Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 835 · 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.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 9 (d) 6
2. 2.What is the mode of 1, 16, 16, 2, 2, 2 and 14? (a) 16 (b) 1 (c) 2 (d) 14
3. 3.What are the roots of x² − 13x + 36 = 0? (a) 2 and 18 (b) 1 and 12 (c) 1 and 36 (d) 4 and 9
4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 3 (d) 2
5. 5.What is the prime factorisation of 280? (a) 2⁴ × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7³ (d) 2² × 5 × 7
6. 6.In a class of 37 children, 13 like maths, 21 like science and 5 like both. How many like neither? (a) 8 (b) 5 (c) 3 (d) 13
7. 7.What is the sum of the roots of x² − 15x + 54 = 0? (a) 15 (b) 54 (c) 14 (d) 16
8. 8.If the side of a square is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
9. 9.What is the mode of 2, 3, 5, 3, 10, 5 and 3? (a) 10 (b) 5 (c) 3 (d) 2
10. 10.The mean of 9 numbers is 34. When the number 74 is added to them, what is the new mean? (a) 38 (b) 34 (c) 39 (d) 54
11. 11.In an isosceles triangle, the two equal angles are 40° each. What is the third angle? (a) 140° (b) 100° (c) 50° (d) 40°
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
13. 13.What is the sum of all the whole numbers from 1 to 70? (a) 2450 (b) 2485 (c) 4970 (d) 2415
14. 14.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 9 times (c) 6 times (d) 27 times
15. 15.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 400 (c) 399 (d) 338
16. 16.What is the product of the roots of x² − 17x + 72 = 0? (a) 73 (b) 71 (c) 17 (d) 72
17. 17.Two angles of a triangle are 70° and 60°. What is the exterior angle at the third corner? (a) 50° (b) 110° (c) 130° (d) 120°
18. 18.What is the mode of 20, 8, 8, 18, 18, 7 and 18? (a) 18 (b) 8 (c) 20 (d) 7
19. 19.What is the mode of 11, 11, 3, 6, 1, 11 and 1? (a) 11 (b) 1 (c) 3 (d) 6
20. 20.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 78 (c) 88 (d) 87
21. 21.The mean of 4 numbers is 31. When the number 21 is added to them, what is the new mean? (a) 31 (b) 26 (c) 30 (d) 29
22. 22.What is the midpoint of the line joining (9, 9) and (21, 11)? (a) (30, 20) (b) (15, 10) (c) (6, 1) (d) (10, 15)
23. 23.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
24. 24.In a class of 35 children, 23 like mangoes, 17 like bananas and 12 like both. How many like at least one of the two? (a) 28 (b) 40 (c) 35 (d) 16
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) 7 (b) 15 (c) 14 (d) 8
26. 26.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 44 cm (d) 22 cm
27. 27.Using (a − b)² = a² − 2ab + b², what is 15²? (a) 375 (b) 625 (c) 235 (d) 225
28. 28.What is the smallest prime factor of 145? (a) 2 (b) 1 (c) 5 (d) 29
29. 29.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 69 (c) 22 (d) 198
30. 30.How many factors does 17 have? (a) 2 (b) 3 (c) 4 (d) 1
31. 31.What is the sum of all the whole numbers from 1 to 16? (a) 272 (b) 128 (c) 136 (d) 120
32. 32.What is the sum of the first 7 terms of the AP 6, 10, 14, …? (a) 252 (b) 126 (c) 30 (d) 140
33. 33.How many factors does 107 have? (a) 1 (b) 3 (c) 4 (d) 2
34. 34.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 528 (c) 430 (d) 538
35. 35.What is the sum of all the whole numbers from 1 to 20? (a) 210 (b) 200 (c) 420 (d) 190
36. 36.A drawer has lots of green, yellow 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) 3 (b) 2 (c) 4 (d) 6
37. 37.How many prime numbers are there between 80 and 100? (a) 4 (b) 3 (c) 5 (d) 2
38. 38.In a class of 24 children, 16 like mangoes, 14 like bananas and 3 like neither. How many like both? (a) 21 (b) 6 (c) 9 (d) 3
39. 39.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 20 (d) 18

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