← Maths Olympiad mock test 2 lesson New set →

Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 730 · 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 sum of the first 10 terms of the AP 8, 13, 18, …? (a) 330 (b) 610 (c) 53 (d) 305
  2. 2.Two straight lines cross. Two vertically opposite angles add up to 90°. What is each of the other two angles? (a) 270° (b) 45° (c) 135° (d) 90°
  3. 3.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 80° (b) 25° (c) 155° (d) 125°
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  5. 5.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) 28 (c) 22 (d) 29
  6. 6.A bag has 6 red, 3 white and 6 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 2/3 (b) 2/5 (c) 3/5 (d) 1/3
  7. 7.In a class of 39 children, 21 like tea, 17 like coffee and 7 like both. How many like neither? (a) 1 (b) 15 (c) 8 (d) 7
  8. 8.In a class of 49 children, 20 like mangoes, 28 like bananas and 9 like both. How many like at least one of the two? (a) 30 (b) 39 (c) 48 (d) 49
  9. 9.How many factors does 48 have? (a) 11 (b) 10 (c) 8 (d) 9
  10. 10.What is the mean of 3, 16, 9, 8, 13 and 11? (a) 9 (b) 10 (c) 12 (d) 11
  11. 11.In a class of 30 children, 11 like cricket, 26 like football and 1 like neither. How many like both? (a) 8 (b) 29 (c) 1 (d) 7
  12. 12.In a class of 33 children, 21 like maths, 16 like science and 6 like both. How many like at least one of the two? (a) 37 (b) 33 (c) 25 (d) 31
  13. 13.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 27 times (b) 3 times (c) 6 times (d) 9 times
  14. 14.What is the smallest prime factor of 57? (a) 2 (b) 1 (c) 3 (d) 19
  15. 15.Two angles of a triangle are 70° and 50°. What is the third angle? (a) 60° (b) 110° (c) 130° (d) 120°
  16. 16.Two straight lines cross. Two vertically opposite angles add up to 250°. What is each of the other two angles? (a) 110° (b) 125° (c) 55° (d) 56°
  17. 17.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/18 (c) 1/36 (d) 1/11
  18. 18.What is the mean of 11, 13, 12 and 16? (a) 13 (b) 14 (c) 15 (d) 12
  19. 19.Three coins are tossed together. What is the probability of getting exactly one head? (a) 3/5 (b) 1/4 (c) 3/8 (d) 5/8
  20. 20.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 132 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 1386 sq cm
  21. 21.Two angles of a triangle are 40° and 20°. What is the third angle? (a) 60° (b) 120° (c) 160° (d) 140°
  22. 22.In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? (a) 40° (b) 50° (c) 65° (d) 130°
  23. 23.What is the midpoint of the line joining (7, 5) and (17, 11)? (a) (24, 16) (b) (8, 12) (c) (12, 8) (d) (5, 3)
  24. 24.What is the prime factorisation of 84? (a) 2² × 3 × 7 (b) 2³ × 3 × 7 (c) 2 × 3 × 7² (d) 2 × 3 × 7
  25. 25.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 30° (b) 150° (c) 25° (d) 15°
  26. 26.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 90 (b) 20 (c) 100 (d) 45
  27. 27.In a class of 33 children, 19 like maths, 17 like science and 1 like neither. How many like both? (a) 4 (b) 32 (c) 3 (d) 1
  28. 28.If a + b = 19 and ab = 88, what is a² + b²? (a) 273 (b) 537 (c) 361 (d) 185
  29. 29.Two angles of a triangle are 65° and 75°. What is the third angle? (a) 115° (b) 140° (c) 105° (d) 40°
  30. 30.A fair dice is rolled once. What is the probability of getting an odd number? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/6
  31. 31.What is the prime factorisation of 504? (a) 2⁴ × 3² × 7 (b) 2³ × 3² × 7 (c) 2 × 3² × 7³ (d) 2² × 3² × 7
  32. 32.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/3 (d) 1/2
  33. 33.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) 15 (c) 8 (d) 14
  34. 34.In a class of 35 children, 9 like maths, 21 like science and 9 like neither. How many like both? (a) 5 (b) 9 (c) 26 (d) 4
  35. 35.If a + b = 6 and ab = 8, what is (a − b)²? (a) 4 (b) 36 (c) 20 (d) 2
  36. 36.What is the prime factorisation of 12? (a) 2 × 3 (b) 2³ × 3 (c) 2² × 3 (d) 2 × 3²
  37. 37.9 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 81 (c) 45 (d) 72
  38. 38.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 55 (b) 121 (c) 22 (d) 110
  39. 39.In how many different ways can the letters of the word CHAIR be arranged? (a) 120 (b) 240 (c) 20 (d) 25
  40. 40.In a class of 32 children, 11 like tea, 22 like coffee and 4 like both. How many like only tea? (a) 11 (b) 18 (c) 10 (d) 7

Answer key

  1. 305
  2. 135°
  3. 25°
  4. 2
  5. 22
  6. 2/5
  7. 8
  8. 39
  9. 10
  10. 10
  11. 8
  12. 31
  13. 9 times
  14. 3
  15. 60°
  16. 55°
  17. 1/36
  18. 13
  19. 3/8
  20. 1386 sq cm
  21. 120°
  22. 65°
  23. (12, 8)
  24. 2² × 3 × 7
  25. 15°
  26. 90
  27. 4
  28. 185
  29. 40°
  30. 1/2
  31. 2³ × 3² × 7
  32. 1/2
  33. 8
  34. 4
  35. 4
  36. 2² × 3
  37. 36
  38. 55
  39. 120
  40. 7

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