Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 433 · 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 a class of 48 children, 27 like mangoes, 20 like bananas and 9 like both. How many like at least one of the two? (a) 48 (b) 47 (c) 38 (d) 29
2. 2.If a + b = 14 and ab = 45, what is a² + b²? (a) 106 (b) 151 (c) 286 (d) 196
3. 3.Using (a + b)² = a² + 2ab + b², what is 21²? (a) 361 (b) 451 (c) 401 (d) 441
4. 4.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
5. 5.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 97 sq cm (c) 96 sq cm (d) 16 sq cm
6. 6.Two angles of a triangle are 35° and 30°. What is the third angle? (a) 65° (b) 150° (c) 145° (d) 115°
7. 7.Two angles of a triangle are 30° and 25°. What is the exterior angle at the third corner? (a) 125° (b) 55° (c) 155° (d) 150°
8. 8.Which term of the AP 4, 8, 12, 16, … is 36? (a) 8th (b) 10th (c) 9th (d) 11th
9. 9.A cube has edges of 3 cm. What is its volume? (a) 9 cu cm (b) 36 cu cm (c) 27 cu cm (d) 54 cu cm
10. 10.What is the product of the roots of x² − 12x + 35 = 0? (a) 34 (b) 35 (c) 12 (d) 36
11. 11.In a class of 33 children, 20 like mangoes, 11 like bananas and 9 like neither. How many like both? (a) 8 (b) 7 (c) 9 (d) 24
12. 12.In how many different ways can the letters of the word PEN be arranged? (a) 9 (b) 12 (c) 6 (d) 3
13. 13.In which quadrant does the point (9, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
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 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) 8 (b) 14 (c) 15 (d) 7
16. 16.The numbers 14 to 22 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) 162 (d) 57
17. 17.A drawer has lots of yellow, blue, green 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) 4 (b) 2 (c) 8 (d) 5
18. 18.What is the distance between the points (4, 5) and (7, 9)? (a) 5 (b) 7 (c) 25 (d) 6
19. 19.What are the roots of x² − 7x + 12 = 0? (a) 1 and 6 (b) 2 and 6 (c) 3 and 4 (d) 1 and 12
20. 20.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 36 (c) 64 (d) 28
21. 21.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 10°
22. 22.What is the sum of the first 7 terms of the AP 6, 8, 10, …? (a) 18 (b) 168 (c) 91 (d) 84
23. 23.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 4/11 (c) 1/11 (d) 1/9
24. 24.What is the mean of 19, 10, 9 and 6? (a) 12 (b) 13 (c) 11 (d) 10
25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
26. 26.If a + b = 17 and ab = 60, what is a² + b²? (a) 169 (b) 289 (c) 409 (d) 229
27. 27.A bag has 5 white balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 7 (b) 2 (c) 14 (d) 6
28. 28.The mean of 3 numbers is 39. When the number 55 is added to them, what is the new mean? (a) 47 (b) 39 (c) 44 (d) 43
29. 29.What is the sum of the first 9 terms of the AP 1, 2, 3, …? (a) 45 (b) 90 (c) 46 (d) 9
30. 30.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
31. 31.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 134 (c) 152 (d) 144
32. 32.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
33. 33.A cuboid is 4 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 8 cu cm (b) 17 cu cm (c) 16 cu cm (d) 40 cu cm
34. 34.A bag has 5 green, 6 blue and 2 red balls. One ball is taken out without looking. What is the probability that it is not blue? (a) 8/13 (b) 1/3 (c) 7/13 (d) 6/13
35. 35.Two angles of a triangle are 75° and 25°. What is the exterior angle at the third corner? (a) 105° (b) 155° (c) 100° (d) 80°
36. 36.What is the sum of the roots of x² − 5x + 6 = 0? (a) 7 (b) 5 (c) 6 (d) 4
37. 37.What is the distance between the points (4, 21) and (20, 9)? (a) 21 (b) 400 (c) 20 (d) 28
38. 38.In a class of 31 children, 23 like maths, 8 like science and 3 like neither. How many like both? (a) 4 (b) 3 (c) 28 (d) 2
39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 3 (d) 4
40. 40.A bag has 3 white balls and 12 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 15 (b) 13 (c) 4 (d) 2

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