← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 699 · 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 a class of 35 children, 21 like mangoes, 24 like bananas and 11 like both. How many like at least one of the two? (a) 45 (b) 23 (c) 34 (d) 35
  2. 2.In how many different ways can the letters of the word STAR be arranged? (a) 16 (b) 48 (c) 24 (d) 12
  3. 3.What is the product of the roots of x² − 15x + 56 = 0? (a) 57 (b) 55 (c) 56 (d) 15
  4. 4.How many factors does 90 have? (a) 10 (b) 13 (c) 12 (d) 11
  5. 5.What is the smallest number of children in a group that makes sure at least three of them were born in the same month? (a) 36 (b) 25 (c) 37 (d) 24
  6. 6.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  7. 7.In a class of 35 children, 9 like maths, 22 like science and 6 like both. How many like at least one of the two? (a) 31 (b) 35 (c) 25 (d) 19
  8. 8.What is the smallest prime factor of 217? (a) 7 (b) 31 (c) 1 (d) 2
  9. 9.Using (a + b)² = a² + 2ab + b², what is 51²? (a) 2401 (b) 2501 (c) 2601 (d) 2611
  10. 10.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
  11. 11.What is the midpoint of the line joining (10, 7) and (22, 11)? (a) (16, 9) (b) (9, 16) (c) (6, 2) (d) (32, 18)
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  13. 13.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/8 (b) 1/4 (c) 3/5 (d) 5/8
  14. 14.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 308 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 88 sq cm
  15. 15.In a class of 46 children, 21 like dance, 24 like music and 6 like both. How many like only dance? (a) 18 (b) 22 (c) 15 (d) 21
  16. 16.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 5/36 (b) 4/11 (c) 1/9 (d) 1/11
  17. 17.What is the 28th term of the AP 8, 11, 14, 17, …? (a) 89 (b) 81 (c) 92 (d) 84
  18. 18.What is the sum of the first 5 terms of the AP 7, 13, 19, …? (a) 31 (b) 95 (c) 110 (d) 190
  19. 19.How many factors does 106 have? (a) 5 (b) 3 (c) 2 (d) 4
  20. 20.What is the median of 19, 5, 21, 32, 39, 34 and 36? (a) 34 (b) 21 (c) 32 (d) 33
  21. 21.Which term of the AP 18, 27, 36, 45, … is 270? (a) 30th (b) 29th (c) 31st (d) 28th
  22. 22.What are the roots of x² − 14x + 45 = 0? (a) 1 and 45 (b) 1 and 13 (c) 5 and 9 (d) 3 and 15
  23. 23.What is the sum of the first 11 terms of the AP 1, 3, 5, …? (a) 121 (b) 132 (c) 21 (d) 242
  24. 24.A drawer has lots of black, green, yellow, red and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 2 (c) 5 (d) 6
  25. 25.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 1/2 (c) 1/4 (d) 3/4
  26. 26.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 404 (c) 498 (d) 499
  27. 27.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
  28. 28.A bag has 7 yellow balls and 3 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 2 (b) 8 (c) 9 (d) 10
  29. 29.Two angles of a triangle are 20° and 120°. What is the third angle? (a) 160° (b) 140° (c) 60° (d) 40°
  30. 30.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 44 cm (b) 154 cm (c) 88 cm (d) 22 cm
  31. 31.Two angles of a triangle are 40° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 70° (c) 250° (d) 140°
  32. 32.What is the missing term in the AP 17, ?, 29, 35, 41? (a) 29 (b) 24 (c) 22 (d) 23
  33. 33.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 88 cm (b) 22 cm (c) 44 cm (d) 154 cm
  34. 34.Two angles of a triangle are 20° and 50°. What is the third angle? (a) 130° (b) 160° (c) 70° (d) 110°
  35. 35.What is the sum of the roots of x² − 16x + 63 = 0? (a) 15 (b) 16 (c) 17 (d) 63
  36. 36.In a class of 46 children, 25 like tea, 23 like coffee and 12 like both. How many like neither? (a) 12 (b) 22 (c) 10 (d) 11
  37. 37.How many factors does 20 have? (a) 4 (b) 5 (c) 7 (d) 6
  38. 38.What is the mean of 9, 5, 11, 2 and 8? (a) 8 (b) 6 (c) 7 (d) 9
  39. 39.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) 13 (b) 12 (c) 25 (d) 24
  40. 40.What is the distance between the points (7, 16) and (19, 0)? (a) 20 (b) 400 (c) 21 (d) 28

Answer key

  1. 34
  2. 24
  3. 56
  4. 12
  5. 25
  6. 9
  7. 25
  8. 7
  9. 2601
  10. 8
  11. (16, 9)
  12. 9
  13. 3/8
  14. 616 sq cm
  15. 15
  16. 1/9
  17. 89
  18. 95
  19. 4
  20. 32
  21. 29th
  22. 5 and 9
  23. 121
  24. 6
  25. 1/4
  26. 498
  27. 132 cm
  28. 9
  29. 40°
  30. 44 cm
  31. 110°
  32. 23
  33. 44 cm
  34. 110°
  35. 16
  36. 10
  37. 6
  38. 7
  39. 13
  40. 20

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