Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 315 · 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 mean of 20, 10, 18, 9, 10 and 17? (a) 12 (b) 15 (c) 14 (d) 13
2. 2.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
3. 3.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 30° (b) 31° (c) 150° (d) 210°
4. 4.In a class of 29 children, 23 like maths, 15 like science and 3 like neither. How many like both? (a) 9 (b) 3 (c) 26 (d) 12
5. 5.In a class of 29 children, 20 like cricket, 8 like football and 5 like both. How many like only cricket? (a) 3 (b) 21 (c) 20 (d) 15
6. 6.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 44 cm (b) 88 cm (c) 176 cm (d) 616 cm
7. 7.What is the product of the roots of x² − 10x + 21 = 0? (a) 20 (b) 10 (c) 22 (d) 21
8. 8.What is the 15th term of the AP 16, 21, 26, 31, …? (a) 91 (b) 70 (c) 86 (d) 75
9. 9.What is the midpoint of the line joining (6, 16) and (16, 6)? (a) (22, 22) (b) (12, 11) (c) (11, 11) (d) (5, 5)
10. 10.6 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 36 (b) 24 (c) 9 (d) 18
11. 11.In a class of 30 children, 24 like maths, 8 like science and 5 like both. How many like neither? (a) 5 (b) 8 (c) 3 (d) 4
12. 12.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 24 (c) 25 (d) 37
13. 13.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 51 (c) 54 (d) 153
14. 14.In which quadrant does the point (−9, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
15. 15.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
16. 16.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/2 (b) 1/3 (c) 2/3 (d) 1/4
17. 17.Which term of the AP 7, 13, 19, 25, … is 97? (a) 18th (b) 15th (c) 17th (d) 16th
18. 18.A drawer has lots of black, red, 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) 5 (b) 4 (c) 8 (d) 2
19. 19.How many factors does 15 have? (a) 3 (b) 4 (c) 5 (d) 2
20. 20.Two angles of a triangle are 35° and 110°. What is the exterior angle at the third corner? (a) 215° (b) 70° (c) 145° (d) 35°
21. 21.What is the 15th term of the AP 17, 26, 35, 44, …? (a) 126 (b) 152 (c) 135 (d) 143
22. 22.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 75° (b) 76° (c) 105° (d) 255°
23. 23.A drawer has lots of black, red, blue, yellow 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) 5 (b) 2 (c) 10 (d) 6
24. 24.A bag has 9 green, 8 red and 8 white balls. One ball is taken out without looking. What is the probability that it is not white? (a) 18/25 (b) 17/25 (c) 8/25 (d) 1/3
25. 25.What is the mode of 17, 2, 12, 2, 17, 14 and 17? (a) 17 (b) 2 (c) 12 (d) 14
26. 26.In a class of 29 children, 19 like mangoes, 13 like bananas and 7 like neither. How many like both? (a) 3 (b) 10 (c) 22 (d) 7
27. 27.What is the prime factorisation of 560? (a) 2 × 5 × 7⁴ (b) 2⁴ × 5 × 7 (c) 2⁵ × 5 × 7 (d) 2³ × 5 × 7
28. 28.What is the prime factorisation of 90? (a) 2 × 3² × 5² (b) 2² × 3² × 5 (c) 2³ × 3² × 5 (d) 2 × 3² × 5
29. 29.Which is the correct factorisation of x² + 10x + 24? (a) (x + 4)(x + 6) (b) (x − 4)(x − 6) (c) (x + 1)(x + 9) (d) (x + 1)(x + 24)
30. 30.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 64 (b) 16 (c) 28 (d) 56
31. 31.What is the mean of 5, 3, 19, 6 and 7? (a) 9 (b) 7 (c) 8 (d) 10
32. 32.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 348 (c) 357 (d) 358
33. 33.What is the 23rd term of the AP 3, 10, 17, 24, …? (a) 154 (b) 157 (c) 161 (d) 164
34. 34.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 616 sq cm (c) 77 sq cm (d) 44 sq cm
35. 35.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 435 (c) 362 (d) 436
36. 36.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 140° (b) 40° (c) 75° (d) 145°
37. 37.What is the mean of 20, 11, 19, 2 and 23? (a) 16 (b) 14 (c) 17 (d) 15
38. 38.In a class of 25 children, 11 like maths, 17 like science and 6 like both. How many like only maths? (a) 11 (b) 5 (c) 8 (d) 6
39. 39.If a + b = 19 and ab = 90, what is a² + b²? (a) 271 (b) 361 (c) 541 (d) 181
40. 40.In a class of 31 children, 21 like mangoes, 18 like bananas and 11 like both. How many like only mangoes? (a) 21 (b) 7 (c) 13 (d) 10

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