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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 120 · 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.A drawer has lots of red, white, yellow and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 5 (b) 2 (c) 8 (d) 4
  2. 2.What is the midpoint of the line joining (2, 11) and (4, 7)? (a) (1, 2) (b) (9, 3) (c) (6, 18) (d) (3, 9)
  3. 3.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
  4. 4.Which is the correct factorisation of x² + 15x + 56? (a) (x + 7)(x + 8) (b) (x − 7)(x − 8) (c) (x + 1)(x + 14) (d) (x + 1)(x + 56)
  5. 5.What is the median of 15, 13, 2, 16, 29, 1 and 21? (a) 16 (b) 15 (c) 14 (d) 13
  6. 6.In which quadrant does the point (−7, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  7. 7.A cube has edges of 7 cm. What is its volume? (a) 294 cu cm (b) 196 cu cm (c) 21 cu cm (d) 343 cu cm
  8. 8.How many prime numbers are there between 30 and 60? (a) 8 (b) 9 (c) 7 (d) 6
  9. 9.What is the 23rd term of the AP 9, 13, 17, 21, …? (a) 101 (b) 88 (c) 97 (d) 92
  10. 10.If a + b = 17 and ab = 70, what is (a − b)²? (a) 289 (b) 3 (c) 9 (d) 149
  11. 11.There are 6 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) 10 (b) 48 (c) 30 (d) 24
  12. 12.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
  13. 13.A bag has 8 green balls and 5 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 6 (d) 13
  14. 14.What is the smallest prime factor of 169? (a) 1 (b) 3 (c) 2 (d) 13
  15. 15.In a league, 8 teams each play every other team once. How many matches are played? (a) 56 (b) 36 (c) 28 (d) 64
  16. 16.What is the midpoint of the line joining (3, 5) and (9, 15)? (a) (6, 10) (b) (10, 6) (c) (12, 20) (d) (3, 5)
  17. 17.Two angles of a triangle are 70° and 35°. What is the third angle? (a) 110° (b) 145° (c) 75° (d) 105°
  18. 18.Using (a + b)² = a² + 2ab + b², what is 52²? (a) 2304 (b) 2704 (c) 2504 (d) 2714
  19. 19.Two straight lines cross. One of the angles is 20°. What is the angle next to it on the same straight line? (a) 160° (b) 20° (c) 70° (d) 340°
  20. 20.What is the sum of the roots of x² − 5x + 6 = 0? (a) 5 (b) 7 (c) 6 (d) 4
  21. 21.What is the sum of the roots of x² − 12x + 32 = 0? (a) 12 (b) 32 (c) 13 (d) 11
  22. 22.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
  23. 23.Which term of the AP 11, 20, 29, 38, … is 263? (a) 30th (b) 29th (c) 31st (d) 28th
  24. 24.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  25. 25.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 25 (c) 10 (d) 15
  26. 26.The mean of 5 numbers is 30. When the number 36 is added to them, what is the new mean? (a) 32 (b) 31 (c) 33 (d) 30
  27. 27.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
  28. 28.In a class of 40 children, 21 like cricket, 19 like football and 6 like both. How many like neither? (a) 7 (b) 0 (c) 12 (d) 6
  29. 29.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 499 (b) 404 (c) 489 (d) 498
  30. 30.A bag has 4 green balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 6 (b) 5 (c) 2 (d) 11
  31. 31.What is the median of 22, 10, 36, 5, 28, 2 and 23? (a) 18 (b) 22 (c) 23 (d) 5
  32. 32.What is the mode of 8, 8, 1, 18, 4, 4 and 8? (a) 8 (b) 18 (c) 4 (d) 1
  33. 33.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 29 (b) 28 (c) 21 (d) 22
  34. 34.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 140° (c) 40° (d) 30°
  35. 35.Two straight lines cross. One of the angles is 145°. What is the angle next to it on the same straight line? (a) 145° (b) 35° (c) 215° (d) 36°
  36. 36.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 3/4 (b) 3/8 (c) 1/4 (d) 1/8
  37. 37.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 22 cm (b) 154 cm (c) 44 cm (d) 88 cm
  38. 38.What is the 12th term of the AP 12, 18, 24, 30, …? (a) 78 (b) 66 (c) 84 (d) 72
  39. 39.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  40. 40.What is the sum of all the whole numbers from 1 to 41? (a) 861 (b) 862 (c) 1722 (d) 820

Answer key

  1. 5
  2. (3, 9)
  3. 154 sq cm
  4. (x + 7)(x + 8)
  5. 15
  6. Second quadrant
  7. 343 cu cm
  8. 7
  9. 97
  10. 9
  11. 24
  12. 7
  13. 9
  14. 13
  15. 28
  16. (6, 10)
  17. 75°
  18. 2704
  19. 160°
  20. 5
  21. 12
  22. 1/2
  23. 29th
  24. 20
  25. 10
  26. 31
  27. 132 cm
  28. 6
  29. 498
  30. 6
  31. 22
  32. 8
  33. 22
  34. 20°
  35. 35°
  36. 3/4
  37. 44 cm
  38. 78
  39. 120
  40. 861

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