Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 169 · 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.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 120° (b) 140° (c) 40° (d) 100°
2. 2.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 140° (b) 40° (c) 30° (d) 20°
3. 3.How many factors does 115 have? (a) 5 (b) 4 (c) 3 (d) 2
4. 4.If a + b = 17 and ab = 72, what is a² + b²? (a) 145 (b) 217 (c) 289 (d) 433
5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 9 (d) 18
6. 6.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 81 (b) 30 (c) 9 (d) 27
7. 7.A bag has 6 yellow balls and 11 blue 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) 7 (c) 12 (d) 17
8. 8.A bag has 11 white balls and 7 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 12 (b) 13 (c) 2 (d) 18
9. 9.What is the 40th term of the AP 3, 10, 17, 24, …? (a) 280 (b) 273 (c) 276 (d) 283
10. 10.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 36 (d) 33
11. 11.In an isosceles triangle, the angle between the two equal sides is 80°. What is each of the other two angles? (a) 100° (b) 10° (c) 80° (d) 50°
12. 12.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 217 sq cm (c) 216 sq cm (d) 36 sq cm
13. 13.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1369 (b) 1849 (c) 1379 (d) 1591
14. 14.A bag has 8 white balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 17 (b) 9 (c) 10 (d) 2
15. 15.In a class of 29 children, 14 like maths, 16 like science and 5 like both. How many like neither? (a) 4 (b) 9 (c) 3 (d) 5
16. 16.What is the distance between the points (3, 17) and (9, 9)? (a) 10 (b) 14 (c) 100 (d) 11
17. 17.How many factors does 102 have? (a) 8 (b) 9 (c) 7 (d) 6
18. 18.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 128 (b) 119 (c) 120 (d) 110
19. 19.A fair dice is rolled once. What is the probability of getting an odd number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
20. 20.The mean of 3 numbers is 22. When the number 18 is added to them, what is the new mean? (a) 20 (b) 23 (c) 21 (d) 22
21. 21.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 24 (c) 12 (d) 16
22. 22.Two angles of a triangle are 35° and 110°. What is the third angle? (a) 145° (b) 35° (c) 215° (d) 70°
23. 23.Two angles of a triangle are 50° and 40°. What is the exterior angle at the third corner? (a) 270° (b) 140° (c) 90° (d) 130°
24. 24.In a class of 31 children, 20 like tea, 12 like coffee and 7 like both. How many like at least one of the two? (a) 32 (b) 18 (c) 25 (d) 31
25. 25.In a class of 42 children, 20 like tea, 27 like coffee and 12 like both. How many like neither? (a) 8 (b) 7 (c) 12 (d) 19
26. 26.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 15 (c) 5 (d) 45
27. 27.What is the 30th term of the AP 2, 4, 6, 8, …? (a) 61 (b) 60 (c) 62 (d) 58
28. 28.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 80° (b) 20° (c) 100° (d) 10°
29. 29.What is the mean of 10, 5, 11, 5 and 9? (a) 7 (b) 8 (c) 10 (d) 9
30. 30.Using (a + b)² = a² + 2ab + b², what is 25²? (a) 425 (b) 225 (c) 635 (d) 625
31. 31.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 616 sq cm (d) 154 sq cm
32. 32.In which quadrant does the point (5, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
33. 33.In a class of 48 children, 29 like mangoes, 19 like bananas and 10 like neither. How many like both? (a) 11 (b) 38 (c) 10 (d) 9
34. 34.What is the sum of the roots of x² − 11x + 30 = 0? (a) 12 (b) 10 (c) 30 (d) 11
35. 35.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 65° (b) 130° (c) 40° (d) 50°
36. 36.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 150° (b) 15° (c) 30° (d) 25°
37. 37.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 616 sq cm (c) 154 sq cm (d) 77 sq cm
38. 38.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 cm (b) 44 cm (c) 616 cm (d) 176 cm
39. 39.How many prime numbers are there between 30 and 50? (a) 6 (b) 4 (c) 5 (d) 7
40. 40.How many prime numbers are there between 10 and 20? (a) 5 (b) 3 (c) 6 (d) 4

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