Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 432 · 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.What is the midpoint of the line joining (6, 10) and (14, 8)? (a) (4, 1) (b) (10, 9) (c) (20, 18) (d) (9, 10)
2. 2.What is the median of 1, 16, 22, 8 and 20? (a) 22 (b) 8 (c) 16 (d) 20
3. 3.In a class of 24 children, 7 like maths, 19 like science and 4 like both. How many like at least one of the two? (a) 26 (b) 24 (c) 22 (d) 18
4. 4.In a class of 44 children, 27 like cricket, 23 like football and 8 like both. How many like neither? (a) 8 (b) 10 (c) 3 (d) 2
5. 5.In a class of 44 children, 26 like dance, 27 like music and 12 like both. How many like neither? (a) 12 (b) 3 (c) 4 (d) 15
6. 6.What is the distance between the points (2, 17) and (11, 5)? (a) 225 (b) 15 (c) 16 (d) 21
7. 7.A bag has 10 black balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 21 (b) 11 (c) 2 (d) 12
8. 8.Two angles of a triangle are 55° and 75°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 125° (d) 50°
9. 9.A bag has 6 white balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 8 (b) 2 (c) 9 (d) 7
10. 10.The mean of 8 numbers is 12. When the number 39 is added to them, what is the new mean? (a) 12 (b) 15 (c) 14 (d) 16
11. 11.In a class of 19 children, 7 like mangoes, 6 like bananas and 2 like both. How many like neither? (a) 2 (b) 6 (c) 10 (d) 8
12. 12.How many factors does 111 have? (a) 3 (b) 2 (c) 4 (d) 5
13. 13.What is the missing term in the AP 7, 10, 13, ?, 19? (a) 15 (b) 17 (c) 16 (d) 19
14. 14.How many factors does 59 have? (a) 3 (b) 4 (c) 2 (d) 1
15. 15.In a class of 40 children, 19 like cricket, 29 like football and 12 like both. How many like neither? (a) 12 (b) 16 (c) 5 (d) 4
16. 16.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 264 cm (c) 132 cm (d) 66 cm
17. 17.What is the sum of the first 19 odd numbers (1 + 3 + 5 + …)? (a) 37 (b) 380 (c) 361 (d) 190
18. 18.What is the median of 37, 40, 35, 3, 7, 2 and 10? (a) 3 (b) 10 (c) 7 (d) 35
19. 19.The mean of 7 numbers is 37. When the number 53 is added to them, what is the new mean? (a) 37 (b) 45 (c) 39 (d) 40
20. 20.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 112 (c) 103 (d) 104
21. 21.Using (a + b)² = a² + 2ab + b², what is 34²? (a) 1156 (b) 916 (c) 1166 (d) 676
22. 22.A bag has 6 white balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 9 (c) 7 (d) 8
23. 23.In a class of 34 children, 11 like cricket, 20 like football and 6 like both. How many like neither? (a) 9 (b) 3 (c) 15 (d) 6
24. 24.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 1/4 (c) 7/8 (d) 3/8
25. 25.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 70° (c) 110° (d) 140°
26. 26.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7² (b) 2 × 3 × 5 × 7 (c) 2² × 3 × 5 × 7 (d) 2³ × 3 × 5 × 7
27. 27.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 70° (b) 340° (c) 160° (d) 20°
28. 28.Which is the correct factorisation of x² + 8x + 15? (a) (x − 3)(x − 5) (b) (x + 3)(x + 5) (c) (x + 1)(x + 15) (d) (x + 1)(x + 7)
29. 29.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 32 (c) 64 (d) 40
30. 30.Using (a + b)² = a² + 2ab + b², what is 65²? (a) 4235 (b) 4225 (c) 3625 (d) 3025
31. 31.What is the distance between the points (5, 9) and (13, 15)? (a) 100 (b) 14 (c) 11 (d) 10
32. 32.What is the median of 18, 31, 17, 12 and 13? (a) 13 (b) 16 (c) 18 (d) 17
33. 33.What is the smallest prime factor of 93? (a) 2 (b) 3 (c) 1 (d) 31
34. 34.What is the sum of the first 5 terms of the AP 7, 11, 15, …? (a) 85 (b) 23 (c) 75 (d) 150
35. 35.In a class of 25 children, 13 like cricket, 10 like football and 6 like both. How many like at least one of the two? (a) 11 (b) 25 (c) 23 (d) 17
36. 36.Two straight lines cross. Two vertically opposite angles add up to 140°. What is each of the other two angles? (a) 40° (b) 220° (c) 70° (d) 110°
37. 37.What is the mean of 12, 16, 4 and 12? (a) 11 (b) 13 (c) 10 (d) 12
38. 38.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 10 times (b) 25 times (c) 5 times (d) 125 times
39. 39.Which is the correct factorisation of x² + 6x + 8? (a) (x + 2)(x + 4) (b) (x + 1)(x + 5) (c) (x + 1)(x + 8) (d) (x − 2)(x − 4)
40. 40.What is the distance between the points (8, 1) and (32, 8)? (a) 31 (b) 26 (c) 25 (d) 625

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