← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 933 · 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 median of 4, 29, 35, 24 and 25? (a) 29 (b) 35 (c) 25 (d) 24
  2. 2.Which term of the AP 11, 14, 17, 20, … is 74? (a) 23rd (b) 24th (c) 22nd (d) 21st
  3. 3.Two straight lines cross. One of the angles is 100°. What is the angle next to it on the same straight line? (a) 100° (b) 81° (c) 260° (d) 80°
  4. 4.What is the smallest prime factor of 341? (a) 1 (b) 11 (c) 31 (d) 2
  5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 1/12 (b) 3/11 (c) 1/11 (d) 1/9
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 19 (d) 8
  7. 7.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 24 (c) 21 (d) 7
  8. 8.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 44 cm (b) 176 cm (c) 616 cm (d) 88 cm
  9. 9.Two straight lines cross. One of the angles is 80°. What is the angle next to it on the same straight line? (a) 80° (b) 280° (c) 10° (d) 100°
  10. 10.Two angles of a triangle are 20° and 35°. What is the third angle? (a) 125° (b) 160° (c) 145° (d) 55°
  11. 11.A cuboid is 9 cm long, 2 cm wide and 2 cm high. What is its volume? (a) 36 cu cm (b) 13 cu cm (c) 80 cu cm (d) 18 cu cm
  12. 12.In a class of 37 children, 20 like mangoes, 18 like bananas and 3 like both. How many like at least one of the two? (a) 32 (b) 38 (c) 35 (d) 37
  13. 13.A fair dice is rolled once. What is the probability of getting a number less than 3? (a) 1/6 (b) 2/3 (c) 1/2 (d) 1/3
  14. 14.A drawer has lots of black and red 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) 2 (c) 3 (d) 4
  15. 15.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 25 times (b) 5 times (c) 125 times (d) 10 times
  16. 16.If the side of a square is made 2 times as long, how many times as big does its area become? (a) 5 times (b) 2 times (c) 8 times (d) 4 times
  17. 17.A fair dice is rolled once. What is the probability of getting a factor of 6? (a) 2/3 (b) 1/3 (c) 1/4 (d) 5/6
  18. 18.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 121 (b) 22 (c) 55 (d) 110
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 20 (d) 19
  20. 20.What is the 11th term of the AP 12, 17, 22, 27, …? (a) 62 (b) 55 (c) 67 (d) 50
  21. 21.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 44 cm (c) 22 cm (d) 88 cm
  22. 22.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  23. 23.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 12 (c) 25 (d) 13
  24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 5/11 (c) 1/6 (d) 1/11
  25. 25.What is the prime factorisation of 120? (a) 2² × 3 × 5 (b) 2⁴ × 3 × 5 (c) 2³ × 3 × 5 (d) 2 × 3 × 5³
  26. 26.Using (a + b)² = a² + 2ab + b², what is 52²? (a) 2304 (b) 2504 (c) 2704 (d) 2714
  27. 27.A bag has 7 green, 3 white and 5 blue balls. One ball is taken out without looking. What is the probability that it is green? (a) 8/15 (b) 1/3 (c) 7/15 (d) 7/8
  28. 28.There are 3 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 12 (b) 6 (c) 5 (d) 9
  29. 29.What is the distance between the points (4, 3) and (20, 15)? (a) 400 (b) 28 (c) 21 (d) 20
  30. 30.In an isosceles triangle, the angle between the two equal sides is 110°. What is each of the other two angles? (a) 45° (b) 35° (c) 110° (d) 70°
  31. 31.What is the prime factorisation of 80? (a) 2⁴ × 5 (b) 2³ × 5 (c) 2⁵ × 5 (d) 2 × 5⁴
  32. 32.In a class of 35 children, 16 like cricket, 30 like football and 1 like neither. How many like both? (a) 11 (b) 34 (c) 1 (d) 12
  33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 7? (a) 7/36 (b) 1/11 (c) 6/11 (d) 1/6
  34. 34.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
  35. 35.Two angles of a triangle are 25° and 120°. What is the third angle? (a) 155° (b) 35° (c) 145° (d) 60°
  36. 36.What is the mean of 7, 15, 16, 3, 10 and 9? (a) 11 (b) 12 (c) 9 (d) 10
  37. 37.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) 21 (b) 28 (c) 22 (d) 29
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 19 (b) 20 (c) 8 (d) 18
  39. 39.What is the median of 32, 3, 37, 27, 19, 16 and 30? (a) 19 (b) 27 (c) 30 (d) 28
  40. 40.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 36 (c) 12 (d) 30

Answer key

  1. 25
  2. 22nd
  3. 80°
  4. 11
  5. 1/12
  6. 19
  7. 21
  8. 88 cm
  9. 100°
  10. 125°
  11. 36 cu cm
  12. 35
  13. 1/3
  14. 3
  15. 125 times
  16. 4 times
  17. 2/3
  18. 55
  19. 20
  20. 62
  21. 44 cm
  22. 5
  23. 13
  24. 5/36
  25. 2³ × 3 × 5
  26. 2704
  27. 7/15
  28. 6
  29. 20
  30. 35°
  31. 2⁴ × 5
  32. 12
  33. 1/6
  34. 1/2
  35. 35°
  36. 10
  37. 22
  38. 19
  39. 27
  40. 30

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