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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 548 · 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.Two straight lines cross. One of the angles is 130°. What is the angle next to it on the same straight line? (a) 130° (b) 51° (c) 50° (d) 230°
  2. 2.What is the prime factorisation of 504? (a) 2⁴ × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7³ (d) 2² × 3² × 7
  3. 3.In which quadrant does the point (1, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  4. 4.7 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 21 (b) 42 (c) 28 (d) 49
  5. 5.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 4 times (c) 2 times (d) 5 times
  6. 6.The mean of 6 numbers is 12. When the number 26 is added to them, what is the new mean? (a) 15 (b) 12 (c) 14 (d) 19
  7. 7.In a class of 36 children, 14 like mangoes, 20 like bananas and 6 like both. How many like only mangoes? (a) 8 (b) 16 (c) 14 (d) 6
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  9. 9.A canteen sells 8 kinds of sandwich and 5 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 13 (b) 80 (c) 40 (d) 48
  10. 10.What is the mode of 11, 14, 14, 2, 14, 20 and 11? (a) 20 (b) 2 (c) 14 (d) 11
  11. 11.In a class of 27 children, 18 like dance, 10 like music and 3 like both. How many like at least one of the two? (a) 25 (b) 22 (c) 27 (d) 28
  12. 12.What is the sum of the roots of x² − 12x + 35 = 0? (a) 35 (b) 11 (c) 13 (d) 12
  13. 13.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 3/4 (c) 1/2 (d) 1/3
  14. 14.What is the mean of 2, 5, 14 and 7? (a) 7 (b) 6 (c) 9 (d) 8
  15. 15.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 10) (b) (x + 5)(x + 6) (c) (x − 5)(x − 6) (d) (x + 1)(x + 30)
  16. 16.If a + b = 4 and ab = 3, what is a² + b²? (a) 16 (b) 10 (c) 22 (d) 13
  17. 17.What is the median of 36, 20, 24, 23, 27, 30 and 35? (a) 27 (b) 24 (c) 30 (d) 23
  18. 18.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 37 (c) 24 (d) 25
  19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  20. 20.A bag has 6 green balls and 12 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 7 (b) 18 (c) 2 (d) 8
  21. 21.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 1/2 (b) 1/3 (c) 1/6 (d) 2/3
  22. 22.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
  23. 23.What is the prime factorisation of 70? (a) 2² × 5 × 7 (b) 2 × 5 × 7² (c) 2 × 5 × 7 (d) 2³ × 5 × 7
  24. 24.A drawer has lots of red, white, yellow, 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) 5 (b) 2 (c) 10 (d) 6
  25. 25.Two angles of a triangle are 25° and 135°. What is the third angle? (a) 155° (b) 45° (c) 160° (d) 20°
  26. 26.What are the roots of x² − 11x + 24 = 0? (a) 2 and 12 (b) 3 and 8 (c) 1 and 24 (d) 1 and 10
  27. 27.What is the mean of 14, 12, 16, 5, 3 and 16? (a) 11 (b) 13 (c) 12 (d) 10
  28. 28.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 88 cm (d) 2464 cm
  29. 29.A bag has 11 black balls and 9 red balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 10 (b) 2 (c) 12 (d) 20
  30. 30.What is the median of 13, 6, 4, 24 and 22? (a) 22 (b) 4 (c) 6 (d) 13
  31. 31.In which quadrant does the point (5, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  32. 32.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 447 (c) 438 (d) 448
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 16 (d) 15
  34. 34.What is the mode of 13, 8, 18, 1, 18, 1 and 1? (a) 1 (b) 13 (c) 18 (d) 8
  35. 35.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) 22 (c) 21 (d) 28
  36. 36.What is the missing term in the AP 5, 7, 9, ?, 13? (a) 12 (b) 11 (c) 13 (d) 10
  37. 37.In how many different ways can the letters of the word PLANT be arranged? (a) 25 (b) 120 (c) 240 (d) 20
  38. 38.What is the missing term in the AP 4, 11, ?, 25, 32? (a) 19 (b) 25 (c) 18 (d) 17
  39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/11 (b) 3/11 (c) 1/9 (d) 1/12
  40. 40.How many prime numbers are there between 10 and 30? (a) 7 (b) 6 (c) 5 (d) 8

Answer key

  1. 50°
  2. 2³ × 3² × 7
  3. First quadrant
  4. 21
  5. 4 times
  6. 14
  7. 8
  8. 17
  9. 40
  10. 14
  11. 25
  12. 12
  13. 3/4
  14. 7
  15. (x + 5)(x + 6)
  16. 10
  17. 27
  18. 25
  19. 15
  20. 8
  21. 1/2
  22. 616 sq cm
  23. 2 × 5 × 7
  24. 6
  25. 20°
  26. 3 and 8
  27. 11
  28. 176 cm
  29. 12
  30. 13
  31. First quadrant
  32. 447
  33. 15
  34. 1
  35. 22
  36. 11
  37. 120
  38. 18
  39. 1/12
  40. 6

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