← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 279 · 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.In how many different ways can the letters of the word CAT be arranged? (a) 12 (b) 3 (c) 6 (d) 9
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  4. 4.What is the sum of the first 5 odd numbers (1 + 3 + 5 + …)? (a) 9 (b) 25 (c) 30 (d) 15
  5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
  6. 6.In a class of 27 children, 14 like tea, 14 like coffee and 10 like both. How many like only tea? (a) 14 (b) 10 (c) 4 (d) 13
  7. 7.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 3/4 (c) 1/8 (d) 3/8
  8. 8.In a class of 37 children, 17 like cricket, 17 like football and 6 like both. How many like neither? (a) 9 (b) 3 (c) 6 (d) 15
  9. 9.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 30° (b) 140° (c) 20° (d) 40°
  10. 10.Which is the correct factorisation of x² + 14x + 48? (a) (x − 6)(x − 8) (b) (x + 1)(x + 13) (c) (x + 6)(x + 8) (d) (x + 1)(x + 48)
  11. 11.In which quadrant does the point (1, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  12. 12.Which is the correct factorisation of x² + 11x + 30? (a) (x − 5)(x − 6) (b) (x + 1)(x + 30) (c) (x + 5)(x + 6) (d) (x + 1)(x + 10)
  13. 13.Two angles of a triangle are 65° and 55°. What is the third angle? (a) 120° (b) 115° (c) 60° (d) 125°
  14. 14.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 693 sq cm (d) 132 sq cm
  15. 15.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) 48 (b) 36 (c) 37 (d) 49
  16. 16.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  17. 17.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 153 (b) 17 (c) 54 (d) 51
  18. 18.A bag has 2 green, 3 white and 3 blue balls. One ball is taken out without looking. What is the probability that it is not green? (a) 3/4 (b) 7/8 (c) 1/3 (d) 1/4
  19. 19.How many factors does 80 have? (a) 11 (b) 10 (c) 8 (d) 9
  20. 20.A bag has 5 red balls and 11 black 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) 6 (c) 16 (d) 12
  21. 21.Two angles of a triangle are 55° and 85°. What is the third angle? (a) 40° (b) 95° (c) 140° (d) 125°
  22. 22.A bag has 4 yellow, 6 green and 4 white balls. One ball is taken out without looking. What is the probability that it is not green? (a) 3/7 (b) 1/3 (c) 9/14 (d) 4/7
  23. 23.In a class of 20 children, 7 like tea, 13 like coffee and 2 like both. How many like only tea? (a) 2 (b) 5 (c) 11 (d) 7
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  25. 25.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  26. 26.What is the distance between the points (6, 7) and (9, 11)? (a) 6 (b) 5 (c) 25 (d) 7
  27. 27.What is the mean of 20, 17, 15, 16 and 7? (a) 16 (b) 14 (c) 17 (d) 15
  28. 28.What is the mean of 18, 9, 16, 9 and 13? (a) 14 (b) 12 (c) 15 (d) 13
  29. 29.In a league, 13 teams each play every other team once. How many matches are played? (a) 91 (b) 78 (c) 169 (d) 156
  30. 30.A drawer has lots of red, green 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) 6 (b) 4 (c) 2 (d) 3
  31. 31.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 30 (b) 36 (c) 15 (d) 12
  32. 32.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 72 (b) 36 (c) 81 (d) 45
  33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/11 (c) 3/11 (d) 1/12
  34. 34.What is the missing term in the AP 15, ?, 29, 36, 43? (a) 21 (b) 23 (c) 29 (d) 22
  35. 35.The mean of 6 numbers is 18. When the number 46 is added to them, what is the new mean? (a) 32 (b) 22 (c) 18 (d) 23
  36. 36.How many factors does 29 have? (a) 1 (b) 4 (c) 3 (d) 2
  37. 37.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 176 cm (c) 616 cm (d) 44 cm
  38. 38.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 14 (b) 49 (c) 21 (d) 42
  39. 39.There are 6 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 13 (b) 48 (c) 42 (d) 84
  40. 40.3 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 18 (b) 12 (c) 6 (d) 9

Answer key

  1. 6
  2. 5
  3. 2
  4. 25
  5. 1/9
  6. 4
  7. 3/4
  8. 9
  9. 20°
  10. (x + 6)(x + 8)
  11. Fourth quadrant
  12. (x + 5)(x + 6)
  13. 60°
  14. 1386 sq cm
  15. 37
  16. 9
  17. 51
  18. 3/4
  19. 10
  20. 12
  21. 40°
  22. 4/7
  23. 5
  24. 7
  25. 10
  26. 5
  27. 15
  28. 13
  29. 78
  30. 4
  31. 15
  32. 36
  33. 1/12
  34. 22
  35. 22
  36. 2
  37. 88 cm
  38. 21
  39. 42
  40. 9

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad