Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 438 · 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.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 3 (b) 5 (c) 2 (d) 4
2. 2.What is the mean of 10, 10, 14, 11 and 10? (a) 10 (b) 11 (c) 13 (d) 12
3. 3.A bag has 4 yellow balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 6 (b) 2 (c) 11 (d) 5
4. 4.What is the prime factorisation of 126? (a) 2 × 3² × 7² (b) 2 × 3² × 7 (c) 2² × 3² × 7 (d) 2³ × 3² × 7
5. 5.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
6. 6.In a class of 47 children, 18 like dance, 30 like music and 10 like neither. How many like both? (a) 1 (b) 11 (c) 10 (d) 37
7. 7.There are 4 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 8 (c) 32 (d) 16
8. 8.What is the midpoint of the line joining (1, 10) and (3, 2)? (a) (4, 12) (b) (1, 4) (c) (6, 2) (d) (2, 6)
9. 9.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) 22 (b) 28 (c) 29 (d) 21
10. 10.What is the smallest prime factor of 51? (a) 2 (b) 3 (c) 17 (d) 1
11. 11.Which is the correct factorisation of x² + 13x + 36? (a) (x + 1)(x + 36) (b) (x − 4)(x − 9) (c) (x + 1)(x + 12) (d) (x + 4)(x + 9)
12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 35 (c) 324 (d) 171
13. 13.Two angles of a triangle are 80° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 100° (c) 70° (d) 150°
14. 14.In a class of 40 children, 11 like mangoes, 24 like bananas and 4 like both. How many like neither? (a) 13 (b) 5 (c) 9 (d) 4
15. 15.What is the missing term in the AP 20, 29, 38, ?, 56? (a) 47 (b) 56 (c) 46 (d) 48
16. 16.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7 (c) 3³ × 7 (d) 3 × 7²
17. 17.If a + b = 16 and ab = 55, what is a² + b²? (a) 366 (b) 146 (c) 256 (d) 201
18. 18.If a + b = 8 and ab = 12, what is a² + b²? (a) 40 (b) 88 (c) 64 (d) 52
19. 19.What is the 21st term of the AP 10, 19, 28, 37, …? (a) 180 (b) 199 (c) 189 (d) 190
20. 20.4 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 10 (c) 24 (d) 48
21. 21.A cuboid is 10 cm long, 7 cm wide and 2 cm high. What is its total surface area? (a) 140 sq cm (b) 104 sq cm (c) 416 sq cm (d) 208 sq cm
22. 22.What is the midpoint of the line joining (1, 9) and (9, 1)? (a) (10, 10) (b) (5, 5) (c) (4, 4) (d) (6, 5)
23. 23.A bag has 11 red balls and 5 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 13 (b) 16 (c) 2 (d) 12
24. 24.A bag has 6 yellow, 4 blue and 2 red balls. One ball is taken out without looking. What is the probability that it is blue? (a) 5/12 (b) 1/2 (c) 1/3 (d) 2/3
25. 25.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 64 times (c) 8 times (d) 16 times
26. 26.In a class of 38 children, 14 like maths, 27 like science and 7 like both. How many like only maths? (a) 20 (b) 14 (c) 11 (d) 7
27. 27.A bag has 4 yellow, 9 red and 2 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 2/5 (c) 2/3 (d) 3/5
28. 28.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/4 (b) 1/3 (c) 5/6 (d) 2/3
29. 29.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/3 (c) 1/2 (d) 2/3
30. 30.A cuboid is 8 cm long, 5 cm wide and 3 cm high. What is its volume? (a) 158 cu cm (b) 16 cu cm (c) 120 cu cm (d) 40 cu cm
31. 31.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 40° (b) 140° (c) 115° (d) 105°
32. 32.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
33. 33.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 100° (b) 80° (c) 20° (d) 10°
34. 34.Which is the correct factorisation of x² + 8x + 15? (a) (x + 3)(x + 5) (b) (x + 1)(x + 15) (c) (x + 1)(x + 7) (d) (x − 3)(x − 5)
35. 35.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 12 (b) 15 (c) 36 (d) 30
36. 36.In a class of 39 children, 22 like maths, 20 like science and 9 like both. How many like only maths? (a) 19 (b) 11 (c) 22 (d) 13
37. 37.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
38. 38.What is the distance between the points (6, 20) and (22, 8)? (a) 28 (b) 20 (c) 21 (d) 400
39. 39.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 303 (c) 304 (d) 274
40. 40.In a class of 38 children, 14 like mangoes, 26 like bananas and 10 like both. How many like at least one of the two? (a) 30 (b) 38 (c) 20 (d) 40

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