← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 409 · 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 missing term in the AP 11, 18, 25, ?, 39? (a) 39 (b) 31 (c) 32 (d) 33
  2. 2.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 28 (b) 46 (c) 37 (d) 38
  3. 3.Two angles of a triangle are 25° and 85°. What is the third angle? (a) 95° (b) 70° (c) 110° (d) 155°
  4. 4.The mean of 7 numbers is 27. When the number 51 is added to them, what is the new mean? (a) 27 (b) 30 (c) 31 (d) 39
  5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/11 (c) 5/36 (d) 1/9
  6. 6.A bag has 4 red balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 6 (b) 2 (c) 15 (d) 5
  7. 7.What is the mode of 16, 5, 11, 16, 11, 1 and 16? (a) 11 (b) 5 (c) 1 (d) 16
  8. 8.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 12 (c) 108 (d) 36
  9. 9.In which quadrant does the point (4, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  10. 10.What is the prime factorisation of 30? (a) 2³ × 3 × 5 (b) 2 × 3 × 5 (c) 2 × 3 × 5² (d) 2² × 3 × 5
  11. 11.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 1/3 (d) 2/3
  12. 12.What is the missing term in the AP 9, ?, 25, 33, 41? (a) 16 (b) 18 (c) 17 (d) 25
  13. 13.How many factors does 75 have? (a) 6 (b) 4 (c) 7 (d) 5
  14. 14.A canteen sells 8 kinds of sandwich and 2 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 24 (b) 10 (c) 16 (d) 32
  15. 15.What is the distance between the points (7, 2) and (10, 6)? (a) 5 (b) 25 (c) 7 (d) 6
  16. 16.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  17. 17.Two angles of a triangle are 75° and 80°. What is the third angle? (a) 155° (b) 105° (c) 100° (d) 25°
  18. 18.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 5° (c) 95° (d) 85°
  19. 19.What is the missing term in the AP 5, 11, ?, 23, 29? (a) 16 (b) 18 (c) 17 (d) 23
  20. 20.Which is the correct factorisation of x² + 5x + 6? (a) (x + 1)(x + 4) (b) (x + 2)(x + 3) (c) (x − 2)(x − 3) (d) (x + 1)(x + 6)
  21. 21.Two angles of a triangle are 60° and 75°. What is the third angle? (a) 120° (b) 135° (c) 105° (d) 45°
  22. 22.In a class of 25 children, 14 like mangoes, 14 like bananas and 6 like both. How many like neither? (a) 6 (b) 9 (c) 4 (d) 3
  23. 23.Two angles of a triangle are 30° and 105°. What is the third angle? (a) 150° (b) 135° (c) 45° (d) 75°
  24. 24.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 45° (b) 136° (c) 315° (d) 135°
  25. 25.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 36 (b) 12 (c) 15 (d) 30
  26. 26.What is the smallest prime factor of 209? (a) 19 (b) 2 (c) 1 (d) 11
  27. 27.What is the prime factorisation of 45? (a) 3² × 5 (b) 3 × 5² (c) 3³ × 5 (d) 3 × 5
  28. 28.How many prime numbers are there between 20 and 40? (a) 6 (b) 5 (c) 4 (d) 3
  29. 29.In an isosceles triangle, the two equal angles are 80° each. What is the third angle? (a) 10° (b) 80° (c) 100° (d) 20°
  30. 30.In a league, 7 teams each play every other team once. How many matches are played? (a) 21 (b) 49 (c) 28 (d) 42
  31. 31.What is the prime factorisation of 24? (a) 2² × 3 (b) 2 × 3³ (c) 2³ × 3 (d) 2⁴ × 3
  32. 32.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 15 (b) 17 (c) 5 (d) 16
  34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  35. 35.How many factors does 86 have? (a) 5 (b) 2 (c) 4 (d) 3
  36. 36.What is the distance between the points (8, 5) and (24, 17)? (a) 28 (b) 21 (c) 20 (d) 400
  37. 37.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 15 (d) 30
  38. 38.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 121 (c) 21 (d) 66
  39. 39.A fair dice is rolled once. What is the probability of getting a number greater than 3? (a) 2/3 (b) 1/2 (c) 1/6 (d) 1/3
  40. 40.If the radius of a circle is made 4 times as long, how many times as big does its area become? (a) 8 times (b) 16 times (c) 4 times (d) 64 times

Answer key

  1. 32
  2. 37
  3. 70°
  4. 30
  5. 1/9
  6. 6
  7. 16
  8. 36
  9. First quadrant
  10. 2 × 3 × 5
  11. 1/2
  12. 17
  13. 6
  14. 16
  15. 5
  16. 6
  17. 25°
  18. 95°
  19. 17
  20. (x + 2)(x + 3)
  21. 45°
  22. 3
  23. 45°
  24. 135°
  25. 30
  26. 11
  27. 3² × 5
  28. 4
  29. 20°
  30. 21
  31. 2³ × 3
  32. 2
  33. 16
  34. 5
  35. 4
  36. 20
  37. 15
  38. 121
  39. 1/2
  40. 16 times

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