Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 195 · 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 product of the roots of x² − 11x + 18 = 0? (a) 11 (b) 18 (c) 19 (d) 17
2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
3. 3.A drawer has lots of green, red, black, yellow 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) 5 (b) 6 (c) 2 (d) 10
4. 4.If every edge of a cube is made 2 times as long, how many times as big does its volume become? (a) 8 times (b) 4 times (c) 2 times (d) 6 times
5. 5.What is the distance between the points (1, 6) and (13, 1)? (a) 13 (b) 14 (c) 17 (d) 169
6. 6.A fair dice is rolled once. What is the probability of getting a number less than 4? (a) 1/3 (b) 1/2 (c) 1/6 (d) 2/3
7. 7.If a + b = 15 and ab = 54, what is (a − b)²? (a) 9 (b) 3 (c) 117 (d) 225
8. 8.What is the smallest prime factor of 209? (a) 19 (b) 2 (c) 11 (d) 1
9. 9.In which quadrant does the point (3, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
10. 10.If a + b = 13 and ab = 42, what is (a − b)²? (a) 85 (b) 127 (c) 1 (d) 169
11. 11.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 21 (b) 42 (c) 14 (d) 49
12. 12.The mean of 3 numbers is 32. When the number 24 is added to them, what is the new mean? (a) 32 (b) 30 (c) 31 (d) 28
13. 13.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 92 (c) 84 (d) 83
14. 14.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
15. 15.What is the median of 31, 3, 36, 8, 21, 1 and 23? (a) 21 (b) 8 (c) 23 (d) 22
16. 16.What is the mean of 3, 13, 15, 6 and 3? (a) 8 (b) 9 (c) 7 (d) 10
17. 17.Using (a + b)² = a² + 2ab + b², what is 82²? (a) 6724 (b) 6734 (c) 6404 (d) 6084
18. 18.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 5/36 (b) 4/11 (c) 1/9 (d) 1/11
19. 19.What is the missing term in the AP 12, ?, 24, 30, 36? (a) 17 (b) 24 (c) 18 (d) 19
20. 20.The mean of 4 numbers is 35. When the number 25 is added to them, what is the new mean? (a) 34 (b) 33 (c) 30 (d) 35
21. 21.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 184 (c) 176 (d) 175
22. 22.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
23. 23.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 22 (b) 21 (c) 14 (d) 15
24. 24.What is the midpoint of the line joining (6, 9) and (18, 21)? (a) (6, 6) (b) (24, 30) (c) (12, 15) (d) (15, 12)
25. 25.How many prime numbers are there between 40 and 70? (a) 7 (b) 6 (c) 9 (d) 8
26. 26.A drawer has lots of blue, green 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) 3 (b) 4 (c) 6 (d) 2
27. 27.What is the smallest prime factor of 169? (a) 2 (b) 3 (c) 13 (d) 1
28. 28.A drawer has lots of black, blue and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 6 (c) 2 (d) 3
29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 19 (b) 18 (c) 8 (d) 20
30. 30.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 1386 sq cm
31. 31.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 75° (c) 285° (d) 105°
32. 32.Which is the correct factorisation of x² + 13x + 42? (a) (x + 1)(x + 12) (b) (x + 1)(x + 42) (c) (x − 6)(x − 7) (d) (x + 6)(x + 7)
33. 33.What is the 39th term of the AP 18, 21, 24, 27, …? (a) 132 (b) 135 (c) 114 (d) 117
34. 34.A drawer has lots of yellow, black, blue, white 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) 6 (b) 10 (c) 5 (d) 2
35. 35.Two coins are tossed together. What is the probability of getting at least one head? (a) 3/4 (b) 1/4 (c) 1/3 (d) 1/2
36. 36.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
37. 37.A bag has 11 red balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 14 (c) 13 (d) 12
38. 38.What is the prime factorisation of 28? (a) 2 × 7² (b) 2 × 7 (c) 2³ × 7 (d) 2² × 7
39. 39.A bag has 6 yellow, 7 white and 3 green balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 3/5 (b) 5/8 (c) 1/3 (d) 3/8
40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 2 (b) 4 (c) 5 (d) 3

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