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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 909 · 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.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) 14 (b) 8 (c) 15 (d) 7
  2. 2.The mean of 7 numbers is 21. When the number 53 is added to them, what is the new mean? (a) 21 (b) 37 (c) 25 (d) 26
  3. 3.There are 3 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 18 (b) 6 (c) 9 (d) 12
  4. 4.What is the midpoint of the line joining (4, 10) and (6, 22)? (a) (16, 5) (b) (10, 32) (c) (1, 6) (d) (5, 16)
  5. 5.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 130° (b) 155° (c) 75° (d) 50°
  6. 6.In a league, 10 teams each play every other team once. How many matches are played? (a) 90 (b) 45 (c) 100 (d) 55
  7. 7.What is the 33rd term of the AP 20, 27, 34, 41, …? (a) 251 (b) 244 (c) 231 (d) 224
  8. 8.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 260° (b) 81° (c) 80° (d) 100°
  9. 9.Which is the correct factorisation of x² + 11x + 28? (a) (x + 1)(x + 10) (b) (x − 4)(x − 7) (c) (x + 4)(x + 7) (d) (x + 1)(x + 28)
  10. 10.A bag has 10 green balls and 5 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 15 (b) 12 (c) 11 (d) 2
  11. 11.If a + b = 14 and ab = 48, what is a² + b²? (a) 100 (b) 292 (c) 196 (d) 148
  12. 12.In which quadrant does the point (−7, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  13. 13.What is the prime factorisation of 48? (a) 2⁵ × 3 (b) 2⁴ × 3 (c) 2³ × 3 (d) 2 × 3⁴
  14. 14.What is the midpoint of the line joining (0, 3) and (4, 5)? (a) (2, 1) (b) (2, 4) (c) (4, 2) (d) (4, 8)
  15. 15.What is the 31st term of the AP 17, 19, 21, 23, …? (a) 60 (b) 62 (c) 77 (d) 79
  16. 16.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2² × 3² × 7 (c) 2⁴ × 3² × 7 (d) 2³ × 3² × 7
  17. 17.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) 49 (d) 48
  18. 18.A bag has 9 blue balls and 5 yellow 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) 6 (c) 10 (d) 14
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 2 (b) 3 (c) 5 (d) 4
  20. 20.Two angles of a triangle are 20° and 45°. What is the third angle? (a) 115° (b) 160° (c) 135° (d) 65°
  21. 21.Two angles of a triangle are 60° and 20°. What is the third angle? (a) 120° (b) 160° (c) 100° (d) 80°
  22. 22.Two angles of a triangle are 70° and 40°. What is the third angle? (a) 140° (b) 250° (c) 70° (d) 110°
  23. 23.Two angles of a triangle are 20° and 145°. What is the third angle? (a) 35° (b) 160° (c) 15° (d) 165°
  24. 24.Using (a + b)² = a² + 2ab + b², what is 23²? (a) 539 (b) 529 (c) 409 (d) 289
  25. 25.What is the 22nd term of the AP 9, 12, 15, 18, …? (a) 63 (b) 75 (c) 66 (d) 72
  26. 26.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 80° (c) 50° (d) 130°
  27. 27.Two angles of a triangle are 60° and 60°. What is the third angle? (a) 120° (b) 61° (c) 60° (d) 240°
  28. 28.What is the prime factorisation of 21? (a) 3² × 7 (b) 3 × 7 (c) 3 × 7² (d) 3³ × 7
  29. 29.Using (a + b)² = a² + 2ab + b², what is 55²? (a) 2025 (b) 3035 (c) 3025 (d) 2525
  30. 30.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 100° (b) 65° (c) 115° (d) 145°
  31. 31.What is the mode of 19, 5, 1, 5, 10, 5 and 10? (a) 10 (b) 19 (c) 5 (d) 1
  32. 32.How many prime numbers are there between 50 and 60? (a) 3 (b) 4 (c) 1 (d) 2
  33. 33.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  34. 34.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  35. 35.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 115° (b) 65° (c) 50° (d) 25°
  36. 36.In how many different ways can the letters of the word PEN be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  37. 37.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) 64 (d) 28
  38. 38.What is the smallest prime factor of 377? (a) 2 (b) 13 (c) 1 (d) 29
  39. 39.A bag has 10 black balls and 12 yellow balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 22 (b) 11 (c) 13 (d) 2
  40. 40.What is the 30th term of the AP 12, 14, 16, 18, …? (a) 58 (b) 60 (c) 70 (d) 72

Answer key

  1. 8
  2. 25
  3. 9
  4. (5, 16)
  5. 130°
  6. 45
  7. 244
  8. 80°
  9. (x + 4)(x + 7)
  10. 12
  11. 100
  12. Second quadrant
  13. 2⁴ × 3
  14. (2, 4)
  15. 77
  16. 2³ × 3² × 7
  17. 37
  18. 10
  19. 4
  20. 115°
  21. 100°
  22. 70°
  23. 15°
  24. 529
  25. 72
  26. 80°
  27. 60°
  28. 3 × 7
  29. 3025
  30. 65°
  31. 5
  32. 2
  33. 9
  34. 17
  35. 50°
  36. 6
  37. 56
  38. 13
  39. 13
  40. 70

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