Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 756 · 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 (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
2. 2.What is the missing term in the AP 15, ?, 23, 27, 31? (a) 18 (b) 19 (c) 23 (d) 20
3. 3.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
4. 4.What is the median of 35, 30, 8, 9, 2, 40 and 7? (a) 9 (b) 30 (c) 10 (d) 8
5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 2 (b) 4 (c) 3 (d) 1
6. 6.If a + b = 9 and ab = 20, what is (a − b)²? (a) 1 (b) 61 (c) 81 (d) 41
7. 7.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 35° (c) 70° (d) 110°
8. 8.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 14 (c) 7 (d) 8
9. 9.A bag has 9 red, 8 white and 5 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 5/22 (b) 5/17 (c) 1/3 (d) 17/22
10. 10.How many factors does 66 have? (a) 9 (b) 7 (c) 6 (d) 8
11. 11.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 22 (c) 29 (d) 28
12. 12.What is the mode of 17, 17, 7, 12, 20, 17 and 20? (a) 20 (b) 7 (c) 17 (d) 12
13. 13.A drawer has lots of blue, yellow, black, green 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) 5 (b) 2 (c) 10 (d) 6
14. 14.What is the product of the roots of x² − 17x + 72 = 0? (a) 71 (b) 73 (c) 17 (d) 72
15. 15.What is the sum of the first 7 terms of the AP 7, 10, 13, …? (a) 25 (b) 224 (c) 112 (d) 115
16. 16.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 15° (c) 30° (d) 75°
17. 17.The mean of 9 numbers is 21. When the number 11 is added to them, what is the new mean? (a) 20 (b) 19 (c) 16 (d) 21
18. 18.A drawer has lots of red, green, 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) 4 (b) 5 (c) 8 (d) 2
19. 19.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 18 (c) 21 (d) 6
20. 20.Two angles of a triangle are 30° and 50°. What is the exterior angle at the third corner? (a) 80° (b) 150° (c) 130° (d) 100°
21. 21.How many factors does 68 have? (a) 4 (b) 7 (c) 6 (d) 5
22. 22.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
23. 23.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 24 (c) 27 (d) 72
24. 24.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
25. 25.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 616 cm (b) 176 cm (c) 88 cm (d) 44 cm
26. 26.What is the median of 16, 29, 6, 32 and 1? (a) 16 (b) 6 (c) 17 (d) 29
27. 27.What is the mean of 7, 10, 18 and 21? (a) 16 (b) 13 (c) 14 (d) 15
28. 28.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 1232 sq cm (c) 9856 sq cm (d) 2464 sq cm
29. 29.Which term of the AP 6, 10, 14, 18, … is 46? (a) 12th (b) 13th (c) 10th (d) 11th
30. 30.6 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) 13 (b) 84 (c) 42 (d) 48
31. 31.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
32. 32.In a class of 31 children, 11 like dance, 16 like music and 6 like both. How many like at least one of the two? (a) 31 (b) 15 (c) 27 (d) 21
33. 33.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 3/4 (c) 1/4 (d) 1/2
34. 34.How many prime numbers are there between 20 and 30? (a) 3 (b) 2 (c) 4 (d) 1
35. 35.If a + b = 15 and ab = 56, what is (a − b)²? (a) 169 (b) 113 (c) 225 (d) 1
36. 36.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 24 (c) 32 (d) 10
37. 37.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
38. 38.A fair dice is rolled once. What is the probability of getting a number less than 5? (a) 1/4 (b) 5/6 (c) 2/3 (d) 1/3
39. 39.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 110 cm (b) 3850 cm (c) 440 cm (d) 220 cm
40. 40.In a class of 37 children, 28 like tea, 18 like coffee and 11 like both. How many like only tea? (a) 7 (b) 28 (c) 17 (d) 19

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