← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 819 · 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.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  4. 4.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 506 (b) 253 (c) 484 (d) 43
  5. 5.What is the mean of 17, 2, 6, 14 and 11? (a) 10 (b) 9 (c) 11 (d) 12
  6. 6.What is the mean of 7, 6, 15 and 12? (a) 9 (b) 8 (c) 11 (d) 10
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 3 (b) 13 (c) 14 (d) 15
  8. 8.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 8 (b) 7 (c) 15 (d) 14
  9. 9.Which is the correct factorisation of x² + 10x + 24? (a) (x − 4)(x − 6) (b) (x + 1)(x + 9) (c) (x + 1)(x + 24) (d) (x + 4)(x + 6)
  10. 10.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  11. 11.In which quadrant does the point (−8, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  12. 12.In a class of 35 children, 17 like mangoes, 18 like bananas and 6 like neither. How many like both? (a) 29 (b) 7 (c) 6 (d) 5
  13. 13.If a + b = 19 and ab = 88, what is (a − b)²? (a) 3 (b) 185 (c) 9 (d) 361
  14. 14.What is the missing term in the AP 2, 6, 10, ?, 18? (a) 18 (b) 14 (c) 13 (d) 15
  15. 15.What is the mean of 2, 3, 2 and 13? (a) 7 (b) 6 (c) 5 (d) 4
  16. 16.Using (a − b)² = a² − 2ab + b², what is 26²? (a) 884 (b) 676 (c) 686 (d) 1156
  17. 17.Three coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/4 (b) 1/8 (c) 3/4 (d) 3/8
  18. 18.In a class of 35 children, 20 like mangoes, 17 like bananas and 9 like both. How many like only mangoes? (a) 18 (b) 8 (c) 11 (d) 20
  19. 19.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 616 sq cm (d) 2464 sq cm
  20. 20.A drawer has lots of green, yellow, black, white 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) 2 (b) 10 (c) 6 (d) 5
  21. 21.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/3 (b) 5/6 (c) 1/5 (d) 1/6
  22. 22.What is the distance between the points (4, 8) and (7, 4)? (a) 25 (b) 6 (c) 7 (d) 5
  23. 23.Which is the correct factorisation of x² + 8x + 12? (a) (x + 2)(x + 6) (b) (x + 1)(x + 7) (c) (x + 1)(x + 12) (d) (x − 2)(x − 6)
  24. 24.What is the sum of the first 7 terms of the AP 6, 9, 12, …? (a) 105 (b) 210 (c) 108 (d) 24
  25. 25.In an isosceles triangle, the angle between the two equal sides is 40°. What is each of the other two angles? (a) 40° (b) 50° (c) 70° (d) 140°
  26. 26.What is the sum of the first 8 terms of the AP 10, 16, 22, …? (a) 248 (b) 52 (c) 496 (d) 272
  27. 27.A bag has 12 black balls and 11 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 13 (b) 2 (c) 14 (d) 23
  28. 28.What is the mode of 8, 13, 13, 20, 13, 19 and 20? (a) 13 (b) 20 (c) 19 (d) 8
  29. 29.Two straight lines cross. One of the angles is 140°. What is the angle next to it on the same straight line? (a) 41° (b) 140° (c) 40° (d) 220°
  30. 30.A team of 2 players is to be chosen from 10 players. How many different teams are possible? (a) 20 (b) 45 (c) 90 (d) 100
  31. 31.Which term of the AP 12, 21, 30, 39, … is 102? (a) 13th (b) 11th (c) 10th (d) 12th
  32. 32.Two coins are tossed together. What is the probability of getting at least one head? (a) 1/3 (b) 3/4 (c) 1/4 (d) 1/2
  33. 33.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 132 sq cm (d) 1386 sq cm
  34. 34.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  35. 35.Two angles of a triangle are 20° and 80°. What is the third angle? (a) 260° (b) 100° (c) 80° (d) 160°
  36. 36.A bag has 6 blue 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) 2 (b) 15 (c) 10 (d) 7
  37. 37.Which is the correct factorisation of x² + 14x + 48? (a) (x + 1)(x + 48) (b) (x − 6)(x − 8) (c) (x + 1)(x + 13) (d) (x + 6)(x + 8)
  38. 38.A bag has 5 blue balls and 6 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 6 (c) 11 (d) 2
  39. 39.What is the circumference of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 cm (b) 88 cm (c) 22 cm (d) 44 cm
  40. 40.How many factors does 97 have? (a) 1 (b) 2 (c) 3 (d) 4

Answer key

  1. 15
  2. 10
  3. 20
  4. 484
  5. 10
  6. 10
  7. 14
  8. 8
  9. (x + 4)(x + 6)
  10. 13
  11. Second quadrant
  12. 6
  13. 9
  14. 14
  15. 5
  16. 676
  17. 3/4
  18. 11
  19. 616 sq cm
  20. 6
  21. 1/6
  22. 5
  23. (x + 2)(x + 6)
  24. 105
  25. 70°
  26. 248
  27. 14
  28. 13
  29. 40°
  30. 45
  31. 11th
  32. 3/4
  33. 1386 sq cm
  34. 8
  35. 80°
  36. 10
  37. (x + 6)(x + 8)
  38. 7
  39. 44 cm
  40. 2

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