Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 887 · 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.Two angles of a triangle are 60° and 70°. What is the third angle? (a) 130° (b) 50° (c) 120° (d) 110°
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/12 (d) 1/9
3. 3.A bag has 5 black balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 10 (b) 7 (c) 2 (d) 6
4. 4.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
5. 5.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 48 (c) 37 (d) 49
6. 6.What is the sum of the first 11 terms of the AP 10, 11, 12, …? (a) 330 (b) 165 (c) 20 (d) 166
7. 7.In how many different ways can the letters of the word STAR be arranged? (a) 12 (b) 16 (c) 48 (d) 24
8. 8.In a league, 15 teams each play every other team once. How many matches are played? (a) 105 (b) 210 (c) 225 (d) 120
9. 9.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 36 (c) 99 (d) 33
10. 10.What is the median of 12, 32, 26, 10, 11, 30 and 38? (a) 26 (b) 30 (c) 10 (d) 12
11. 11.How many factors does 16 have? (a) 4 (b) 6 (c) 5 (d) 3
12. 12.Which term of the AP 12, 20, 28, 36, … is 292? (a) 35th (b) 37th (c) 36th (d) 38th
13. 13.A drawer has lots of white, blue 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) 4 (b) 2 (c) 3 (d) 6
14. 14.In how many different ways can the letters of the word MATHS be arranged? (a) 20 (b) 240 (c) 25 (d) 120
15. 15.A bag has 8 red balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 14 (c) 9 (d) 2
16. 16.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
17. 17.What is the 21st term of the AP 1, 9, 17, 25, …? (a) 161 (b) 168 (c) 160 (d) 169
18. 18.A bag has 8 black balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 12 (b) 9 (c) 5 (d) 2
19. 19.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 2 times (b) 4 times (c) 6 times (d) 8 times
20. 20.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 100° (c) 115° (d) 80°
21. 21.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 80° (c) 260° (d) 100°
22. 22.A bag has 8 green balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 4 (d) 11
23. 23.What is the prime factorisation of 80? (a) 2⁵ × 5 (b) 2⁴ × 5 (c) 2 × 5⁴ (d) 2³ × 5
24. 24.A cube has edges of 11 cm. What is its volume? (a) 33 cu cm (b) 1331 cu cm (c) 726 cu cm (d) 484 cu cm
25. 25.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 7 (c) 14 (d) 15
26. 26.Two angles of a triangle are 65° and 60°. What is the third angle? (a) 115° (b) 55° (c) 125° (d) 120°
27. 27.What is the distance between the points (2, 8) and (18, 20)? (a) 20 (b) 400 (c) 21 (d) 28
28. 28.A drawer has lots of blue, red, yellow, green 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) 5 (b) 10 (c) 2 (d) 6
29. 29.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
30. 30.What is the prime factorisation of 14? (a) 2 × 7 (b) 2³ × 7 (c) 2 × 7² (d) 2² × 7
31. 31.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 90 (c) 20 (d) 100
32. 32.What is the mean of 13, 11, 18, 4, 14 and 6? (a) 10 (b) 13 (c) 12 (d) 11
33. 33.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 30° (b) 75° (c) 15° (d) 105°
34. 34.A cube has edges of 4 cm. What is its total surface area? (a) 96 sq cm (b) 16 sq cm (c) 64 sq cm (d) 97 sq cm
35. 35.A drawer has lots of blue, white, green, black 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) 10 (c) 6 (d) 5
36. 36.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 120° (b) 30° (c) 70° (d) 60°
37. 37.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 1/4 (b) 1/3 (c) 5/6 (d) 2/3
38. 38.In a class of 31 children, 23 like dance, 18 like music and 11 like both. How many like at least one of the two? (a) 31 (b) 41 (c) 30 (d) 19
39. 39.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
40. 40.The numbers 2 to 10 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) 6 (c) 21 (d) 18

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