← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 93 · 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.If a + b = 14 and ab = 48, what is a² + b²? (a) 292 (b) 148 (c) 196 (d) 100
  2. 2.Two dice are rolled together. What is the probability that the two numbers add up to 3? (a) 2/11 (b) 1/18 (c) 1/11 (d) 1/12
  3. 3.Using (a + b)² = a² + 2ab + b², what is 105²? (a) 10025 (b) 11025 (c) 11035 (d) 9025
  4. 4.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  5. 5.What is the sum of the first 7 terms of the AP 3, 8, 13, …? (a) 33 (b) 252 (c) 131 (d) 126
  6. 6.What is the midpoint of the line joining (8, 8) and (12, 2)? (a) (2, 3) (b) (10, 5) (c) (20, 10) (d) (5, 10)
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  8. 8.What is the sum of the first 12 terms of the AP 2, 5, 8, …? (a) 222 (b) 444 (c) 240 (d) 35
  9. 9.What is the distance between the points (3, 11) and (15, 6)? (a) 14 (b) 17 (c) 169 (d) 13
  10. 10.A cuboid is 8 cm long, 4 cm wide and 6 cm high. What is its volume? (a) 192 cu cm (b) 32 cu cm (c) 208 cu cm (d) 18 cu cm
  11. 11.How many prime numbers are there between 20 and 30? (a) 3 (b) 4 (c) 2 (d) 1
  12. 12.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
  13. 13.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 189 (c) 63 (d) 66
  14. 14.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) 25 (b) 36 (c) 24 (d) 37
  15. 15.What is the midpoint of the line joining (1, 17) and (7, 9)? (a) (3, 4) (b) (13, 4) (c) (4, 13) (d) (8, 26)
  16. 16.In a class of 40 children, 21 like tea, 14 like coffee and 2 like both. How many like at least one of the two? (a) 33 (b) 40 (c) 35 (d) 31
  17. 17.What is the product of the roots of x² − 11x + 28 = 0? (a) 11 (b) 27 (c) 29 (d) 28
  18. 18.There are 6 roads from town A to town B and 5 roads from town B to town C. How many different routes go from A to C through B? (a) 60 (b) 30 (c) 36 (d) 11
  19. 19.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) 3 (c) 5 (d) 2
  20. 20.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) 22 (b) 14 (c) 15 (d) 21
  21. 21.What is the missing term in the AP 13, 15, 17, ?, 21? (a) 20 (b) 19 (c) 21 (d) 18
  22. 22.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 2 times (c) 5 times (d) 4 times
  23. 23.A bag has 7 green balls and 10 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 8 (b) 9 (c) 17 (d) 2
  24. 24.Two dice are rolled together. What is the probability that the two numbers add up to 12? (a) 1/12 (b) 1/11 (c) 1/18 (d) 1/36
  25. 25.What is the mean of 12, 15, 17 and 4? (a) 13 (b) 12 (c) 16 (d) 11
  26. 26.Using (a − b)² = a² − 2ab + b², what is 66²? (a) 5476 (b) 4356 (c) 4884 (d) 4366
  27. 27.What is the median of 7, 4, 36, 20, 6, 31 and 18? (a) 20 (b) 7 (c) 19 (d) 18
  28. 28.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 44 sq cm (b) 77 sq cm (c) 154 sq cm (d) 616 sq cm
  29. 29.What is the distance between the points (8, 16) and (16, 1)? (a) 23 (b) 17 (c) 18 (d) 289
  30. 30.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 80° (b) 140° (c) 100° (d) 120°
  31. 31.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  32. 32.A drawer has lots of green 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) 5 (b) 3 (c) 2 (d) 4
  33. 33.What is the median of 26, 39, 19, 1 and 18? (a) 26 (b) 19 (c) 18 (d) 20
  34. 34.What is the distance between the points (4, 5) and (16, 10)? (a) 14 (b) 17 (c) 169 (d) 13
  35. 35.How many prime numbers are there between 10 and 20? (a) 3 (b) 4 (c) 6 (d) 5
  36. 36.The mean of 6 numbers is 32. When the number 46 is added to them, what is the new mean? (a) 32 (b) 35 (c) 34 (d) 39
  37. 37.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4
  38. 38.Two angles of a triangle are 35° and 120°. What is the third angle? (a) 25° (b) 155° (c) 60° (d) 145°
  39. 39.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 66 cm (d) 264 cm
  40. 40.What is the sum of the first 11 terms of the AP 7, 13, 19, …? (a) 814 (b) 67 (c) 407 (d) 440

Answer key

  1. 100
  2. 1/18
  3. 11025
  4. 25
  5. 126
  6. (10, 5)
  7. 20
  8. 222
  9. 13
  10. 192 cu cm
  11. 2
  12. 1/2
  13. 63
  14. 25
  15. (4, 13)
  16. 33
  17. 28
  18. 30
  19. 3
  20. 15
  21. 19
  22. 4 times
  23. 9
  24. 1/36
  25. 12
  26. 4356
  27. 18
  28. 154 sq cm
  29. 17
  30. 100°
  31. 17
  32. 3
  33. 19
  34. 13
  35. 4
  36. 34
  37. 1/2
  38. 25°
  39. 132 cm
  40. 407

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