← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 967 · 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 prime factorisation of 60? (a) 2 × 3 × 5 (b) 2² × 3 × 5 (c) 2 × 3 × 5² (d) 2³ × 3 × 5
  2. 2.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 559 (c) 444 (d) 558
  3. 3.In a class of 29 children, 16 like dance, 15 like music and 3 like both. How many like only dance? (a) 16 (b) 13 (c) 12 (d) 14
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 50° (b) 51° (c) 100° (d) 130°
  5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9
  7. 7.What is the distance between the points (7, 16) and (16, 4)? (a) 15 (b) 225 (c) 21 (d) 16
  8. 8.If a + b = 19 and ab = 90, what is a² + b²? (a) 361 (b) 181 (c) 541 (d) 271
  9. 9.What is the median of 7, 24, 38, 37, 25, 32 and 10? (a) 24 (b) 32 (c) 37 (d) 25
  10. 10.What are the roots of x² − 14x + 48 = 0? (a) 6 and 8 (b) 2 and 24 (c) 1 and 13 (d) 1 and 48
  11. 11.What is the circumference of a circle of radius 35 cm? (Use π = 22/7.) (a) 220 cm (b) 3850 cm (c) 110 cm (d) 440 cm
  12. 12.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2 × 3 × 5 × 7 (c) 2³ × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
  13. 13.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 66 cm (b) 1386 cm (c) 132 cm (d) 264 cm
  14. 14.What is the 23rd term of the AP 3, 11, 19, 27, …? (a) 179 (b) 176 (c) 184 (d) 187
  15. 15.Two dice are rolled together. What is the probability that the two numbers add up to 8? (a) 5/36 (b) 1/11 (c) 5/11 (d) 1/6
  16. 16.What is the sum of all the whole numbers from 1 to 94? (a) 4371 (b) 8930 (c) 4465 (d) 4418
  17. 17.A captain and a vice-captain are to be chosen from 9 players. In how many ways can this be done? (a) 18 (b) 81 (c) 72 (d) 36
  18. 18.Two angles of a triangle are 25° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 60° (c) 120° (d) 155°
  19. 19.In a class of 17 children, 8 like dance, 9 like music and 2 like both. How many like only dance? (a) 7 (b) 8 (c) 2 (d) 6
  20. 20.What is the distance between the points (2, 9) and (5, 5)? (a) 25 (b) 7 (c) 5 (d) 6
  21. 21.What is the midpoint of the line joining (1, 10) and (11, 16)? (a) (12, 26) (b) (5, 3) (c) (6, 13) (d) (13, 6)
  22. 22.What are the roots of x² − 9x + 20 = 0? (a) 2 and 10 (b) 1 and 8 (c) 4 and 5 (d) 1 and 20
  23. 23.If the radius of a circle is made 5 times as long, how many times as big does its area become? (a) 125 times (b) 5 times (c) 10 times (d) 25 times
  24. 24.A bag has 6 black balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 7 (b) 8 (c) 15 (d) 2
  25. 25.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 63 (c) 20 (d) 180
  26. 26.What is the mode of 12, 20, 20, 6, 19, 20 and 19? (a) 19 (b) 12 (c) 20 (d) 6
  27. 27.Three coins are tossed together. What is the probability of getting at least one head? (a) 3/8 (b) 7/8 (c) 1/8 (d) 1/4
  28. 28.Two angles of a triangle are 30° and 110°. What is the exterior angle at the third corner? (a) 150° (b) 40° (c) 70° (d) 140°
  29. 29.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  30. 30.What is the mean of 15, 12, 16, 7, 12 and 10? (a) 11 (b) 14 (c) 12 (d) 13
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 14 (b) 15 (c) 13 (d) 3
  32. 32.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) 7 (b) 14 (c) 8 (d) 15
  33. 33.What is the circumference of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 cm (b) 132 cm (c) 264 cm (d) 66 cm
  34. 34.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 2 times (b) 5 times (c) 4 times (d) 8 times
  35. 35.What is the smallest prime factor of 77? (a) 2 (b) 11 (c) 1 (d) 7
  36. 36.Which term of the AP 11, 14, 17, 20, … is 47? (a) 12th (b) 15th (c) 14th (d) 13th
  37. 37.In a class of 40 children, 20 like cricket, 24 like football and 5 like neither. How many like both? (a) 9 (b) 5 (c) 35 (d) 4
  38. 38.What is the sum of the roots of x² − 15x + 56 = 0? (a) 16 (b) 56 (c) 15 (d) 14
  39. 39.What is the mode of 16, 18, 9, 18, 9, 18 and 7? (a) 9 (b) 7 (c) 16 (d) 18
  40. 40.Two angles of a triangle are 40° and 25°. What is the exterior angle at the third corner? (a) 140° (b) 115° (c) 65° (d) 155°

Answer key

  1. 2² × 3 × 5
  2. 558
  3. 13
  4. 50°
  5. 13
  6. 20
  7. 15
  8. 181
  9. 25
  10. 6 and 8
  11. 220 cm
  12. 2 × 3 × 5 × 7
  13. 132 cm
  14. 179
  15. 5/36
  16. 4465
  17. 72
  18. 60°
  19. 6
  20. 5
  21. (6, 13)
  22. 4 and 5
  23. 25 times
  24. 8
  25. 60
  26. 20
  27. 7/8
  28. 140°
  29. 15
  30. 12
  31. 14
  32. 8
  33. 132 cm
  34. 4 times
  35. 7
  36. 13th
  37. 9
  38. 15
  39. 18
  40. 65°

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