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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 992 · 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 18th term of the AP 2, 10, 18, 26, …? (a) 136 (b) 144 (c) 138 (d) 146
  2. 2.In a class of 27 children, 16 like mangoes, 17 like bananas and 2 like neither. How many like both? (a) 6 (b) 8 (c) 2 (d) 25
  3. 3.In a class of 34 children, 26 like dance, 16 like music and 12 like both. How many like neither? (a) 5 (b) 12 (c) 4 (d) 16
  4. 4.Using (a + b)² = a² + 2ab + b², what is 85²? (a) 5625 (b) 7225 (c) 7235 (d) 6425
  5. 5.What is the 24th term of the AP 4, 12, 20, 28, …? (a) 184 (b) 192 (c) 196 (d) 188
  6. 6.If a + b = 16 and ab = 48, what is a² + b²? (a) 256 (b) 160 (c) 352 (d) 208
  7. 7.What is the midpoint of the line joining (0, 0) and (4, 10)? (a) (3, 5) (b) (4, 10) (c) (5, 2) (d) (2, 5)
  8. 8.What is the prime factorisation of 12? (a) 2 × 3 (b) 2² × 3 (c) 2³ × 3 (d) 2 × 3²
  9. 9.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 2/3 (c) 1/3 (d) 1/4
  10. 10.A cube has edges of 8 cm. What is its total surface area? (a) 512 sq cm (b) 384 sq cm (c) 256 sq cm (d) 64 sq cm
  11. 11.In a class of 38 children, 22 like dance, 17 like music and 3 like both. How many like neither? (a) 3 (b) 5 (c) 2 (d) 1
  12. 12.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 1232 sq cm (b) 9856 sq cm (c) 176 sq cm (d) 2464 sq cm
  13. 13.What is the area of a circle of diameter 56 cm? (Use π = 22/7.) (a) 176 sq cm (b) 2464 sq cm (c) 1232 sq cm (d) 9856 sq cm
  14. 14.In a class of 23 children, 11 like mangoes, 12 like bananas and 6 like both. How many like at least one of the two? (a) 18 (b) 11 (c) 17 (d) 23
  15. 15.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
  16. 16.What is the prime factorisation of 70? (a) 2³ × 5 × 7 (b) 2² × 5 × 7 (c) 2 × 5 × 7² (d) 2 × 5 × 7
  17. 17.If a + b = 11 and ab = 10, what is a² + b²? (a) 141 (b) 101 (c) 121 (d) 111
  18. 18.A bag has 8 green balls and 10 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 10 (b) 18 (c) 9 (d) 2
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  20. 20.In how many different ways can the letters of the word CHAIR be arranged? (a) 240 (b) 120 (c) 25 (d) 20
  21. 21.In a class of 13 children, 9 like mangoes, 5 like bananas and 1 like neither. How many like both? (a) 3 (b) 12 (c) 2 (d) 1
  22. 22.12 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 132 (b) 66 (c) 144 (d) 78
  23. 23.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) 29 (b) 28 (c) 21 (d) 22
  24. 24.5 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) 35 (b) 11 (c) 30 (d) 60
  25. 25.Two dice are rolled together. What is the probability that the two numbers add up to 10? (a) 1/12 (b) 1/9 (c) 3/11 (d) 1/11
  26. 26.Two angles of a triangle are 80° and 55°. What is the third angle? (a) 100° (b) 45° (c) 135° (d) 125°
  27. 27.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 240 (c) 25 (d) 20
  28. 28.In a class of 26 children, 9 like cricket, 18 like football and 5 like neither. How many like both? (a) 1 (b) 5 (c) 21 (d) 6
  29. 29.Using (a − b)² = a² − 2ab + b², what is 79²? (a) 6561 (b) 6399 (c) 6251 (d) 6241
  30. 30.In a class of 47 children, 20 like cricket, 24 like football and 5 like both. How many like neither? (a) 5 (b) 13 (c) 8 (d) 3
  31. 31.A team of 2 players is to be chosen from 11 players. How many different teams are possible? (a) 110 (b) 22 (c) 121 (d) 55
  32. 32.What is the midpoint of the line joining (0, 9) and (10, 21)? (a) (5, 6) (b) (5, 15) (c) (10, 30) (d) (15, 5)
  33. 33.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 213 (c) 222 (d) 223
  34. 34.In a class of 28 children, 22 like cricket, 11 like football and 6 like both. How many like neither? (a) 6 (b) 7 (c) 1 (d) 2
  35. 35.Three coins are tossed together. What is the probability of getting exactly one head? (a) 1/4 (b) 3/5 (c) 5/8 (d) 3/8
  36. 36.6 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 30 (b) 60 (c) 36 (d) 11
  37. 37.In which quadrant does the point (−2, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.What is the 22nd term of the AP 4, 8, 12, 16, …? (a) 84 (b) 89 (c) 88 (d) 92
  39. 39.Two angles of a triangle are 70° and 25°. What is the exterior angle at the third corner? (a) 95° (b) 155° (c) 85° (d) 110°
  40. 40.What is the smallest prime factor of 341? (a) 31 (b) 1 (c) 11 (d) 2

Answer key

  1. 138
  2. 8
  3. 4
  4. 7225
  5. 188
  6. 160
  7. (2, 5)
  8. 2² × 3
  9. 1/2
  10. 384 sq cm
  11. 2
  12. 2464 sq cm
  13. 2464 sq cm
  14. 17
  15. 154 sq cm
  16. 2 × 5 × 7
  17. 101
  18. 10
  19. 2
  20. 120
  21. 2
  22. 66
  23. 22
  24. 30
  25. 1/12
  26. 45°
  27. 120
  28. 6
  29. 6241
  30. 8
  31. 55
  32. (5, 15)
  33. 222
  34. 1
  35. 3/8
  36. 30
  37. Second quadrant
  38. 88
  39. 95°
  40. 11

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