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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 151 · 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 sum of all the whole numbers from 1 to 79? (a) 3161 (b) 3081 (c) 6320 (d) 3160
  2. 2.What is the distance between the points (4, 1) and (20, 13)? (a) 28 (b) 400 (c) 20 (d) 21
  3. 3.Two angles of a triangle are 45° and 100°. What is the third angle? (a) 135° (b) 145° (c) 80° (d) 35°
  4. 4.Two angles of a triangle are 45° and 45°. What is the exterior angle at the third corner? (a) 270° (b) 90° (c) 135° (d) 91°
  5. 5.If a + b = 6 and ab = 8, what is (a − b)²? (a) 36 (b) 4 (c) 20 (d) 2
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 155° (c) 25° (d) 50°
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 57? (a) 7 (b) 4 (c) 5 (d) 6
  8. 8.How many prime numbers are there between 40 and 70? (a) 9 (b) 8 (c) 6 (d) 7
  9. 9.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 15 (b) 36 (c) 21 (d) 30
  10. 10.In a class of 35 children, 24 like cricket, 17 like football and 11 like both. How many like only cricket? (a) 6 (b) 13 (c) 18 (d) 24
  11. 11.A drawer has lots of yellow, green, red, blue and white 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) 10 (c) 6 (d) 2
  12. 12.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/2 (b) 1/3 (c) 3/4 (d) 1/4
  13. 13.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) 49 (b) 37 (c) 48 (d) 36
  14. 14.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 176 sq cm (c) 2464 sq cm (d) 9856 sq cm
  15. 15.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 100° (b) 150° (c) 70° (d) 110°
  16. 16.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  17. 17.Three coins are tossed together. What is the probability of getting at least one head? (a) 7/8 (b) 3/8 (c) 1/8 (d) 1/4
  18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  19. 19.A bag has 12 yellow balls and 3 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 2 (b) 15 (c) 13 (d) 14
  20. 20.What is the 19th term of the AP 9, 17, 25, 33, …? (a) 144 (b) 153 (c) 152 (d) 161
  21. 21.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 499 (c) 498 (d) 404
  22. 22.If the radius of a circle is made 2 times as long, how many times as big does its area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
  23. 23.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 176 cm (d) 2464 cm
  24. 24.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 182 (c) 196 (d) 105
  25. 25.If every edge of a cube is made 4 times as long, how many times as big does its surface area become? (a) 4 times (b) 16 times (c) 8 times (d) 64 times
  26. 26.How many prime numbers are there between 50 and 80? (a) 8 (b) 6 (c) 9 (d) 7
  27. 27.What is the smallest prime factor of 341? (a) 1 (b) 11 (c) 31 (d) 2
  28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  29. 29.What is the median of 15, 28, 10, 1, 17, 4 and 12? (a) 10 (b) 15 (c) 12 (d) 1
  30. 30.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 4 times (b) 16 times (c) 64 times (d) 8 times
  31. 31.A canteen sells 4 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 16 (b) 12 (c) 6 (d) 8
  32. 32.What is the sum of the first 5 terms of the AP 8, 12, 16, …? (a) 80 (b) 90 (c) 160 (d) 24
  33. 33.What is the mode of 11, 11, 10, 10, 19, 11 and 17? (a) 10 (b) 11 (c) 19 (d) 17
  34. 34.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 1386 cm (b) 66 cm (c) 264 cm (d) 132 cm
  35. 35.What is the sum of the first 10 terms of the AP 2, 5, 8, …? (a) 310 (b) 170 (c) 155 (d) 29
  36. 36.The mean of 6 numbers is 36. When the number 8 is added to them, what is the new mean? (a) 22 (b) 33 (c) 32 (d) 36
  37. 37.A bag has 9 white balls and 5 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 14 (b) 11 (c) 10 (d) 2
  38. 38.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 158 (c) 168 (d) 167
  39. 39.A canteen sells 6 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 8 (b) 24 (c) 18 (d) 12
  40. 40.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) 15 (b) 14 (c) 8 (d) 7

Answer key

  1. 3160
  2. 20
  3. 35°
  4. 90°
  5. 4
  6. 25°
  7. 6
  8. 7
  9. 15
  10. 13
  11. 6
  12. 3/4
  13. 37
  14. 2464 sq cm
  15. 70°
  16. 2
  17. 7/8
  18. 25
  19. 14
  20. 153
  21. 498
  22. 4 times
  23. 176 cm
  24. 91
  25. 16 times
  26. 7
  27. 11
  28. 5
  29. 12
  30. 16 times
  31. 8
  32. 80
  33. 11
  34. 132 cm
  35. 155
  36. 32
  37. 11
  38. 167
  39. 12
  40. 8

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