← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 467 · 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 mean of 14, 20, 17, 11 and 3? (a) 13 (b) 15 (c) 14 (d) 12
  2. 2.Two angles of a triangle are 35° and 105°. What is the exterior angle at the third corner? (a) 75° (b) 145° (c) 140° (d) 40°
  3. 3.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1379 (b) 1591 (c) 1849 (d) 1369
  4. 4.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 1/18 (b) 2/11 (c) 1/11 (d) 1/12
  5. 5.Two dice are rolled together. What is the probability that the two numbers add up to 11? (a) 1/12 (b) 1/18 (c) 2/11 (d) 1/11
  6. 6.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  7. 7.In an isosceles triangle, the angle between the two equal sides is 120°. What is each of the other two angles? (a) 30° (b) 60° (c) 40° (d) 120°
  8. 8.In how many different ways can the letters of the word LAMP be arranged? (a) 16 (b) 24 (c) 12 (d) 48
  9. 9.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/2 (c) 2/3 (d) 1/4
  10. 10.In a class of 35 children, 16 like cricket, 16 like football and 4 like both. How many like at least one of the two? (a) 28 (b) 35 (c) 24 (d) 32
  11. 11.A drawer has lots of blue, white, green 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) 4 (b) 5 (c) 2 (d) 8
  12. 12.A drawer has lots of red, yellow and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 6 (b) 4 (c) 2 (d) 3
  13. 13.Using (a − b)² = a² − 2ab + b², what is 78²? (a) 6084 (b) 6396 (c) 6724 (d) 6094
  14. 14.If a + b = 4 and ab = 3, what is a² + b²? (a) 10 (b) 22 (c) 13 (d) 16
  15. 15.How many factors does 82 have? (a) 2 (b) 5 (c) 4 (d) 3
  16. 16.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 2464 cm (c) 88 cm (d) 176 cm
  17. 17.What is the 10th term of the AP 9, 12, 15, 18, …? (a) 36 (b) 27 (c) 39 (d) 30
  18. 18.What is the smallest prime factor of 77? (a) 1 (b) 2 (c) 7 (d) 11
  19. 19.What is the midpoint of the line joining (5, 6) and (17, 8)? (a) (22, 14) (b) (7, 11) (c) (11, 7) (d) (6, 1)
  20. 20.If the side of a square is made 3 times as long, how many times as big does its area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
  21. 21.Which term of the AP 20, 23, 26, 29, … is 92? (a) 26th (b) 24th (c) 27th (d) 25th
  22. 22.What is the mean of 3, 6, 5, 5 and 6? (a) 4 (b) 5 (c) 7 (d) 6
  23. 23.In a class of 42 children, 16 like mangoes, 23 like bananas and 4 like both. How many like only mangoes? (a) 4 (b) 12 (c) 19 (d) 16
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  25. 25.In how many different ways can the letters of the word KITE be arranged? (a) 16 (b) 12 (c) 24 (d) 48
  26. 26.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 32 (c) 50 (d) 41
  27. 27.Which is the correct factorisation of x² + 17x + 72? (a) (x + 8)(x + 9) (b) (x + 1)(x + 72) (c) (x + 1)(x + 16) (d) (x − 8)(x − 9)
  28. 28.What is the sum of the first 12 terms of the AP 8, 11, 14, …? (a) 588 (b) 294 (c) 312 (d) 41
  29. 29.What is the sum of all the whole numbers from 1 to 66? (a) 2211 (b) 2145 (c) 2178 (d) 4422
  30. 30.Two straight lines cross. One of the angles is 45°. What is the angle next to it on the same straight line? (a) 315° (b) 45° (c) 136° (d) 135°
  31. 31.Two angles of a triangle are 75° and 50°. What is the third angle? (a) 55° (b) 105° (c) 125° (d) 130°
  32. 32.What is the smallest prime factor of 217? (a) 31 (b) 2 (c) 1 (d) 7
  33. 33.What is the smallest prime factor of 35? (a) 2 (b) 5 (c) 7 (d) 1
  34. 34.A bag has 4 yellow balls and 7 blue 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) 8 (c) 11 (d) 5
  35. 35.How many prime numbers are there between 60 and 70? (a) 3 (b) 2 (c) 1 (d) 4
  36. 36.Two angles of a triangle are 50° and 50°. What is the third angle? (a) 80° (b) 260° (c) 130° (d) 100°
  37. 37.In an isosceles triangle, the two equal angles are 30° each. What is the third angle? (a) 30° (b) 120° (c) 60° (d) 150°
  38. 38.3 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 9 (b) 12 (c) 6 (d) 5
  39. 39.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  40. 40.10 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 55 (b) 100 (c) 45 (d) 90

Answer key

  1. 13
  2. 140°
  3. 1369
  4. 1/18
  5. 1/18
  6. 25
  7. 30°
  8. 24
  9. 1/2
  10. 28
  11. 5
  12. 4
  13. 6084
  14. 10
  15. 4
  16. 176 cm
  17. 36
  18. 7
  19. (11, 7)
  20. 9 times
  21. 25th
  22. 5
  23. 12
  24. 7
  25. 24
  26. 41
  27. (x + 8)(x + 9)
  28. 294
  29. 2211
  30. 135°
  31. 55°
  32. 7
  33. 5
  34. 8
  35. 2
  36. 80°
  37. 120°
  38. 6
  39. 8
  40. 45

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