← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 168 · 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 smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 22 (c) 21 (d) 15
  2. 2.In a class of 24 children, 10 like mangoes, 10 like bananas and 10 like neither. How many like both? (a) 7 (b) 10 (c) 14 (d) 6
  3. 3.What is the distance between the points (6, 0) and (11, 12)? (a) 14 (b) 169 (c) 13 (d) 17
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  5. 5.In a class of 37 children, 20 like mangoes, 15 like bananas and 4 like both. How many like only mangoes? (a) 16 (b) 11 (c) 22 (d) 20
  6. 6.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 176 cm (d) 352 cm
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  8. 8.A bag has 8 blue balls and 4 green 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) 12 (c) 5 (d) 9
  9. 9.Which term of the AP 8, 14, 20, 26, … is 92? (a) 14th (b) 15th (c) 17th (d) 16th
  10. 10.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 176 sq cm (c) 1232 sq cm (d) 2464 sq cm
  11. 11.Which term of the AP 9, 11, 13, 15, … is 71? (a) 33rd (b) 31st (c) 32nd (d) 34th
  12. 12.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 2464 sq cm (d) 308 sq cm
  13. 13.How many prime numbers are there between 10 and 40? (a) 7 (b) 9 (c) 10 (d) 8
  14. 14.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 8 times (c) 4 times (d) 64 times
  15. 15.How many prime numbers are there between 90 and 110? (a) 5 (b) 4 (c) 7 (d) 6
  16. 16.Using (a + b)² = a² + 2ab + b², what is 101²? (a) 10001 (b) 10211 (c) 9801 (d) 10201
  17. 17.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 60 (c) 50 (d) 59
  18. 18.Two angles of a triangle are 20° and 85°. What is the third angle? (a) 160° (b) 95° (c) 105° (d) 75°
  19. 19.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 9 (c) 12 (d) 6
  20. 20.What is the missing term in the AP 12, ?, 30, 39, 48? (a) 22 (b) 30 (c) 21 (d) 20
  21. 21.If every edge of a cube is made 5 times as long, how many times as big does its volume become? (a) 10 times (b) 25 times (c) 125 times (d) 5 times
  22. 22.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 3/11 (c) 1/9 (d) 1/11
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 4 (b) 6 (c) 3 (d) 5
  24. 24.What is the missing term in the AP 9, 12, 15, ?, 21? (a) 19 (b) 18 (c) 17 (d) 21
  25. 25.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  26. 26.In which quadrant does the point (1, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 45 (b) 90 (c) 20 (d) 100
  28. 28.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/4
  29. 29.What is the sum of the first 10 terms of the AP 2, 4, 6, …? (a) 110 (b) 220 (c) 120 (d) 20
  30. 30.Using (a − b)² = a² − 2ab + b², what is 15²? (a) 225 (b) 235 (c) 375 (d) 625
  31. 31.What is the smallest prime factor of 143? (a) 11 (b) 2 (c) 1 (d) 13
  32. 32.What is the mode of 12, 13, 12, 14, 12, 13 and 5? (a) 14 (b) 5 (c) 12 (d) 13
  33. 33.Which is the correct factorisation of x² + 12x + 35? (a) (x + 5)(x + 7) (b) (x − 5)(x − 7) (c) (x + 1)(x + 11) (d) (x + 1)(x + 35)
  34. 34.What is the smallest prime factor of 87? (a) 1 (b) 29 (c) 2 (d) 3
  35. 35.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/11 (c) 1/18 (d) 1/36
  36. 36.The mean of 3 numbers is 17. When the number 29 is added to them, what is the new mean? (a) 17 (b) 23 (c) 20 (d) 21
  37. 37.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 42 (c) 126 (d) 45
  38. 38.What is the 13th term of the AP 15, 24, 33, 42, …? (a) 123 (b) 108 (c) 117 (d) 132
  39. 39.A bag has 7 green, 2 blue and 3 red balls. One ball is taken out without looking. What is the probability that it is not green? (a) 5/12 (b) 5/7 (c) 7/12 (d) 1/3
  40. 40.Using (a + b)² = a² + 2ab + b², what is 22²? (a) 404 (b) 324 (c) 484 (d) 494

Answer key

  1. 15
  2. 6
  3. 13
  4. 6
  5. 16
  6. 176 cm
  7. 5
  8. 9
  9. 15th
  10. 2464 sq cm
  11. 32nd
  12. 616 sq cm
  13. 8
  14. 64 times
  15. 5
  16. 10201
  17. 59
  18. 75°
  19. 6
  20. 21
  21. 125 times
  22. 1/12
  23. 5
  24. 18
  25. 20
  26. First quadrant
  27. 45
  28. 1/2
  29. 110
  30. 225
  31. 11
  32. 12
  33. (x + 5)(x + 7)
  34. 3
  35. 1/36
  36. 20
  37. 42
  38. 123
  39. 5/12
  40. 484

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