← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 489 · 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 which quadrant does the point (9, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  2. 2.What is the smallest prime factor of 69? (a) 3 (b) 23 (c) 2 (d) 1
  3. 3.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 2/3 (b) 1/3 (c) 1/6 (d) 1/2
  4. 4.What is the 36th term of the AP 19, 26, 33, 40, …? (a) 264 (b) 271 (c) 245 (d) 252
  5. 5.Two angles of a triangle are 65° and 35°. What is the exterior angle at the third corner? (a) 100° (b) 115° (c) 80° (d) 145°
  6. 6.Two angles of a triangle are 70° and 95°. What is the third angle? (a) 110° (b) 85° (c) 15° (d) 165°
  7. 7.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/18 (b) 1/11 (c) 1/36 (d) 1/12
  8. 8.What is the median of 19, 36, 30, 8, 23, 9 and 35? (a) 30 (b) 8 (c) 19 (d) 23
  9. 9.In a class of 23 children, 9 like dance, 9 like music and 3 like both. How many like neither? (a) 11 (b) 5 (c) 3 (d) 8
  10. 10.If a + b = 17 and ab = 72, what is (a − b)²? (a) 289 (b) 217 (c) 145 (d) 1
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 18 (b) 17 (c) 19 (d) 8
  12. 12.What is the 10th term of the AP 14, 18, 22, 26, …? (a) 50 (b) 40 (c) 54 (d) 36
  13. 13.What is the distance between the points (8, 1) and (20, 17)? (a) 28 (b) 21 (c) 400 (d) 20
  14. 14.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
  15. 15.What is the median of 13, 2, 12, 10 and 16? (a) 12 (b) 10 (c) 11 (d) 13
  16. 16.What is the circumference of a circle of diameter 56 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
  17. 17.Two straight lines cross. One of the angles is 105°. What is the angle next to it on the same straight line? (a) 105° (b) 76° (c) 75° (d) 255°
  18. 18.Which is the correct factorisation of x² + 15x + 54? (a) (x + 6)(x + 9) (b) (x − 6)(x − 9) (c) (x + 1)(x + 54) (d) (x + 1)(x + 14)
  19. 19.In a class of 38 children, 16 like tea, 22 like coffee and 3 like both. How many like at least one of the two? (a) 32 (b) 38 (c) 36 (d) 35
  20. 20.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/3 (b) 1/6 (c) 1/2 (d) 2/3
  21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  22. 22.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 132 (c) 78 (d) 144
  23. 23.A drawer has lots of yellow 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) 4 (b) 2 (c) 5 (d) 3
  24. 24.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 88 cm (d) 616 cm
  25. 25.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 80° (b) 20° (c) 160° (d) 70°
  26. 26.In a class of 26 children, 15 like mangoes, 19 like bananas and 12 like both. How many like only mangoes? (a) 7 (b) 12 (c) 15 (d) 3
  27. 27.A bag has 6 white, 6 yellow and 2 blue balls. One ball is taken out without looking. What is the probability that it is not white? (a) 3/7 (b) 9/14 (c) 4/7 (d) 1/3
  28. 28.Two straight lines cross. Two vertically opposite angles add up to 280°. What is each of the other two angles? (a) 80° (b) 140° (c) 41° (d) 40°
  29. 29.What is the median of 8, 26, 30, 34 and 22? (a) 22 (b) 30 (c) 26 (d) 24
  30. 30.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 55 (b) 19 (c) 110 (d) 100
  31. 31.A bag has 7 black balls and 10 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 11 (c) 2 (d) 8
  32. 32.A bag has 3 black balls and 3 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 4 (b) 6 (c) 5 (d) 2
  33. 33.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 1/9 (c) 4/11 (d) 5/36
  34. 34.What is the mode of 17, 19, 17, 1, 19, 10 and 17? (a) 17 (b) 10 (c) 19 (d) 1
  35. 35.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 77 sq cm (b) 154 sq cm (c) 616 sq cm (d) 44 sq cm
  36. 36.If a + b = 6 and ab = 5, what is (a − b)²? (a) 26 (b) 4 (c) 36 (d) 16
  37. 37.A captain and a vice-captain are to be chosen from 12 players. In how many ways can this be done? (a) 66 (b) 144 (c) 132 (d) 24
  38. 38.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 40° (b) 80° (c) 50° (d) 100°
  39. 39.How many factors does 29 have? (a) 3 (b) 2 (c) 4 (d) 1
  40. 40.What is the midpoint of the line joining (7, 7) and (11, 19)? (a) (13, 9) (b) (18, 26) (c) (2, 6) (d) (9, 13)

Answer key

  1. Fourth quadrant
  2. 3
  3. 1/3
  4. 264
  5. 100°
  6. 15°
  7. 1/36
  8. 23
  9. 8
  10. 1
  11. 18
  12. 50
  13. 20
  14. 2464 sq cm
  15. 12
  16. 176 cm
  17. 75°
  18. (x + 6)(x + 9)
  19. 35
  20. 1/2
  21. 10
  22. 66
  23. 3
  24. 88 cm
  25. 80°
  26. 3
  27. 4/7
  28. 40°
  29. 26
  30. 100
  31. 11
  32. 5
  33. 1/9
  34. 17
  35. 154 sq cm
  36. 16
  37. 132
  38. 40°
  39. 2
  40. (9, 13)

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