← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 349 · 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.Two coins are tossed together. What is the probability of getting exactly one head? (a) 2/3 (b) 1/4 (c) 1/2 (d) 1/3
  2. 2.What is the sum of the first 8 odd numbers (1 + 3 + 5 + …)? (a) 15 (b) 36 (c) 72 (d) 64
  3. 3.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 33 (b) 90 (c) 10 (d) 30
  4. 4.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 128 (b) 144 (c) 30 (d) 256
  5. 5.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 1386 sq cm (c) 132 sq cm (d) 693 sq cm
  6. 6.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 66 (b) 78 (c) 144 (d) 132
  7. 7.What is the median of 19, 29, 36, 2 and 31? (a) 31 (b) 19 (c) 36 (d) 29
  8. 8.A drawer has lots of red and yellow 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) 4 (c) 2 (d) 3
  9. 9.In how many different ways can the letters of the word FISH be arranged? (a) 48 (b) 16 (c) 12 (d) 24
  10. 10.There are 3 roads from town A to town B and 7 roads from town B to town C. How many different routes go from A to C through B? (a) 10 (b) 42 (c) 21 (d) 24
  11. 11.In a class of 23 children, 15 like dance, 16 like music and 9 like both. How many like only dance? (a) 7 (b) 9 (c) 6 (d) 15
  12. 12.What is the area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
  13. 13.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  14. 14.How many factors does 41 have? (a) 1 (b) 4 (c) 2 (d) 3
  15. 15.Using (a − b)² = a² − 2ab + b², what is 37²? (a) 1379 (b) 1369 (c) 1849 (d) 1591
  16. 16.In an isosceles triangle, the two equal angles are 45° each. What is the third angle? (a) 45° (b) 90° (c) 135° (d) 91°
  17. 17.How many factors does 48 have? (a) 10 (b) 9 (c) 8 (d) 11
  18. 18.14 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 182 (b) 196 (c) 91 (d) 105
  19. 19.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  20. 20.What is the missing term in the AP 10, ?, 18, 22, 26? (a) 14 (b) 15 (c) 13 (d) 18
  21. 21.If a + b = 11 and ab = 24, what is (a − b)²? (a) 121 (b) 25 (c) 73 (d) 5
  22. 22.What is the prime factorisation of 70? (a) 2 × 5 × 7 (b) 2³ × 5 × 7 (c) 2 × 5 × 7² (d) 2² × 5 × 7
  23. 23.Two straight lines cross. One of the angles is 150°. What is the angle next to it on the same straight line? (a) 31° (b) 210° (c) 30° (d) 150°
  24. 24.How many prime numbers are there between 70 and 80? (a) 5 (b) 2 (c) 3 (d) 4
  25. 25.What is the prime factorisation of 12? (a) 2³ × 3 (b) 2 × 3 (c) 2 × 3² (d) 2² × 3
  26. 26.What is the distance between the points (6, 12) and (30, 5)? (a) 625 (b) 26 (c) 31 (d) 25
  27. 27.What is the smallest prime factor of 145? (a) 29 (b) 1 (c) 2 (d) 5
  28. 28.A bag has 10 blue balls and 9 green balls. Without looking, how many balls must you take out to be sure of getting 2 green balls? (a) 2 (b) 19 (c) 11 (d) 12
  29. 29.What is the mean of 19, 2, 9 and 6? (a) 8 (b) 9 (c) 10 (d) 12
  30. 30.Two angles of a triangle are 40° and 60°. What is the exterior angle at the third corner? (a) 120° (b) 80° (c) 100° (d) 140°
  31. 31.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  32. 32.How many factors does 61 have? (a) 3 (b) 1 (c) 4 (d) 2
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 2 (b) 3 (c) 1 (d) 4
  34. 34.A captain and a vice-captain are to be chosen from 6 players. In how many ways can this be done? (a) 15 (b) 30 (c) 12 (d) 36
  35. 35.8 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 56 (c) 64 (d) 28
  36. 36.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  37. 37.Two angles of a triangle are 75° and 90°. What is the third angle? (a) 90° (b) 15° (c) 165° (d) 105°
  38. 38.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 8 times (b) 64 times (c) 16 times (d) 4 times
  39. 39.The mean of 3 numbers is 19. When the number 3 is added to them, what is the new mean? (a) 19 (b) 16 (c) 11 (d) 15
  40. 40.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 88 cm (b) 352 cm (c) 2464 cm (d) 176 cm

Answer key

  1. 1/2
  2. 64
  3. 30
  4. 128
  5. 1386 sq cm
  6. 66
  7. 29
  8. 3
  9. 24
  10. 21
  11. 6
  12. 154 sq cm
  13. 25
  14. 2
  15. 1369
  16. 90°
  17. 10
  18. 91
  19. First quadrant
  20. 14
  21. 25
  22. 2 × 5 × 7
  23. 30°
  24. 3
  25. 2² × 3
  26. 25
  27. 5
  28. 12
  29. 9
  30. 100°
  31. 7
  32. 2
  33. 3
  34. 30
  35. 28
  36. 25
  37. 15°
  38. 64 times
  39. 15
  40. 176 cm

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