← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 13 · 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 dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 2/11 (c) 1/11 (d) 1/12
  2. 2.What is the mode of 10, 6, 18, 3, 18, 18 and 6? (a) 18 (b) 10 (c) 3 (d) 6
  3. 3.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 363 (b) 373 (c) 320 (d) 372
  4. 4.Which is the correct factorisation of x² + 10x + 24? (a) (x + 4)(x + 6) (b) (x + 1)(x + 24) (c) (x + 1)(x + 9) (d) (x − 4)(x − 6)
  5. 5.How many factors does 119 have? (a) 4 (b) 3 (c) 2 (d) 5
  6. 6.What is the prime factorisation of 18? (a) 2² × 3 (b) 2² × 3² (c) 2 × 3³ (d) 2 × 3²
  7. 7.How many factors does 35 have? (a) 2 (b) 5 (c) 4 (d) 3
  8. 8.Two angles of a triangle are 25° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 130° (c) 155° (d) 50°
  9. 9.A bag has 5 red balls and 8 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 13 (b) 7 (c) 2 (d) 6
  10. 10.In a class of 30 children, 15 like maths, 23 like science and 2 like neither. How many like both? (a) 10 (b) 2 (c) 8 (d) 28
  11. 11.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
  12. 12.In a class of 36 children, 16 like maths, 20 like science and 3 like both. How many like at least one of the two? (a) 36 (b) 34 (c) 30 (d) 33
  13. 13.What is the prime factorisation of 144? (a) 2³ × 3² (b) 2⁵ × 3² (c) 2⁴ × 3² (d) 2² × 3⁴
  14. 14.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  15. 15.In a league, 5 teams each play every other team once. How many matches are played? (a) 10 (b) 15 (c) 20 (d) 25
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 17 (d) 18
  17. 17.How many factors does 87 have? (a) 5 (b) 3 (c) 2 (d) 4
  18. 18.What is the 12th term of the AP 19, 28, 37, 46, …? (a) 99 (b) 127 (c) 118 (d) 108
  19. 19.In a class of 30 children, 21 like cricket, 7 like football and 6 like neither. How many like both? (a) 4 (b) 6 (c) 5 (d) 24
  20. 20.Two angles of a triangle are 20° and 110°. What is the third angle? (a) 70° (b) 160° (c) 50° (d) 130°
  21. 21.5 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 20 (b) 15 (c) 25 (d) 10
  22. 22.How many factors does 105 have? (a) 6 (b) 8 (c) 9 (d) 7
  23. 23.In which quadrant does the point (−5, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  24. 24.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 564 (c) 565 (d) 448
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  26. 26.Two angles of a triangle are 25° and 55°. What is the third angle? (a) 125° (b) 100° (c) 80° (d) 155°
  27. 27.A drawer has lots of red, white, blue, green 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) 5 (b) 6 (c) 2 (d) 10
  28. 28.What is the sum of all the whole numbers from 1 to 67? (a) 4556 (b) 2279 (c) 2211 (d) 2278
  29. 29.What is the prime factorisation of 84? (a) 2³ × 3 × 7 (b) 2 × 3 × 7 (c) 2² × 3 × 7 (d) 2 × 3 × 7²
  30. 30.A bag has 8 yellow, 6 blue and 7 red balls. One ball is taken out without looking. What is the probability that it is yellow? (a) 8/13 (b) 1/3 (c) 8/21 (d) 13/21
  31. 31.A bag has 10 blue balls and 7 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 11 (b) 8 (c) 2 (d) 17
  32. 32.Two angles of a triangle are 70° and 25°. What is the third angle? (a) 95° (b) 155° (c) 85° (d) 110°
  33. 33.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 105° (b) 75° (c) 30° (d) 15°
  34. 34.In a class of 51 children, 25 like maths, 30 like science and 12 like both. How many like at least one of the two? (a) 51 (b) 31 (c) 43 (d) 55
  35. 35.In which quadrant does the point (−9, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  36. 36.In a class of 41 children, 18 like maths, 25 like science and 12 like both. How many like only maths? (a) 18 (b) 6 (c) 13 (d) 16
  37. 37.What is the distance between the points (1, 0) and (13, 16)? (a) 20 (b) 400 (c) 28 (d) 21
  38. 38.What is the mean of 15, 4, 6, 7, 14 and 20? (a) 12 (b) 10 (c) 11 (d) 13
  39. 39.How many factors does 68 have? (a) 6 (b) 5 (c) 4 (d) 7
  40. 40.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20

Answer key

  1. 1/18
  2. 18
  3. 372
  4. (x + 4)(x + 6)
  5. 4
  6. 2 × 3²
  7. 4
  8. 130°
  9. 7
  10. 10
  11. 2464 sq cm
  12. 33
  13. 2⁴ × 3²
  14. 9
  15. 10
  16. 18
  17. 4
  18. 118
  19. 4
  20. 50°
  21. 10
  22. 8
  23. Third quadrant
  24. 564
  25. 9
  26. 100°
  27. 6
  28. 2278
  29. 2² × 3 × 7
  30. 8/21
  31. 11
  32. 85°
  33. 30°
  34. 43
  35. Third quadrant
  36. 6
  37. 20
  38. 11
  39. 6
  40. 20

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