Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 972 · 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.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 240 (c) 25 (d) 120
2. 2.Using (a + b)² = a² + 2ab + b², what is 92²? (a) 7744 (b) 8104 (c) 8464 (d) 8474
3. 3.What is the missing term in the AP 9, 16, 23, ?, 37? (a) 29 (b) 30 (c) 37 (d) 31
4. 4.In a class of 27 children, 12 like mangoes, 17 like bananas and 9 like both. How many like at least one of the two? (a) 29 (b) 27 (c) 11 (d) 20
5. 5.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 85° (b) 170° (c) 86° (d) 95°
6. 6.A bag has 6 green, 2 white and 6 red balls. One ball is taken out without looking. What is the probability that it is not white? (a) 1/7 (b) 1/3 (c) 13/14 (d) 6/7
7. 7.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
8. 8.What is the midpoint of the line joining (10, 10) and (22, 18)? (a) (6, 4) (b) (14, 16) (c) (32, 28) (d) (16, 14)
9. 9.A bag has 7 black balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 8 (b) 10 (c) 2 (d) 9
10. 10.Using (a + b)² = a² + 2ab + b², what is 71²? (a) 5051 (b) 4901 (c) 4761 (d) 5041
11. 11.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) 72 (c) 24 (d) 27
12. 12.What is the mean of 12, 5, 16, 20, 15 and 16? (a) 13 (b) 12 (c) 15 (d) 14
13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 19 (b) 7 (c) 18 (d) 17
14. 14.In a class of 45 children, 23 like cricket, 25 like football and 11 like both. How many like neither? (a) 11 (b) 19 (c) 8 (d) 9
15. 15.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) 22 (b) 28 (c) 29 (d) 21
16. 16.A cuboid is 5 cm long, 3 cm wide and 9 cm high. What is its total surface area? (a) 174 sq cm (b) 348 sq cm (c) 87 sq cm (d) 135 sq cm
17. 17.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) 153 (c) 54 (d) 51
18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 8 (d) 20
19. 19.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
20. 20.Using (a + b)² = a² + 2ab + b², what is 43²? (a) 1609 (b) 1369 (c) 1849 (d) 1859
21. 21.What is the median of 12, 39, 9, 28, 27, 19 and 11? (a) 28 (b) 27 (c) 19 (d) 12
22. 22.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/2 (b) 2/3 (c) 1/6 (d) 1/3
23. 23.A cuboid is 6 cm long, 2 cm wide and 5 cm high. What is its volume? (a) 104 cu cm (b) 13 cu cm (c) 12 cu cm (d) 60 cu cm
24. 24.What is the sum of the first 21 odd numbers (1 + 3 + 5 + …)? (a) 41 (b) 462 (c) 231 (d) 441
25. 25.How many factors does 54 have? (a) 9 (b) 6 (c) 7 (d) 8
26. 26.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 1/11 (c) 1/9 (d) 3/11
27. 27.If the radius of a circle is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 6 times (d) 9 times
28. 28.The mean of 9 numbers is 36. When the number 16 is added to them, what is the new mean? (a) 35 (b) 26 (c) 36 (d) 34
29. 29.In a class of 29 children, 9 like cricket, 18 like football and 3 like both. How many like at least one of the two? (a) 21 (b) 24 (c) 27 (d) 29
30. 30.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 88 sq cm (c) 616 sq cm (d) 308 sq cm
31. 31.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 22 (c) 32 (d) 31
32. 32.Two straight lines cross. Two vertically opposite angles add up to 320°. What is each of the other two angles? (a) 160° (b) 21° (c) 40° (d) 20°
33. 33.How many factors does 58 have? (a) 4 (b) 3 (c) 2 (d) 5
34. 34.If every edge of a cube is made 3 times as long, how many times as big does its volume become? (a) 3 times (b) 6 times (c) 9 times (d) 27 times
35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 16 (b) 15 (c) 5 (d) 17
36. 36.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 132 cm (b) 66 cm (c) 264 cm (d) 1386 cm
37. 37.What is the midpoint of the line joining (8, 4) and (18, 12)? (a) (8, 13) (b) (13, 8) (c) (5, 4) (d) (26, 16)
38. 38.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
39. 39.A cube has edges of 7 cm. What is its total surface area? (a) 343 sq cm (b) 196 sq cm (c) 49 sq cm (d) 294 sq cm
40. 40.What is the median of 38, 14, 20, 39, 15, 27 and 23? (a) 23 (b) 27 (c) 39 (d) 20

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