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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 275 · 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 the first 11 odd numbers (1 + 3 + 5 + …)? (a) 66 (b) 121 (c) 21 (d) 132
  2. 2.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) 7 (d) 15
  3. 3.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
  4. 4.What is the mean of 3, 18, 3, 7 and 19? (a) 12 (b) 10 (c) 9 (d) 11
  5. 5.What is the mode of 16, 10, 3, 8, 3, 8 and 3? (a) 10 (b) 16 (c) 3 (d) 8
  6. 6.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 222 (c) 225 (d) 226
  7. 7.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 64 times (b) 8 times (c) 16 times (d) 4 times
  8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 44 cm (d) 616 cm
  9. 9.A cube has edges of 4 cm. What is its total surface area? (a) 64 sq cm (b) 96 sq cm (c) 97 sq cm (d) 16 sq cm
  10. 10.What is the distance between the points (0, 18) and (16, 6)? (a) 21 (b) 20 (c) 28 (d) 400
  11. 11.A bag has 5 red balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 7 (c) 6 (d) 9
  12. 12.How many prime numbers are there between 50 and 80? (a) 8 (b) 7 (c) 9 (d) 6
  13. 13.If a + b = 6 and ab = 8, what is (a − b)²? (a) 4 (b) 2 (c) 20 (d) 36
  14. 14.Which term of the AP 16, 22, 28, 34, … is 64? (a) 10th (b) 11th (c) 8th (d) 9th
  15. 15.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 45 (b) 20 (c) 100 (d) 90
  16. 16.In a class of 47 children, 24 like dance, 23 like music and 10 like both. How many like at least one of the two? (a) 38 (b) 37 (c) 47 (d) 27
  17. 17.A canteen sells 3 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 42 (c) 21 (d) 10
  18. 18.If a + b = 17 and ab = 66, what is a² + b²? (a) 421 (b) 157 (c) 289 (d) 223
  19. 19.What is the distance between the points (7, 13) and (23, 1)? (a) 21 (b) 20 (c) 400 (d) 28
  20. 20.5 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
  21. 21.In which quadrant does the point (1, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.In a class of 23 children, 15 like tea, 15 like coffee and 8 like both. How many like only tea? (a) 15 (b) 7 (c) 8 (d) 6
  23. 23.A bag has 4 red balls and 5 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 5 (b) 6 (c) 2 (d) 9
  24. 24.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 14 (b) 16 (c) 21 (d) 15
  25. 25.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 99 (c) 11 (d) 36
  26. 26.How many prime numbers are there between 10 and 20? (a) 6 (b) 4 (c) 3 (d) 5
  27. 27.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 110 cm (b) 220 cm (c) 440 cm (d) 3850 cm
  28. 28.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 49 (b) 13 (c) 84 (d) 42
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 5 (b) 4 (c) 3 (d) 2
  30. 30.A bag has 7 blue balls and 8 white 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) 15 (c) 9 (d) 8
  31. 31.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 12 (c) 15 (d) 30
  32. 32.What is the midpoint of the line joining (0, 8) and (4, 18)? (a) (2, 5) (b) (2, 13) (c) (13, 2) (d) (4, 26)
  33. 33.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 12 (c) 48 (d) 24
  34. 34.What is the mode of 20, 2, 9, 3, 3, 2 and 3? (a) 9 (b) 2 (c) 20 (d) 3
  35. 35.What is the distance between the points (7, 11) and (15, 5)? (a) 100 (b) 14 (c) 10 (d) 11
  36. 36.Using (a − b)² = a² − 2ab + b², what is 18²? (a) 396 (b) 484 (c) 334 (d) 324
  37. 37.What is the prime factorisation of 140? (a) 2² × 5 × 7 (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7²
  38. 38.What is the sum of the first 9 terms of the AP 3, 8, 13, …? (a) 212 (b) 43 (c) 207 (d) 414
  39. 39.What is the midpoint of the line joining (10, 4) and (12, 6)? (a) (5, 11) (b) (11, 5) (c) (22, 10) (d) (1, 1)
  40. 40.What is the product of the roots of x² − 6x + 8 = 0? (a) 7 (b) 6 (c) 8 (d) 9

Answer key

  1. 121
  2. 8
  3. 1/2
  4. 10
  5. 3
  6. 225
  7. 16 times
  8. 88 cm
  9. 96 sq cm
  10. 20
  11. 7
  12. 7
  13. 4
  14. 9th
  15. 90
  16. 37
  17. 21
  18. 157
  19. 20
  20. 10
  21. First quadrant
  22. 7
  23. 6
  24. 15
  25. 33
  26. 4
  27. 220 cm
  28. 42
  29. 4
  30. 9
  31. 15
  32. (2, 13)
  33. 24
  34. 3
  35. 10
  36. 324
  37. 2² × 5 × 7
  38. 207
  39. (11, 5)
  40. 8

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