Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 834 · 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 many prime numbers are there between 30 and 60? (a) 6 (b) 8 (c) 9 (d) 7
2. 2.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 3850 cm (b) 220 cm (c) 440 cm (d) 110 cm
3. 3.What is the sum of the roots of x² − 13x + 40 = 0? (a) 14 (b) 40 (c) 12 (d) 13
4. 4.What is the sum of the roots of x² − 16x + 63 = 0? (a) 15 (b) 63 (c) 17 (d) 16
5. 5.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 3/4 (b) 1/3 (c) 1/4 (d) 1/2
6. 6.In a class of 32 children, 24 like maths, 7 like science and 5 like neither. How many like both? (a) 3 (b) 4 (c) 5 (d) 27
7. 7.What is the 38th term of the AP 14, 17, 20, 23, …? (a) 114 (b) 128 (c) 111 (d) 125
8. 8.There are 5 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 20 (b) 30 (c) 15 (d) 8
9. 9.What is the mode of 1, 14, 18, 14, 17, 18 and 14? (a) 1 (b) 18 (c) 17 (d) 14
10. 10.In a class of 34 children, 19 like cricket, 18 like football and 5 like both. How many like neither? (a) 5 (b) 3 (c) 7 (d) 2
11. 11.In how many different ways can the letters of the word TIGER be arranged? (a) 240 (b) 120 (c) 20 (d) 25
12. 12.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 25 (c) 120 (d) 240
13. 13.Using (a − b)² = a² − 2ab + b², what is 58²? (a) 3374 (b) 3596 (c) 3844 (d) 3364
14. 14.In a class of 31 children, 15 like cricket, 12 like football and 8 like neither. How many like both? (a) 23 (b) 4 (c) 5 (d) 8
15. 15.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 152 (c) 160 (d) 151
16. 16.A drawer has lots of white, green, 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) 8 (b) 2 (c) 5 (d) 4
17. 17.How many prime numbers are there between 90 and 100? (a) 1 (b) 3 (c) 0 (d) 2
18. 18.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
19. 19.A cube has edges of 10 cm. What is its volume? (a) 600 cu cm (b) 1000 cu cm (c) 400 cu cm (d) 30 cu cm
20. 20.What is the 39th term of the AP 4, 7, 10, 13, …? (a) 114 (b) 117 (c) 121 (d) 118
21. 21.What is the smallest prime factor of 221? (a) 17 (b) 2 (c) 1 (d) 13
22. 22.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 324 sq cm (c) 729 sq cm (d) 81 sq cm
23. 23.What is the distance between the points (8, 9) and (20, 25)? (a) 400 (b) 21 (c) 20 (d) 28
24. 24.If a + b = 18 and ab = 80, what is a² + b²? (a) 244 (b) 324 (c) 164 (d) 484
25. 25.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
26. 26.Two angles of a triangle are 30° and 45°. What is the third angle? (a) 150° (b) 105° (c) 135° (d) 75°
27. 27.The mean of 9 numbers is 12. When the number 52 is added to them, what is the new mean? (a) 16 (b) 12 (c) 17 (d) 32
28. 28.Using (a + b)² = a² + 2ab + b², what is 21²? (a) 401 (b) 441 (c) 451 (d) 361
29. 29.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 280 (c) 270 (d) 258
30. 30.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 88 sq cm
31. 31.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 5 (b) 6 (c) 12 (d) 9
32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 19 (b) 7 (c) 18 (d) 17
33. 33.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 120° (b) 125° (c) 115° (d) 60°
34. 34.A drawer has lots of black, white, yellow, green 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) 10 (b) 2 (c) 5 (d) 6
35. 35.A bag has 5 yellow balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 6 (b) 2 (c) 7 (d) 11
36. 36.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 3/11 (b) 1/11 (c) 1/12 (d) 1/9
37. 37.How many factors does 39 have? (a) 2 (b) 4 (c) 5 (d) 3
38. 38.A bag has 9 white, 9 blue and 7 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 17/25 (b) 9/25 (c) 16/25 (d) 1/3
39. 39.A bag has 4 red balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 6 (c) 10 (d) 2
40. 40.In a league, 9 teams each play every other team once. How many matches are played? (a) 81 (b) 72 (c) 45 (d) 36

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