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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 255 · 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 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) 28 (b) 29 (c) 21 (d) 22
  2. 2.What is the prime factorisation of 45? (a) 3 × 5² (b) 3 × 5 (c) 3² × 5 (d) 3³ × 5
  3. 3.Two angles of a triangle are 80° and 35°. What is the third angle? (a) 145° (b) 65° (c) 115° (d) 100°
  4. 4.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 20 (c) 240 (d) 120
  5. 5.A bag has 12 white balls and 12 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 24 (b) 2 (c) 14 (d) 13
  6. 6.What is the missing term in the AP 3, 9, ?, 21, 27? (a) 14 (b) 16 (c) 21 (d) 15
  7. 7.In a class of 37 children, 18 like mangoes, 27 like bananas and 9 like both. How many like only mangoes? (a) 9 (b) 18 (c) 10 (d) 8
  8. 8.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 132 cm (c) 1386 cm (d) 66 cm
  9. 9.What is the sum of all the whole numbers from 1 to 76? (a) 2888 (b) 2926 (c) 2850 (d) 5852
  10. 10.How many prime numbers are there between 90 and 110? (a) 7 (b) 5 (c) 4 (d) 6
  11. 11.In how many different ways can the letters of the word CAT be arranged? (a) 6 (b) 9 (c) 3 (d) 12
  12. 12.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) 36 (b) 37 (c) 49 (d) 48
  13. 13.A drawer has lots of black, white, blue, red and yellow socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 10 (c) 2 (d) 5
  14. 14.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 78 (c) 144 (d) 66
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 14 (d) 15
  16. 16.What is the prime factorisation of 504? (a) 2³ × 3² × 7 (b) 2 × 3² × 7³ (c) 2⁴ × 3² × 7 (d) 2² × 3² × 7
  17. 17.What is the missing term in the AP 18, 26, 34, ?, 50? (a) 42 (b) 43 (c) 41 (d) 50
  18. 18.What is the midpoint of the line joining (0, 7) and (6, 5)? (a) (3, 1) (b) (6, 3) (c) (6, 12) (d) (3, 6)
  19. 19.A drawer has lots of yellow, red, black, 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) 10 (b) 6 (c) 5 (d) 2
  20. 20.What is the sum of the first 11 terms of the AP 6, 8, 10, …? (a) 187 (b) 352 (c) 26 (d) 176
  21. 21.4 T-shirts and 4 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 20 (b) 8 (c) 16 (d) 32
  22. 22.Using (a + b)² = a² + 2ab + b², what is 22²? (a) 404 (b) 494 (c) 484 (d) 324
  23. 23.What is the midpoint of the line joining (1, 3) and (3, 11)? (a) (2, 7) (b) (1, 4) (c) (4, 14) (d) (7, 2)
  24. 24.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
  25. 25.What is the prime factorisation of 21? (a) 3³ × 7 (b) 3 × 7² (c) 3² × 7 (d) 3 × 7
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
  27. 27.Using (a − b)² = a² − 2ab + b², what is 26²? (a) 884 (b) 686 (c) 676 (d) 1156
  28. 28.A bag has 2 white, 4 blue and 9 red balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 2/5 (c) 2/3 (d) 3/5
  29. 29.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 468 (c) 459 (d) 469
  30. 30.What is the prime factorisation of 210? (a) 2 × 3 × 5 × 7 (b) 2² × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  31. 31.In which quadrant does the point (2, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  32. 32.Which term of the AP 15, 24, 33, 42, … is 321? (a) 36th (b) 35th (c) 34th (d) 37th
  33. 33.What is the missing term in the AP 17, ?, 23, 26, 29? (a) 21 (b) 19 (c) 23 (d) 20
  34. 34.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 90 (c) 100 (d) 45
  35. 35.How many factors does 77 have? (a) 2 (b) 4 (c) 5 (d) 3
  36. 36.What is the smallest prime factor of 143? (a) 13 (b) 1 (c) 11 (d) 2
  37. 37.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  38. 38.Using (a + b)² = a² + 2ab + b², what is 75²? (a) 4925 (b) 4225 (c) 5635 (d) 5625
  39. 39.How many factors does 119 have? (a) 3 (b) 4 (c) 5 (d) 2
  40. 40.What is the mean of 9, 16, 8 and 19? (a) 13 (b) 14 (c) 15 (d) 12

Answer key

  1. 22
  2. 3² × 5
  3. 65°
  4. 120
  5. 14
  6. 15
  7. 9
  8. 132 cm
  9. 2926
  10. 5
  11. 6
  12. 37
  13. 6
  14. 66
  15. 15
  16. 2³ × 3² × 7
  17. 42
  18. (3, 6)
  19. 6
  20. 176
  21. 16
  22. 484
  23. (2, 7)
  24. 1/2
  25. 3 × 7
  26. 2
  27. 676
  28. 3/5
  29. 468
  30. 2 × 3 × 5 × 7
  31. First quadrant
  32. 35th
  33. 20
  34. 90
  35. 4
  36. 11
  37. Fourth quadrant
  38. 5625
  39. 4
  40. 13

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