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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 577 · 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.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 21° (b) 20° (c) 200° (d) 160°
  2. 2.In which quadrant does the point (−5, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  3. 3.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 24 (c) 132 (d) 144
  4. 4.What is the missing term in the AP 6, 12, ?, 24, 30? (a) 24 (b) 19 (c) 18 (d) 17
  5. 5.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 446 (b) 552 (c) 561 (d) 562
  6. 6.What is the smallest prime factor of 133? (a) 1 (b) 7 (c) 19 (d) 2
  7. 7.What is the mode of 16, 17, 18, 16, 17, 16 and 12? (a) 12 (b) 18 (c) 16 (d) 17
  8. 8.Two angles of a triangle are 65° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 60° (c) 120° (d) 115°
  9. 9.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 40° (b) 30° (c) 20° (d) 140°
  10. 10.Which is the correct factorisation of x² + 15x + 56? (a) (x + 1)(x + 56) (b) (x − 7)(x − 8) (c) (x + 7)(x + 8) (d) (x + 1)(x + 14)
  11. 11.In a class of 42 children, 19 like cricket, 21 like football and 2 like both. How many like only cricket? (a) 2 (b) 17 (c) 21 (d) 19
  12. 12.In a league, 6 teams each play every other team once. How many matches are played? (a) 36 (b) 21 (c) 30 (d) 15
  13. 13.Two straight lines cross. One of the angles is 125°. What is the angle next to it on the same straight line? (a) 56° (b) 55° (c) 235° (d) 125°
  14. 14.In which quadrant does the point (3, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 6 (d) 12
  16. 16.In a class of 26 children, 11 like maths, 19 like science and 7 like both. How many like at least one of the two? (a) 30 (b) 26 (c) 23 (d) 16
  17. 17.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/6
  18. 18.What is the sum of all the whole numbers from 1 to 15? (a) 105 (b) 120 (c) 121 (d) 240
  19. 19.Which is the correct factorisation of x² + 16x + 63? (a) (x + 7)(x + 9) (b) (x − 7)(x − 9) (c) (x + 1)(x + 63) (d) (x + 1)(x + 15)
  20. 20.If a + b = 20 and ab = 96, what is a² + b²? (a) 304 (b) 592 (c) 400 (d) 208
  21. 21.Two angles of a triangle are 65° and 45°. What is the third angle? (a) 115° (b) 70° (c) 110° (d) 135°
  22. 22.In a class of 20 children, 8 like mangoes, 11 like bananas and 5 like neither. How many like both? (a) 3 (b) 4 (c) 15 (d) 5
  23. 23.Two angles of a triangle are 75° and 95°. What is the third angle? (a) 85° (b) 170° (c) 105° (d) 10°
  24. 24.Using (a + b)² = a² + 2ab + b², what is 35²? (a) 925 (b) 1235 (c) 1225 (d) 625
  25. 25.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 30° (c) 15° (d) 75°
  26. 26.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 2/3 (c) 1/3 (d) 1/2
  27. 27.In which quadrant does the point (−5, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  28. 28.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 45 (c) 100 (d) 20
  29. 29.What is the 26th term of the AP 2, 4, 6, 8, …? (a) 53 (b) 52 (c) 50 (d) 54
  30. 30.What is the 14th term of the AP 15, 19, 23, 27, …? (a) 71 (b) 67 (c) 52 (d) 56
  31. 31.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 361 (b) 399 (c) 441 (d) 371
  32. 32.Two straight lines cross. One of the angles is 75°. What is the angle next to it on the same straight line? (a) 15° (b) 75° (c) 105° (d) 285°
  33. 33.A bag has 3 blue balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 5 (b) 4 (c) 6 (d) 2
  34. 34.A cuboid is 10 cm long, 6 cm wide and 2 cm high. What is its volume? (a) 60 cu cm (b) 184 cu cm (c) 120 cu cm (d) 18 cu cm
  35. 35.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 140° (c) 50° (d) 70°
  36. 36.In a class of 30 children, 14 like dance, 9 like music and 2 like both. How many like at least one of the two? (a) 30 (b) 23 (c) 19 (d) 21
  37. 37.How many factors does 94 have? (a) 3 (b) 2 (c) 4 (d) 5
  38. 38.What is the median of 1, 18, 2, 3 and 26? (a) 10 (b) 18 (c) 2 (d) 3
  39. 39.What is the distance between the points (1, 11) and (9, 5)? (a) 14 (b) 11 (c) 10 (d) 100
  40. 40.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 27 times (b) 9 times (c) 3 times (d) 6 times

Answer key

  1. 20°
  2. Second quadrant
  3. 132
  4. 18
  5. 561
  6. 7
  7. 16
  8. 120°
  9. 20°
  10. (x + 7)(x + 8)
  11. 17
  12. 15
  13. 55°
  14. First quadrant
  15. 6
  16. 23
  17. 1/2
  18. 120
  19. (x + 7)(x + 9)
  20. 208
  21. 70°
  22. 4
  23. 10°
  24. 1225
  25. 30°
  26. 1/3
  27. Second quadrant
  28. 90
  29. 52
  30. 67
  31. 361
  32. 105°
  33. 5
  34. 120 cu cm
  35. 70°
  36. 21
  37. 4
  38. 3
  39. 10
  40. 9 times

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