← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 384 · 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.There are 7 roads from town A to town B and 3 roads from town B to town C. How many different routes go from A to C through B? (a) 21 (b) 42 (c) 28 (d) 10
  2. 2.A cube has edges of 7 cm. What is its volume? (a) 21 cu cm (b) 196 cu cm (c) 294 cu cm (d) 343 cu cm
  3. 3.How many prime numbers are there between 20 and 30? (a) 2 (b) 3 (c) 1 (d) 4
  4. 4.What is the midpoint of the line joining (5, 2) and (15, 10)? (a) (20, 12) (b) (6, 10) (c) (10, 6) (d) (5, 4)
  5. 5.How many prime numbers are there between 50 and 60? (a) 1 (b) 4 (c) 3 (d) 2
  6. 6.In an isosceles triangle, the two equal angles are 50° each. What is the third angle? (a) 40° (b) 50° (c) 80° (d) 130°
  7. 7.What is the mode of 4, 2, 5, 1, 5, 2 and 5? (a) 4 (b) 2 (c) 5 (d) 1
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 7 (b) 9 (c) 11 (d) 12
  10. 10.Using (a − b)² = a² − 2ab + b², what is 39²? (a) 1681 (b) 1521 (c) 1531 (d) 1599
  11. 11.In an isosceles triangle, the angle between the two equal sides is 140°. What is each of the other two angles? (a) 20° (b) 30° (c) 40° (d) 140°
  12. 12.In a class of 52 children, 26 like dance, 25 like music and 7 like both. How many like neither? (a) 8 (b) 15 (c) 1 (d) 7
  13. 13.In a class of 18 children, 7 like maths, 11 like science and 3 like neither. How many like both? (a) 2 (b) 15 (c) 3 (d) 4
  14. 14.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/9 (b) 1/12 (c) 1/11 (d) 3/11
  15. 15.How many prime numbers are there between 10 and 30? (a) 8 (b) 7 (c) 6 (d) 5
  16. 16.What is the prime factorisation of 144? (a) 2⁴ × 3² (b) 2³ × 3² (c) 2² × 3⁴ (d) 2⁵ × 3²
  17. 17.What is the mean of 12, 18, 4, 6 and 20? (a) 12 (b) 15 (c) 10 (d) 13
  18. 18.What is the 13th term of the AP 10, 19, 28, 37, …? (a) 127 (b) 117 (c) 118 (d) 108
  19. 19.If a + b = 14 and ab = 24, what is a² + b²? (a) 196 (b) 244 (c) 172 (d) 148
  20. 20.What is the midpoint of the line joining (2, 8) and (4, 6)? (a) (1, 1) (b) (6, 14) (c) (7, 3) (d) (3, 7)
  21. 21.Using (a + b)² = a² + 2ab + b², what is 81²? (a) 6401 (b) 6571 (c) 6561 (d) 6241
  22. 22.What is the missing term in the AP 15, 19, ?, 27, 31? (a) 27 (b) 22 (c) 24 (d) 23
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 1 (b) 4 (c) 3 (d) 2
  24. 24.A bag has 6 white balls and 12 red 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) 18 (c) 7 (d) 13
  25. 25.In which quadrant does the point (−3, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.In a class of 33 children, 16 like cricket, 25 like football and 12 like both. How many like at least one of the two? (a) 41 (b) 33 (c) 17 (d) 29
  27. 27.What is the mode of 19, 4, 13, 8, 4, 13 and 4? (a) 4 (b) 13 (c) 8 (d) 19
  28. 28.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 28 (c) 56 (d) 64
  29. 29.What is the smallest prime factor of 91? (a) 13 (b) 2 (c) 1 (d) 7
  30. 30.A cube has edges of 9 cm. What is its total surface area? (a) 486 sq cm (b) 729 sq cm (c) 81 sq cm (d) 324 sq cm
  31. 31.What is the distance between the points (6, 1) and (15, 13)? (a) 225 (b) 15 (c) 16 (d) 21
  32. 32.What is the mean of 8, 2, 4, 9, 16 and 3? (a) 9 (b) 7 (c) 8 (d) 6
  33. 33.What is the sum of all the whole numbers from 1 to 19? (a) 171 (b) 191 (c) 380 (d) 190
  34. 34.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 440 (c) 553 (d) 552
  35. 35.A cuboid is 6 cm long, 4 cm wide and 3 cm high. What is its volume? (a) 72 cu cm (b) 108 cu cm (c) 13 cu cm (d) 24 cu cm
  36. 36.A team of 2 players is to be chosen from 6 players. How many different teams are possible? (a) 36 (b) 30 (c) 15 (d) 12
  37. 37.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
  38. 38.What is the median of 3, 40, 36, 6, 31, 33 and 5? (a) 33 (b) 22 (c) 31 (d) 6
  39. 39.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6
  40. 40.What is the mean of 19, 19, 9, 11 and 22? (a) 20 (b) 16 (c) 15 (d) 17

Answer key

  1. 21
  2. 343 cu cm
  3. 2
  4. (10, 6)
  5. 2
  6. 80°
  7. 5
  8. 6
  9. 11
  10. 1521
  11. 20°
  12. 8
  13. 3
  14. 1/12
  15. 6
  16. 2⁴ × 3²
  17. 12
  18. 118
  19. 148
  20. (3, 7)
  21. 6561
  22. 23
  23. 3
  24. 13
  25. Second quadrant
  26. 29
  27. 4
  28. 28
  29. 7
  30. 486 sq cm
  31. 15
  32. 7
  33. 190
  34. 552
  35. 72 cu cm
  36. 15
  37. 1386 sq cm
  38. 31
  39. 1/3
  40. 16

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