← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 895 · 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 missing term in the AP 18, 27, ?, 45, 54? (a) 37 (b) 35 (c) 45 (d) 36
  2. 2.A team of 2 players is to be chosen from 8 players. How many different teams are possible? (a) 16 (b) 64 (c) 28 (d) 56
  3. 3.11 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 110 (b) 55 (c) 121 (d) 66
  4. 4.How many factors does 41 have? (a) 4 (b) 1 (c) 2 (d) 3
  5. 5.What is the midpoint of the line joining (6, 7) and (12, 19)? (a) (18, 26) (b) (9, 13) (c) (13, 9) (d) (3, 6)
  6. 6.What is the distance between the points (9, 14) and (24, 6)? (a) 289 (b) 17 (c) 18 (d) 23
  7. 7.In a class of 32 children, 11 like mangoes, 19 like bananas and 4 like both. How many like at least one of the two? (a) 32 (b) 22 (c) 26 (d) 30
  8. 8.In a class of 26 children, 13 like tea, 17 like coffee and 5 like neither. How many like both? (a) 21 (b) 5 (c) 9 (d) 4
  9. 9.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 423 (c) 433 (d) 432
  10. 10.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 693 sq cm (b) 5544 sq cm (c) 1386 sq cm (d) 132 sq cm
  11. 11.How many factors does 74 have? (a) 3 (b) 4 (c) 2 (d) 5
  12. 12.5 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 60 (b) 35 (c) 11 (d) 30
  13. 13.What is the sum of the roots of x² − 7x + 12 = 0? (a) 12 (b) 6 (c) 7 (d) 8
  14. 14.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 55° (b) 125° (c) 56° (d) 110°
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 7 (b) 5 (c) 6 (d) 4
  16. 16.What is the smallest number of children in a group that makes sure at least four of them were born in the same day of the week? (a) 21 (b) 22 (c) 28 (d) 29
  17. 17.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  18. 18.Using (a − b)² = a² − 2ab + b², what is 88²? (a) 8464 (b) 7744 (c) 7754 (d) 8096
  19. 19.In which quadrant does the point (7, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.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
  21. 21.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 244 (c) 243 (d) 234
  22. 22.In a class of 26 children, 12 like tea, 8 like coffee and 4 like both. How many like only tea? (a) 18 (b) 4 (c) 8 (d) 12
  23. 23.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/3 (b) 1/4 (c) 1/2 (d) 3/4
  24. 24.In an isosceles triangle, the angle between the two equal sides is 60°. What is each of the other two angles? (a) 60° (b) 70° (c) 30° (d) 120°
  25. 25.What is the midpoint of the line joining (4, 9) and (12, 11)? (a) (8, 10) (b) (10, 8) (c) (4, 1) (d) (16, 20)
  26. 26.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 77 sq cm (c) 154 sq cm (d) 44 sq cm
  27. 27.What is the distance between the points (4, 4) and (16, 13)? (a) 21 (b) 15 (c) 16 (d) 225
  28. 28.What is the prime factorisation of 126? (a) 2³ × 3² × 7 (b) 2 × 3² × 7 (c) 2 × 3² × 7² (d) 2² × 3² × 7
  29. 29.Using (a + b)² = a² + 2ab + b², what is 53²? (a) 2509 (b) 2209 (c) 2809 (d) 2819
  30. 30.A drawer has lots of red and green 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
  31. 31.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  32. 32.What is the 21st term of the AP 14, 17, 20, 23, …? (a) 74 (b) 77 (c) 60 (d) 63
  33. 33.In a class of 36 children, 16 like dance, 28 like music and 10 like both. How many like at least one of the two? (a) 44 (b) 34 (c) 36 (d) 24
  34. 34.What is the sum of all the whole numbers from 1 to 23? (a) 552 (b) 277 (c) 276 (d) 253
  35. 35.In a class of 30 children, 18 like dance, 18 like music and 10 like both. How many like only dance? (a) 12 (b) 8 (c) 18 (d) 10
  36. 36.In a class of 38 children, 27 like cricket, 12 like football and 8 like both. How many like only cricket? (a) 26 (b) 19 (c) 27 (d) 4
  37. 37.A canteen sells 7 kinds of sandwich and 6 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 42 (b) 49 (c) 13 (d) 84
  38. 38.What is the circumference of a circle of radius 21 cm? (Use π = 22/7.) (a) 264 cm (b) 1386 cm (c) 132 cm (d) 66 cm
  39. 39.What is the missing term in the AP 16, ?, 22, 25, 28? (a) 19 (b) 22 (c) 18 (d) 20
  40. 40.Two straight lines cross. Two vertically opposite angles add up to 230°. What is each of the other two angles? (a) 65° (b) 130° (c) 115° (d) 66°

Answer key

  1. 36
  2. 28
  3. 55
  4. 2
  5. (9, 13)
  6. 17
  7. 26
  8. 9
  9. 432
  10. 1386 sq cm
  11. 4
  12. 30
  13. 7
  14. 55°
  15. 6
  16. 22
  17. 20
  18. 7744
  19. Fourth quadrant
  20. 1/18
  21. 243
  22. 8
  23. 1/4
  24. 60°
  25. (8, 10)
  26. 154 sq cm
  27. 15
  28. 2 × 3² × 7
  29. 2809
  30. 3
  31. 9
  32. 74
  33. 34
  34. 276
  35. 8
  36. 19
  37. 42
  38. 132 cm
  39. 19
  40. 65°

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