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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 889 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.If a + b = 17 and ab = 66, what is a² + b²? (a) 157 (b) 421 (c) 289 (d) 223
  2. 2.How many factors does 80 have? (a) 8 (b) 11 (c) 9 (d) 10
  3. 3.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 125 times (c) 10 times (d) 5 times
  4. 4.Using (a + b)² = a² + 2ab + b², what is 24²? (a) 416 (b) 586 (c) 256 (d) 576
  5. 5.In a class of 18 children, 10 like maths, 8 like science and 2 like both. How many like at least one of the two? (a) 16 (b) 18 (c) 17 (d) 14
  6. 6.Two angles of a triangle are 80° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 150° (c) 30° (d) 100°
  7. 7.Two straight lines cross. One of the angles is 70°. What is the angle next to it on the same straight line? (a) 290° (b) 20° (c) 70° (d) 110°
  8. 8.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 55° (b) 160° (c) 125° (d) 145°
  9. 9.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 100 (c) 45 (d) 20
  10. 10.Two angles of a triangle are 65° and 40°. What is the exterior angle at the third corner? (a) 75° (b) 140° (c) 115° (d) 105°
  11. 11.3 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) 10 (b) 24 (c) 21 (d) 42
  12. 12.The mean of 4 numbers is 27. When the number 22 is added to them, what is the new mean? (a) 28 (b) 25 (c) 26 (d) 27
  13. 13.How many factors does 112 have? (a) 8 (b) 11 (c) 10 (d) 9
  14. 14.In a class of 37 children, 21 like maths, 18 like science and 8 like both. How many like neither? (a) 8 (b) 7 (c) 14 (d) 6
  15. 15.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
  16. 16.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
  17. 17.Two angles of a triangle are 55° and 50°. What is the third angle? (a) 125° (b) 105° (c) 75° (d) 130°
  18. 18.How many prime numbers are there between 30 and 60? (a) 8 (b) 6 (c) 7 (d) 9
  19. 19.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 20° (b) 70° (c) 80° (d) 160°
  20. 20.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 69 (c) 198 (d) 66
  21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  22. 22.How many factors does 72 have? (a) 11 (b) 13 (c) 12 (d) 10
  23. 23.What is the product of the roots of x² − 8x + 15 = 0? (a) 16 (b) 8 (c) 14 (d) 15
  24. 24.How many prime numbers are there between 70 and 80? (a) 2 (b) 4 (c) 5 (d) 3
  25. 25.In a class of 41 children, 16 like cricket, 28 like football and 11 like both. How many like only cricket? (a) 5 (b) 17 (c) 16 (d) 13
  26. 26.A bag has 10 red balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 19 (b) 10 (c) 11 (d) 2
  27. 27.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 636 (b) 496 (c) 627 (d) 637
  28. 28.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 130° (c) 50° (d) 80°
  29. 29.In how many different ways can the letters of the word BOAT be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  30. 30.A cube has edges of 11 cm. What is its volume? (a) 1331 cu cm (b) 33 cu cm (c) 484 cu cm (d) 726 cu cm
  31. 31.What is the mean of 8, 2, 7, 9, 4 and 6? (a) 8 (b) 5 (c) 6 (d) 7
  32. 32.What is the sum of the first 9 terms of the AP 3, 5, 7, …? (a) 99 (b) 198 (c) 19 (d) 108
  33. 33.Two angles of a triangle are 50° and 80°. What is the third angle? (a) 100° (b) 130° (c) 230° (d) 50°
  34. 34.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 406 (c) 812 (d) 784
  35. 35.What is the product of the roots of x² − 13x + 36 = 0? (a) 37 (b) 13 (c) 35 (d) 36
  36. 36.What is the sum of the roots of x² − 10x + 24 = 0? (a) 24 (b) 11 (c) 10 (d) 9
  37. 37.Using (a + b)² = a² + 2ab + b², what is 35²? (a) 625 (b) 1235 (c) 925 (d) 1225
  38. 38.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  39. 39.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 70° (c) 50° (d) 140°
  40. 40.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 49 (c) 48 (d) 37

Answer key

  1. 157
  2. 10
  3. 125 times
  4. 576
  5. 16
  6. 150°
  7. 110°
  8. 125°
  9. 90
  10. 105°
  11. 21
  12. 26
  13. 10
  14. 6
  15. 616 sq cm
  16. 88 cm
  17. 75°
  18. 7
  19. 80°
  20. 66
  21. 17
  22. 12
  23. 15
  24. 3
  25. 5
  26. 11
  27. 636
  28. 80°
  29. 24
  30. 1331 cu cm
  31. 6
  32. 99
  33. 50°
  34. 784
  35. 36
  36. 10
  37. 1225
  38. 9
  39. 70°
  40. 37

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