635 (b) 6375 (c) 7225 (d) 5625
5. 5.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 2/3 (c) 1/3 (d) 1/2
6. 6.In a class of 45 children, 27 like cricket, 20 like football and 12 like both. How many like neither? (a) 10 (b) 11 (c) 22 (d) 12
7. 7.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 4 times (c) 8 times (d) 5 times
8. 8.What is the product of the roots of x² − 14x + 45 = 0? (a) 46 (b) 45 (c) 44 (d) 14
9. 9.In a class of 43 children, 31 like tea, 22 like coffee and 12 like both. How many like at least one of the two? (a) 29 (b) 53 (c) 43 (d) 41
10. 10.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 205° (b) 155° (c) 26° (d) 25°
11. 11.What is the prime factorisation of 120? (a) 2³ × 3 × 5 (b) 2 × 3 × 5³ (c) 2⁴ × 3 × 5 (d) 2² × 3 × 5
12. 12.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 5/6 (c) 1/4 (d) 1/3
13. 13.In which quadrant does the point (−4, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
14. 14.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 18 (c) 162 (d) 57
15. 15.A bag has 3 black balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 15 (b) 4 (c) 2 (d) 5
16. 16.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
17. 17.A drawer has lots of 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) 4 (b) 5 (c) 2 (d) 3
18. 18.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 8 times (c) 2 times (d) 4 times
19. 19.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 132 sq cm (c) 693 sq cm (d) 1386 sq cm
20. 20.Which is the correct factorisation of x² + 13x + 40? (a) (x + 5)(x + 8) (b) (x + 1)(x + 40) (c) (x − 5)(x − 8) (d) (x + 1)(x + 12)
21. 21.The mean of 5 numbers is 36. When the number 12 is added to them, what is the new mean? (a) 33 (b) 32 (c) 36 (d) 24
22. 22.In a class of 45 children, 23 like dance, 24 like music and 3 like neither. How many like both? (a) 42 (b) 2 (c) 3 (d) 5
23. 23.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 182 (c) 196 (d) 105
24. 24.A bag has 5 red, 2 blue and 2 white balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 2/9 (b) 7/9 (c) 8/9 (d) 1/3
25. 25.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
26. 26.What is the smallest prime factor of 143? (a) 1 (b) 11 (c) 2 (d) 13
27. 27.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 120° (b) 60° (c) 40° (d) 30°
28. 28.Using (a − b)² = a² − 2ab + b², what is 27²? (a) 891 (b) 739 (c) 729 (d) 1089
29. 29.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 101 (c) 102 (d) 92
30. 30.How many factors does 93 have? (a) 4 (b) 2 (c) 3 (d) 5
31. 31.In a class of 24 children, 15 like maths, 14 like science and 11 like both. How many like at least one of the two? (a) 24 (b) 7 (c) 29 (d) 18
32. 32.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 140° (b) 40° (c) 41° (d) 80°
33. 33.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 15 (c) 30 (d) 36
34. 34.5 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 12 (b) 40 (c) 70 (d) 35
35. 35.What is the missing term in the AP 19, 27, ?, 43, 51? (a) 43 (b) 35 (c) 34 (d) 36
36. 36.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 48 (d) 16
37. 37.A bag has 6 yellow balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 8 (b) 18 (c) 2 (d) 7
38. 38.What is the mode of 3, 7, 19, 7, 19, 7 and 16? (a) 19 (b) 16 (c) 3 (d) 7
39. 39.A cuboid is 6 cm long, 5 cm wide and 2 cm high. What is its total surface area? (a) 208 sq cm (b) 60 sq cm (c) 104 sq cm (d) 52 sq cm
40. 40.A bag has 6 white balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 16 (c) 2 (d) 11

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