Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 593 · 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 book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 297 (c) 270 (d) 288
2. 2.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
3. 3.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
4. 4.How many factors does 30 have? (a) 8 (b) 9 (c) 6 (d) 7
5. 5.In which quadrant does the point (8, 3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
6. 6.If a + b = 12 and ab = 11, what is (a − b)²? (a) 122 (b) 100 (c) 144 (d) 10
7. 7.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) 27 (b) 8 (c) 24 (d) 72
8. 8.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) 37 (b) 24 (c) 36 (d) 25
9. 9.A bag has 3 yellow, 6 red and 7 green balls. One ball is taken out without looking. What is the probability that it is not red? (a) 1/3 (b) 11/16 (c) 5/8 (d) 3/8
10. 10.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 55° (d) 125°
11. 11.In a class of 42 children, 22 like mangoes, 21 like bananas and 10 like neither. How many like both? (a) 11 (b) 32 (c) 1 (d) 10
12. 12.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 132 sq cm (c) 5544 sq cm (d) 693 sq cm
13. 13.In how many different ways can the letters of the word LAMP be arranged? (a) 48 (b) 16 (c) 24 (d) 12
14. 14.If a + b = 20 and ab = 96, what is a² + b²? (a) 304 (b) 400 (c) 208 (d) 592
15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 19 (d) 9
16. 16.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 171 (c) 57 (d) 60
17. 17.What is the median of 3, 40, 18, 22, 17, 7 and 4? (a) 22 (b) 18 (c) 7 (d) 17
18. 18.A bag has 9 green balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 10 (b) 15 (c) 11 (d) 2
19. 19.In a class of 33 children, 13 like maths, 22 like science and 6 like both. How many like only maths? (a) 16 (b) 11 (c) 13 (d) 7
20. 20.A bag has 5 red balls and 11 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 2 (b) 6 (c) 16 (d) 12
21. 21.What is the mean of 13, 20, 19, 11 and 17? (a) 17 (b) 15 (c) 20 (d) 16
22. 22.In a class of 20 children, 14 like tea, 7 like coffee and 2 like both. How many like at least one of the two? (a) 21 (b) 17 (c) 19 (d) 20
23. 23.In a class of 31 children, 13 like mangoes, 17 like bananas and 4 like both. How many like only mangoes? (a) 14 (b) 4 (c) 9 (d) 13
24. 24.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 1/2 (c) 3/4 (d) 1/4
25. 25.A bag has 5 red, 3 yellow and 7 blue balls. One ball is taken out without looking. What is the probability that it is blue? (a) 1/3 (b) 8/15 (c) 7/8 (d) 7/15
26. 26.What are the roots of x² − 11x + 18 = 0? (a) 1 and 10 (b) 1 and 18 (c) 3 and 6 (d) 2 and 9
27. 27.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 110° (c) 20° (d) 55°
28. 28.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 35° (b) 25° (c) 50° (d) 130°
29. 29.What is the distance between the points (9, 3) and (14, 15)? (a) 17 (b) 14 (c) 169 (d) 13
30. 30.A bag has 6 white balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 11 (b) 7 (c) 8 (d) 2
31. 31.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 95° (b) 170° (c) 85° (d) 86°
32. 32.A bag has 9 black balls and 8 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 2 (c) 10 (d) 9
33. 33.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 90° (b) 55° (c) 45° (d) 46°
34. 34.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 25 (c) 240 (d) 20
35. 35.In how many different ways can the letters of the word KITE be arranged? (a) 24 (b) 48 (c) 12 (d) 16
36. 36.What is the 40th term of the AP 6, 11, 16, 21, …? (a) 195 (b) 206 (c) 200 (d) 201
37. 37.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 236 sq cm (b) 70 sq cm (c) 118 sq cm (d) 59 sq cm
38. 38.A bag has 9 green, 5 red and 6 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 3/10 (b) 1/3 (c) 3/7 (d) 7/10
39. 39.If a + b = 7 and ab = 6, what is (a − b)²? (a) 5 (b) 49 (c) 25 (d) 37
40. 40.A bag has 3 black balls and 8 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 9 (c) 4 (d) 2

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