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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 118 · 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 39th term of the AP 16, 23, 30, 37, …? (a) 266 (b) 289 (c) 273 (d) 282
  2. 2.Two angles of a triangle are 75° and 85°. What is the third angle? (a) 160° (b) 105° (c) 20° (d) 95°
  3. 3.What is the sum of the first 8 terms of the AP 6, 7, 8, …? (a) 80 (b) 76 (c) 13 (d) 152
  4. 4.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 9 (c) 36 (d) 18
  5. 5.What is the sum of the roots of x² − 11x + 30 = 0? (a) 30 (b) 11 (c) 10 (d) 12
  6. 6.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  7. 7.In a class of 40 children, 13 like tea, 28 like coffee and 10 like both. How many like only tea? (a) 18 (b) 12 (c) 13 (d) 3
  8. 8.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) 8 (b) 14 (c) 7 (d) 15
  9. 9.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 64 times (d) 16 times
  10. 10.What is the sum of the roots of x² − 15x + 54 = 0? (a) 16 (b) 15 (c) 54 (d) 14
  11. 11.How many prime numbers are there between 20 and 40? (a) 5 (b) 4 (c) 3 (d) 6
  12. 12.What is the 11th term of the AP 7, 12, 17, 22, …? (a) 50 (b) 57 (c) 62 (d) 55
  13. 13.What is the distance between the points (9, 9) and (21, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
  15. 15.Two straight lines cross. Two vertically opposite angles add up to 190°. What is each of the other two angles? (a) 170° (b) 95° (c) 85° (d) 86°
  16. 16.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 5/8 (c) 3/5 (d) 3/8
  17. 17.What is the smallest prime factor of 133? (a) 2 (b) 1 (c) 7 (d) 19
  18. 18.How many prime numbers are there between 70 and 100? (a) 7 (b) 6 (c) 5 (d) 8
  19. 19.In a class of 43 children, 17 like maths, 25 like science and 8 like both. How many like at least one of the two? (a) 43 (b) 42 (c) 26 (d) 34
  20. 20.What is the circumference of a circle of diameter 70 cm? (Use π = 22/7.) (a) 220 cm (b) 110 cm (c) 440 cm (d) 3850 cm
  21. 21.A drawer has lots of black, blue and green socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 2 (c) 6 (d) 3
  22. 22.Two angles of a triangle are 50° and 60°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 120° (d) 130°
  23. 23.A bag has 12 red balls and 7 green 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) 19 (c) 8 (d) 13
  24. 24.Which is the correct factorisation of x² + 13x + 42? (a) (x + 6)(x + 7) (b) (x + 1)(x + 12) (c) (x − 6)(x − 7) (d) (x + 1)(x + 42)
  25. 25.In a class of 28 children, 13 like tea, 14 like coffee and 8 like both. How many like only tea? (a) 14 (b) 5 (c) 6 (d) 13
  26. 26.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5
  27. 27.If a + b = 5 and ab = 6, what is (a − b)²? (a) 25 (b) 13 (c) 19 (d) 1
  28. 28.There are 8 roads from town A to town B and 4 roads from town B to town C. How many different routes go from A to C through B? (a) 32 (b) 64 (c) 12 (d) 40
  29. 29.What is the distance between the points (2, 0) and (7, 12)? (a) 14 (b) 13 (c) 169 (d) 17
  30. 30.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 372 (b) 21 (c) 192 (d) 186
  31. 31.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 88 cm (c) 2464 cm (d) 176 cm
  32. 32.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 52 (c) 70 (d) 61
  33. 33.If a + b = 21 and ab = 108, what is a² + b²? (a) 225 (b) 441 (c) 333 (d) 657
  34. 34.Two straight lines cross. Two vertically opposite angles add up to 210°. What is each of the other two angles? (a) 105° (b) 150° (c) 75° (d) 76°
  35. 35.In which quadrant does the point (−3, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.Which is the correct factorisation of x² + 7x + 10? (a) (x + 1)(x + 10) (b) (x − 2)(x − 5) (c) (x + 2)(x + 5) (d) (x + 1)(x + 6)
  37. 37.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 90 (c) 45 (d) 100
  38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  39. 39.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
  40. 40.A drawer has lots of yellow, white, red, blue and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 5 (d) 2

Answer key

  1. 282
  2. 20°
  3. 76
  4. 18
  5. 11
  6. 8
  7. 3
  8. 8
  9. 16 times
  10. 15
  11. 4
  12. 57
  13. 15
  14. 1/9
  15. 85°
  16. 3/8
  17. 7
  18. 6
  19. 34
  20. 220 cm
  21. 4
  22. 110°
  23. 13
  24. (x + 6)(x + 7)
  25. 5
  26. 2² × 3 × 5
  27. 1
  28. 32
  29. 13
  30. 186
  31. 176 cm
  32. 61
  33. 225
  34. 75°
  35. Second quadrant
  36. (x + 2)(x + 5)
  37. 45
  38. 25
  39. 1386 sq cm
  40. 6

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