← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 457 · 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.Which term of the AP 9, 14, 19, 24, … is 79? (a) 14th (b) 16th (c) 17th (d) 15th
  2. 2.How many factors does 63 have? (a) 5 (b) 6 (c) 7 (d) 4
  3. 3.The mean of 3 numbers is 26. When the number 34 is added to them, what is the new mean? (a) 28 (b) 30 (c) 26 (d) 29
  4. 4.In a class of 27 children, 14 like mangoes, 19 like bananas and 8 like both. How many like at least one of the two? (a) 33 (b) 27 (c) 25 (d) 17
  5. 5.In a class of 40 children, 25 like dance, 23 like music and 2 like neither. How many like both? (a) 10 (b) 8 (c) 38 (d) 2
  6. 6.In an isosceles triangle, the angle between the two equal sides is 100°. What is each of the other two angles? (a) 80° (b) 100° (c) 50° (d) 40°
  7. 7.If the side of a square is made 5 times as long, how many times as big does its area become? (a) 5 times (b) 25 times (c) 125 times (d) 10 times
  8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  9. 9.In an isosceles triangle, the angle between the two equal sides is 90°. What is each of the other two angles? (a) 55° (b) 45° (c) 46° (d) 90°
  10. 10.A bag has 2 green, 8 red and 4 white balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/3 (b) 1/6 (c) 6/7 (d) 1/7
  11. 11.A fair dice is rolled once. What is the probability of getting a multiple of 3? (a) 1/2 (b) 1/6 (c) 1/3 (d) 2/3
  12. 12.What is the 35th term of the AP 12, 14, 16, 18, …? (a) 70 (b) 68 (c) 80 (d) 82
  13. 13.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
  14. 14.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 5/8 (d) 3/8
  15. 15.What is the sum of the roots of x² − 5x + 6 = 0? (a) 6 (b) 5 (c) 4 (d) 7
  16. 16.Two angles of a triangle are 55° and 115°. What is the third angle? (a) 170° (b) 10° (c) 65° (d) 125°
  17. 17.In a class of 23 children, 14 like mangoes, 8 like bananas and 2 like both. How many like neither? (a) 5 (b) 1 (c) 3 (d) 2
  18. 18.What is the midpoint of the line joining (9, 4) and (15, 14)? (a) (12, 9) (b) (3, 5) (c) (9, 12) (d) (24, 18)
  19. 19.Using (a − b)² = a² − 2ab + b², what is 36²? (a) 1296 (b) 1306 (c) 1936 (d) 1584
  20. 20.What is the distance between the points (7, 12) and (12, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  21. 21.What is the smallest prime factor of 91? (a) 1 (b) 2 (c) 13 (d) 7
  22. 22.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) 22 (c) 29 (d) 28
  23. 23.What is the sum of the first 5 terms of the AP 2, 7, 12, …? (a) 65 (b) 60 (c) 22 (d) 120
  24. 24.What is the distance between the points (2, 1) and (11, 13)? (a) 21 (b) 225 (c) 16 (d) 15
  25. 25.A cuboid is 4 cm long, 3 cm wide and 5 cm high. What is its volume? (a) 60 cu cm (b) 61 cu cm (c) 12 cu cm (d) 94 cu cm
  26. 26.In a class of 30 children, 13 like dance, 19 like music and 6 like both. How many like only dance? (a) 11 (b) 13 (c) 7 (d) 6
  27. 27.A canteen sells 8 kinds of sandwich and 4 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 32 (b) 64 (c) 12 (d) 40
  28. 28.A bag has 8 green balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 9 (b) 2 (c) 10 (d) 17
  29. 29.In a class of 19 children, 9 like maths, 9 like science and 5 like neither. How many like both? (a) 5 (b) 3 (c) 4 (d) 14
  30. 30.What is the distance between the points (7, 14) and (22, 6)? (a) 17 (b) 23 (c) 289 (d) 18
  31. 31.A cube has edges of 10 cm. What is its volume? (a) 400 cu cm (b) 600 cu cm (c) 30 cu cm (d) 1000 cu cm
  32. 32.What is the distance between the points (3, 15) and (11, 9)? (a) 100 (b) 14 (c) 10 (d) 11
  33. 33.A cube has edges of 4 cm. What is its volume? (a) 96 cu cm (b) 12 cu cm (c) 65 cu cm (d) 64 cu cm
  34. 34.In how many different ways can the letters of the word KITE be arranged? (a) 48 (b) 16 (c) 24 (d) 12
  35. 35.Two angles of a triangle are 50° and 55°. What is the exterior angle at the third corner? (a) 130° (b) 105° (c) 75° (d) 125°
  36. 36.What is the midpoint of the line joining (2, 6) and (6, 10)? (a) (4, 8) (b) (2, 2) (c) (8, 4) (d) (8, 16)
  37. 37.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 4/11 (b) 1/11 (c) 1/9 (d) 5/36
  38. 38.What is the median of 13, 40, 16, 39 and 31? (a) 32 (b) 16 (c) 39 (d) 31
  39. 39.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 56 (c) 112 (d) 64
  40. 40.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 114 (c) 106 (d) 96

Answer key

  1. 15th
  2. 6
  3. 28
  4. 25
  5. 10
  6. 40°
  7. 25 times
  8. 20
  9. 45°
  10. 1/7
  11. 1/3
  12. 80
  13. 616 sq cm
  14. 3/8
  15. 5
  16. 10°
  17. 3
  18. (12, 9)
  19. 1296
  20. 13
  21. 7
  22. 22
  23. 60
  24. 15
  25. 60 cu cm
  26. 7
  27. 32
  28. 10
  29. 4
  30. 17
  31. 1000 cu cm
  32. 10
  33. 64 cu cm
  34. 24
  35. 105°
  36. (4, 8)
  37. 1/9
  38. 31
  39. 56
  40. 105

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