Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 660 · 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.Which term of the AP 2, 9, 16, 23, … is 114? (a) 19th (b) 18th (c) 17th (d) 16th
2. 2.What is the mode of 6, 14, 20, 20, 14, 12 and 20? (a) 6 (b) 20 (c) 14 (d) 12
3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
4. 4.What is the sum of all the whole numbers from 1 to 84? (a) 3486 (b) 7140 (c) 3528 (d) 3570
5. 5.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 306 (c) 342 (d) 352
6. 6.Which term of the AP 10, 14, 18, 22, … is 74? (a) 18th (b) 17th (c) 16th (d) 19th
7. 7.Which term of the AP 2, 4, 6, 8, … is 26? (a) 14th (b) 13th (c) 12th (d) 15th
8. 8.What is the distance between the points (4, 12) and (8, 9)? (a) 25 (b) 6 (c) 5 (d) 7
9. 9.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 9 times (b) 6 times (c) 3 times (d) 27 times
10. 10.If a + b = 12 and ab = 27, what is (a − b)²? (a) 90 (b) 144 (c) 36 (d) 6
11. 11.In a class of 37 children, 18 like cricket, 21 like football and 9 like both. How many like only cricket? (a) 16 (b) 12 (c) 18 (d) 9
12. 12.Two angles of a triangle are 20° and 85°. What is the exterior angle at the third corner? (a) 75° (b) 160° (c) 105° (d) 95°
13. 13.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 75 (c) 72 (d) 216
14. 14.In a class of 20 children, 13 like mangoes, 12 like bananas and 8 like both. How many like neither? (a) 4 (b) 8 (c) 11 (d) 3
15. 15.Two angles of a triangle are 60° and 60°. What is the exterior angle at the third corner? (a) 121° (b) 60° (c) 120° (d) 240°
16. 16.What is the product of the roots of x² − 13x + 36 = 0? (a) 35 (b) 13 (c) 36 (d) 37
17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 7 (b) 19 (c) 18 (d) 17
18. 18.What is the mode of 13, 2, 2, 7, 2, 7 and 12? (a) 2 (b) 12 (c) 13 (d) 7
19. 19.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 44 sq cm (d) 77 sq cm
20. 20.In a class of 50 children, 28 like dance, 27 like music and 3 like neither. How many like both? (a) 5 (b) 3 (c) 8 (d) 47
21. 21.How many factors does 93 have? (a) 3 (b) 5 (c) 4 (d) 2
22. 22.The mean of 5 numbers is 22. When the number 34 is added to them, what is the new mean? (a) 28 (b) 25 (c) 22 (d) 24
23. 23.What is the 21st term of the AP 12, 18, 24, 30, …? (a) 120 (b) 138 (c) 126 (d) 132
24. 24.In which quadrant does the point (2, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
25. 25.Using (a + b)² = a² + 2ab + b², what is 65²? (a) 3625 (b) 4225 (c) 3025 (d) 4235
26. 26.What are the roots of x² − 15x + 56 = 0? (a) 1 and 14 (b) 2 and 28 (c) 7 and 8 (d) 1 and 56
27. 27.What is the smallest prime factor of 55? (a) 5 (b) 2 (c) 11 (d) 1
28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
29. 29.A canteen sells 5 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 11 (b) 35 (c) 60 (d) 30
30. 30.A drawer has lots of green, red 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) 6 (b) 2 (c) 4 (d) 3
31. 31.What is the prime factorisation of 70? (a) 2 × 5 × 7² (b) 2³ × 5 × 7 (c) 2² × 5 × 7 (d) 2 × 5 × 7
32. 32.Two angles of a triangle are 70° and 85°. What is the third angle? (a) 155° (b) 95° (c) 110° (d) 25°
33. 33.What is the sum of the first 7 terms of the AP 4, 7, 10, …? (a) 182 (b) 22 (c) 94 (d) 91
34. 34.A cube has edges of 10 cm. What is its total surface area? (a) 600 sq cm (b) 100 sq cm (c) 1000 sq cm (d) 400 sq cm
35. 35.How many factors does 67 have? (a) 1 (b) 4 (c) 2 (d) 3
36. 36.How many prime numbers are there between 20 and 40? (a) 6 (b) 4 (c) 5 (d) 3
37. 37.A bag has 3 black balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 15 (b) 4 (c) 2 (d) 5
38. 38.Using (a − b)² = a² − 2ab + b², what is 75²? (a) 5635 (b) 7225 (c) 5625 (d) 6375
39. 39.The mean of 5 numbers is 36. When the number 12 is added to them, what is the new mean? (a) 32 (b) 36 (c) 24 (d) 33
40. 40.What is the median of 37, 22, 20, 24, 18, 17 and 27? (a) 24 (b) 23 (c) 22 (d) 20

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