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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 908 · 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. Two vertically opposite angles add up to 80°. What is each of the other two angles? (a) 280° (b) 40° (c) 140° (d) 100°
  2. 2.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 sq cm (b) 154 sq cm (c) 77 sq cm (d) 616 sq cm
  3. 3.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 15 (c) 48 (d) 45
  4. 4.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 100 (c) 90 (d) 45
  5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/11 (c) 1/12 (d) 1/18
  6. 6.What is the sum of the first 6 terms of the AP 2, 7, 12, …? (a) 174 (b) 27 (c) 87 (d) 102
  7. 7.In a class of 33 children, 17 like dance, 25 like music and 10 like both. How many like only dance? (a) 7 (b) 17 (c) 8 (d) 15
  8. 8.In which quadrant does the point (−7, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  9. 9.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) 37 (c) 48 (d) 49
  10. 10.Two angles of a triangle are 50° and 30°. What is the exterior angle at the third corner? (a) 100° (b) 80° (c) 150° (d) 130°
  11. 11.What is the median of 1, 35, 20, 11 and 28? (a) 20 (b) 28 (c) 11 (d) 19
  12. 12.What is the midpoint of the line joining (10, 10) and (16, 20)? (a) (3, 5) (b) (13, 15) (c) (15, 13) (d) (26, 30)
  13. 13.What is the midpoint of the line joining (2, 4) and (10, 14)? (a) (9, 6) (b) (12, 18) (c) (6, 9) (d) (4, 5)
  14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 2464 sq cm
  15. 15.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
  16. 16.A bag has 3 blue balls and 4 black 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) 5 (d) 4
  17. 17.Two angles of a triangle are 25° and 100°. What is the third angle? (a) 125° (b) 155° (c) 80° (d) 55°
  18. 18.A cube has edges of 6 cm. What is its total surface area? (a) 144 sq cm (b) 216 sq cm (c) 36 sq cm (d) 217 sq cm
  19. 19.What is the mode of 2, 11, 11, 13, 11, 2 and 18? (a) 18 (b) 2 (c) 13 (d) 11
  20. 20.If a + b = 9 and ab = 8, what is (a − b)²? (a) 7 (b) 49 (c) 81 (d) 65
  21. 21.Two angles of a triangle are 45° and 85°. What is the exterior angle at the third corner? (a) 50° (b) 135° (c) 130° (d) 95°
  22. 22.What is the prime factorisation of 14? (a) 2³ × 7 (b) 2 × 7 (c) 2 × 7² (d) 2² × 7
  23. 23.What is the sum of all the whole numbers from 1 to 89? (a) 8010 (b) 3916 (c) 4005 (d) 4006
  24. 24.If a + b = 14 and ab = 48, what is a² + b²? (a) 196 (b) 148 (c) 292 (d) 100
  25. 25.What is the sum of the first 28 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 784 (c) 812 (d) 406
  26. 26.In a league, 11 teams each play every other team once. How many matches are played? (a) 121 (b) 110 (c) 66 (d) 55
  27. 27.What is the distance between the points (4, 11) and (12, 5)? (a) 14 (b) 100 (c) 10 (d) 11
  28. 28.What is the 40th term of the AP 17, 25, 33, 41, …? (a) 320 (b) 329 (c) 337 (d) 312
  29. 29.In a class of 32 children, 15 like dance, 23 like music and 8 like both. How many like only dance? (a) 15 (b) 9 (c) 8 (d) 7
  30. 30.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 2/3 (c) 1/3 (d) 1/2
  31. 31.Two angles of a triangle are 25° and 50°. What is the exterior angle at the third corner? (a) 105° (b) 130° (c) 75° (d) 155°
  32. 32.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 50° (b) 80° (c) 130° (d) 40°
  33. 33.In how many different ways can the letters of the word CHAIR be arranged? (a) 25 (b) 120 (c) 20 (d) 240
  34. 34.In which quadrant does the point (1, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  35. 35.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 55° (b) 130° (c) 125° (d) 105°
  36. 36.Two angles of a triangle are 55° and 80°. What is the exterior angle at the third corner? (a) 100° (b) 135° (c) 45° (d) 125°
  37. 37.What is the midpoint of the line joining (6, 5) and (8, 7)? (a) (14, 12) (b) (6, 7) (c) (7, 6) (d) (1, 1)
  38. 38.What is the 34th term of the AP 1, 7, 13, 19, …? (a) 205 (b) 204 (c) 198 (d) 199
  39. 39.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 56 (b) 16 (c) 28 (d) 64
  40. 40.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/36 (c) 1/11 (d) 1/12

Answer key

  1. 140°
  2. 154 sq cm
  3. 45
  4. 45
  5. 1/18
  6. 87
  7. 7
  8. Third quadrant
  9. 37
  10. 80°
  11. 20
  12. (13, 15)
  13. (6, 9)
  14. 2464 sq cm
  15. 1/2
  16. 5
  17. 55°
  18. 216 sq cm
  19. 11
  20. 49
  21. 130°
  22. 2 × 7
  23. 4005
  24. 100
  25. 784
  26. 55
  27. 10
  28. 329
  29. 7
  30. 1/2
  31. 75°
  32. 80°
  33. 120
  34. First quadrant
  35. 55°
  36. 135°
  37. (7, 6)
  38. 199
  39. 56
  40. 1/36

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