Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 340 · 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.A captain and a vice-captain are to be chosen from 11 players. In how many ways can this be done? (a) 121 (b) 22 (c) 110 (d) 55
2. 2.What is the 11th term of the AP 18, 27, 36, 45, …? (a) 99 (b) 108 (c) 90 (d) 117
3. 3.What is the midpoint of the line joining (6, 4) and (12, 10)? (a) (7, 9) (b) (3, 3) (c) (9, 7) (d) (18, 14)
4. 4.What is the smallest prime factor of 253? (a) 2 (b) 1 (c) 23 (d) 11
5. 5.A drawer has lots of yellow, blue, black 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) 2 (b) 8 (c) 5 (d) 4
6. 6.If a + b = 15 and ab = 56, what is a² + b²? (a) 169 (b) 113 (c) 337 (d) 225
7. 7.A cuboid is 11 cm long, 4 cm wide and 5 cm high. What is its total surface area? (a) 220 sq cm (b) 119 sq cm (c) 238 sq cm (d) 476 sq cm
8. 8.Two angles of a triangle are 40° and 55°. What is the exterior angle at the third corner? (a) 140° (b) 95° (c) 125° (d) 85°
9. 9.How many prime numbers are there between 70 and 80? (a) 3 (b) 4 (c) 5 (d) 2
10. 10.The mean of 4 numbers is 11. When the number 31 is added to them, what is the new mean? (a) 16 (b) 15 (c) 21 (d) 11
11. 11.What is the median of 36, 21, 3, 40, 38, 19 and 11? (a) 21 (b) 40 (c) 36 (d) 24
12. 12.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
13. 13.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 6 (b) 16 (c) 12 (d) 8
14. 14.Two angles of a triangle are 75° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 50° (c) 130° (d) 105°
15. 15.How many factors does 56 have? (a) 8 (b) 7 (c) 6 (d) 9
16. 16.A bag has 4 green, 7 blue and 4 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 4/15 (b) 1/3 (c) 4/11 (d) 11/15
17. 17.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 45° (b) 90° (c) 270° (d) 135°
18. 18.A drawer has lots of green, blue, 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) 5 (b) 8 (c) 4 (d) 2
19. 19.A drawer has lots of red 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) 3 (b) 5 (c) 4 (d) 2
20. 20.4 T-shirts and 7 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 56 (c) 32 (d) 11
21. 21.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 7 (d) 5
22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/36 (b) 1/11 (c) 1/18 (d) 1/12
23. 23.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/4 (d) 3/8
24. 24.If a + b = 19 and ab = 88, what is a² + b²? (a) 361 (b) 537 (c) 273 (d) 185
25. 25.The mean of 3 numbers is 29. When the number 13 is added to them, what is the new mean? (a) 26 (b) 29 (c) 25 (d) 21
26. 26.In a class of 21 children, 10 like mangoes, 12 like bananas and 3 like both. How many like at least one of the two? (a) 21 (b) 16 (c) 22 (d) 19
27. 27.There are 6 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 8 (c) 12 (d) 24
28. 28.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 40° (c) 100° (d) 50°
29. 29.Two straight lines cross. Two vertically opposite angles add up to 120°. What is each of the other two angles? (a) 60° (b) 240° (c) 121° (d) 120°
30. 30.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/4
31. 31.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
32. 32.In a class of 42 children, 14 like cricket, 21 like football and 3 like both. How many like at least one of the two? (a) 42 (b) 29 (c) 35 (d) 32
33. 33.Two angles of a triangle are 50° and 30°. What is the third angle? (a) 80° (b) 100° (c) 150° (d) 130°
34. 34.A drawer has lots of 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) 5 (b) 4 (c) 2 (d) 3
35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/11 (b) 1/18 (c) 1/12 (d) 2/11
36. 36.What is the 40th term of the AP 16, 18, 20, 22, …? (a) 94 (b) 80 (c) 78 (d) 96
37. 37.If a + b = 15 and ab = 44, what is a² + b²? (a) 181 (b) 137 (c) 225 (d) 313
38. 38.What is the mean of 6, 3, 16, 17 and 18? (a) 10 (b) 12 (c) 13 (d) 15
39. 39.In which quadrant does the point (−1, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
40. 40.Which is the correct factorisation of x² + 17x + 72? (a) (x − 8)(x − 9) (b) (x + 1)(x + 72) (c) (x + 8)(x + 9) (d) (x + 1)(x + 16)

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