Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 86 · 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 far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
2. 2.Using (a − b)² = a² − 2ab + b², what is 67²? (a) 5329 (b) 4891 (c) 4489 (d) 4499
3. 3.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 12) (b) (x − 5)(x − 8) (c) (x + 5)(x + 8) (d) (x + 1)(x + 40)
4. 4.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 72 (b) 12 (c) 144 (d) 73
5. 5.How many factors does 101 have? (a) 4 (b) 1 (c) 3 (d) 2
6. 6.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 6 (b) 8 (c) 9 (d) 7
7. 7.What is the mode of 9, 9, 8, 18, 8, 1 and 9? (a) 8 (b) 18 (c) 1 (d) 9
8. 8.A bag has 11 green balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 5 (c) 12 (d) 15
9. 9.A drawer has lots of red, blue, yellow and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 8 (b) 5 (c) 2 (d) 4
10. 10.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 154 cm (d) 22 cm
11. 11.What is the mode of 18, 17, 5, 17, 11, 5 and 17? (a) 17 (b) 5 (c) 18 (d) 11
12. 12.A cube has edges of 6 cm. What is its volume? (a) 18 cu cm (b) 217 cu cm (c) 144 cu cm (d) 216 cu cm
13. 13.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 1/4 (d) 5/6
14. 14.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 121 (c) 110 (d) 22
15. 15.In a class of 27 children, 12 like cricket, 9 like football and 4 like both. How many like at least one of the two? (a) 13 (b) 27 (c) 17 (d) 21
16. 16.In a class of 27 children, 21 like tea, 11 like coffee and 7 like both. How many like only tea? (a) 21 (b) 16 (c) 4 (d) 14
17. 17.In a class of 34 children, 17 like maths, 21 like science and 8 like both. How many like neither? (a) 12 (b) 4 (c) 8 (d) 5
18. 18.What is the mean of 13, 2, 12 and 17? (a) 10 (b) 13 (c) 12 (d) 11
19. 19.What is the midpoint of the line joining (3, 16) and (11, 6)? (a) (14, 22) (b) (4, 5) (c) (11, 7) (d) (7, 11)
20. 20.A bag has 8 blue balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 11 (c) 18 (d) 9
21. 21.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
22. 22.What is the prime factorisation of 240? (a) 2 × 3 × 5⁴ (b) 2³ × 3 × 5 (c) 2⁴ × 3 × 5 (d) 2⁵ × 3 × 5
23. 23.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
24. 24.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 2464 sq cm (d) 1232 sq cm
25. 25.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/6
26. 26.How many factors does 95 have? (a) 5 (b) 4 (c) 3 (d) 2
27. 27.A bag has 3 blue, 7 green and 2 yellow balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 1/4 (b) 3/4 (c) 5/6 (d) 1/3
28. 28.If a + b = 16 and ab = 63, what is a² + b²? (a) 256 (b) 382 (c) 130 (d) 193
29. 29.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 131 (b) 132 (c) 122 (d) 140
30. 30.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 616 cm (b) 44 cm (c) 88 cm (d) 176 cm
31. 31.How many factors does 78 have? (a) 9 (b) 6 (c) 7 (d) 8
32. 32.A drawer has lots of red and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 5 (c) 3 (d) 4
33. 33.What is the sum of the first 15 odd numbers (1 + 3 + 5 + …)? (a) 120 (b) 29 (c) 240 (d) 225
34. 34.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 12 (c) 16 (d) 48
35. 35.What is the median of 1, 20, 11, 16, 40, 26 and 39? (a) 26 (b) 16 (c) 21 (d) 20
36. 36.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 183 (c) 192 (d) 193
37. 37.The mean of 6 numbers is 14. When the number 21 is added to them, what is the new mean? (a) 14 (b) 17 (c) 16 (d) 15
38. 38.In a class of 42 children, 21 like maths, 27 like science and 4 like neither. How many like both? (a) 10 (b) 4 (c) 38 (d) 6
39. 39.A bag has 5 green balls and 9 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 14 (b) 7 (c) 6 (d) 2
40. 40.In a league, 14 teams each play every other team once. How many matches are played? (a) 182 (b) 196 (c) 105 (d) 91

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