Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 334 · 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 bag has 8 red balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 10 (b) 9 (c) 15 (d) 2
2. 2.A cuboid is 6 cm long, 3 cm wide and 2 cm high. What is its total surface area? (a) 73 sq cm (b) 36 sq cm (c) 144 sq cm (d) 72 sq cm
3. 3.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/2 (b) 3/4 (c) 1/3 (d) 1/4
4. 4.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 117 (c) 42 (d) 13
5. 5.What is the smallest prime factor of 203? (a) 1 (b) 2 (c) 7 (d) 29
6. 6.A cuboid is 5 cm long, 4 cm wide and 7 cm high. What is its volume? (a) 20 cu cm (b) 140 cu cm (c) 16 cu cm (d) 166 cu cm
7. 7.What is the smallest prime factor of 57? (a) 2 (b) 3 (c) 1 (d) 19
8. 8.A drawer has lots of red 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) 3 (c) 5 (d) 2
9. 9.Two angles of a triangle are 35° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 105° (c) 140° (d) 145°
10. 10.What is the sum of all the whole numbers from 1 to 87? (a) 7656 (b) 3829 (c) 3741 (d) 3828
11. 11.Which term of the AP 7, 16, 25, 34, … is 214? (a) 25th (b) 26th (c) 24th (d) 23rd
12. 12.What is the prime factorisation of 48? (a) 2³ × 3 (b) 2 × 3⁴ (c) 2⁴ × 3 (d) 2⁵ × 3
13. 13.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 171 (c) 60 (d) 57
14. 14.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 1/4 (c) 1/8 (d) 3/8
15. 15.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 20° (b) 110° (c) 90° (d) 160°
16. 16.Two angles of a triangle are 80° and 90°. What is the third angle? (a) 100° (b) 10° (c) 170° (d) 90°
17. 17.In which quadrant does the point (−6, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
18. 18.A bag has 10 black balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 18 (b) 12 (c) 11 (d) 2
19. 19.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 44 sq cm (c) 616 sq cm (d) 154 sq cm
20. 20.What is the sum of all the whole numbers from 1 to 27? (a) 378 (b) 756 (c) 351 (d) 379
21. 21.How many factors does 98 have? (a) 6 (b) 4 (c) 7 (d) 5
22. 22.What is the midpoint of the line joining (2, 7) and (4, 19)? (a) (3, 13) (b) (6, 26) (c) (13, 3) (d) (1, 6)
23. 23.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 1/6 (b) 1/11 (c) 5/11 (d) 5/36
25. 25.What are the roots of x² − 15x + 56 = 0? (a) 7 and 8 (b) 1 and 56 (c) 1 and 14 (d) 2 and 28
26. 26.Using (a + b)² = a² + 2ab + b², what is 93²? (a) 7569 (b) 8649 (c) 8659 (d) 8109
27. 27.How many factors does 21 have? (a) 2 (b) 5 (c) 3 (d) 4
28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
29. 29.How many prime numbers are there between 40 and 50? (a) 3 (b) 5 (c) 4 (d) 2
30. 30.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) 22 (c) 29 (d) 21
31. 31.In a class of 27 children, 13 like dance, 9 like music and 2 like both. How many like neither? (a) 7 (b) 5 (c) 2 (d) 9
32. 32.A cube has edges of 5 cm. What is its total surface area? (a) 25 sq cm (b) 100 sq cm (c) 125 sq cm (d) 150 sq cm
33. 33.A bag has 7 red balls and 11 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 18 (b) 2 (c) 8 (d) 12
34. 34.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 313 (c) 312 (d) 280
35. 35.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/4 (c) 1/3 (d) 5/6
36. 36.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 130° (b) 40° (c) 65° (d) 50°
37. 37.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 196 (c) 105 (d) 182
38. 38.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 88 sq cm (c) 616 sq cm (d) 2464 sq cm
39. 39.A bag has 11 black balls and 10 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 2 (c) 12 (d) 21
40. 40.A bag has 9 white, 3 green and 8 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 3/5 (b) 2/5 (c) 1/3 (d) 2/3

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