Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 855 · 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 captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 24 (b) 144 (c) 132 (d) 66
2. 2.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 693 sq cm (d) 5544 sq cm
3. 3.In an isosceles triangle, the two equal angles are 35° each. What is the third angle? (a) 110° (b) 145° (c) 35° (d) 55°
4. 4.If a + b = 14 and ab = 24, what is (a − b)²? (a) 196 (b) 148 (c) 100 (d) 10
5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 4 (d) 5
6. 6.A drawer has lots of yellow, red, white, blue 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) 6 (b) 5 (c) 10 (d) 2
7. 7.What is the prime factorisation of 20? (a) 2 × 5² (b) 2 × 5 (c) 2² × 5 (d) 2³ × 5
8. 8.What is the 11th term of the AP 14, 17, 20, 23, …? (a) 33 (b) 47 (c) 30 (d) 44
9. 9.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 230° (b) 50° (c) 130° (d) 51°
10. 10.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 588 (c) 470 (d) 598
11. 11.What is the missing term in the AP 1, 7, ?, 19, 25? (a) 12 (b) 13 (c) 19 (d) 14
12. 12.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 120° (b) 60° (c) 59° (d) 61°
13. 13.Using (a + b)² = a² + 2ab + b², what is 43²? (a) 1369 (b) 1859 (c) 1849 (d) 1609
14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 7 (d) 17
15. 15.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 72 (b) 81 (c) 36 (d) 18
16. 16.In a class of 60 children, 31 like dance, 31 like music and 11 like both. How many like at least one of the two? (a) 60 (b) 40 (c) 62 (d) 51
17. 17.What is the mode of 2, 1, 2, 4, 5, 2 and 4? (a) 4 (b) 1 (c) 2 (d) 5
18. 18.What is the mean of 9, 17, 9 and 9? (a) 10 (b) 12 (c) 13 (d) 11
19. 19.A bag has 4 red balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 5 (b) 9 (c) 2 (d) 6
20. 20.How many prime numbers are there between 90 and 120? (a) 8 (b) 6 (c) 7 (d) 5
21. 21.What is the sum of the first 11 terms of the AP 5, 11, 17, …? (a) 418 (b) 65 (c) 770 (d) 385
22. 22.What is the sum of the first 8 terms of the AP 6, 12, 18, …? (a) 432 (b) 216 (c) 240 (d) 48
23. 23.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
24. 24.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 15 (c) 21 (d) 30
25. 25.In a class of 29 children, 12 like dance, 21 like music and 8 like both. How many like at least one of the two? (a) 29 (b) 17 (c) 25 (d) 33
26. 26.In a class of 30 children, 19 like maths, 18 like science and 9 like both. How many like only maths? (a) 12 (b) 10 (c) 19 (d) 9
27. 27.A canteen sells 3 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 21 (b) 18 (c) 9 (d) 36
28. 28.In a class of 44 children, 18 like mangoes, 30 like bananas and 12 like both. How many like at least one of the two? (a) 36 (b) 48 (c) 44 (d) 24
29. 29.How many prime numbers are there between 60 and 80? (a) 7 (b) 6 (c) 4 (d) 5
30. 30.How many prime numbers are there between 70 and 80? (a) 2 (b) 5 (c) 3 (d) 4
31. 31.Using (a − b)² = a² − 2ab + b², what is 29²? (a) 961 (b) 841 (c) 899 (d) 851
32. 32.What is the mode of 3, 3, 3, 14, 1, 6 and 6? (a) 6 (b) 1 (c) 14 (d) 3
33. 33.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 25 times (b) 5 times (c) 10 times (d) 125 times
34. 34.What is the distance between the points (4, 2) and (20, 14)? (a) 28 (b) 400 (c) 20 (d) 21
35. 35.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
36. 36.In a class of 43 children, 30 like mangoes, 18 like bananas and 11 like both. How many like only mangoes? (a) 30 (b) 7 (c) 19 (d) 25
37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 4 (b) 13 (c) 15 (d) 14
38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 3 (d) 2
39. 39.There are 5 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 30 (b) 35 (c) 11 (d) 60
40. 40.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 100 (c) 20 (d) 45

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