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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 299 · 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 median of 31, 34, 14, 10 and 16? (a) 31 (b) 21 (c) 14 (d) 16
  2. 2.What is the mode of 5, 16, 9, 16, 5, 5 and 8? (a) 9 (b) 5 (c) 16 (d) 8
  3. 3.15 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 225 (b) 210 (c) 120 (d) 105
  4. 4.Two straight lines cross. One of the angles is 155°. What is the angle next to it on the same straight line? (a) 25° (b) 155° (c) 26° (d) 205°
  5. 5.A drawer has lots of red, black, yellow and white socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 4 (b) 8 (c) 5 (d) 2
  6. 6.6 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 36 (b) 21 (c) 30 (d) 15
  7. 7.A cuboid is 3 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 42 sq cm (b) 82 sq cm (c) 164 sq cm (d) 41 sq cm
  8. 8.Two angles of a triangle are 55° and 55°. What is the third angle? (a) 125° (b) 110° (c) 250° (d) 70°
  9. 9.In how many different ways can the letters of the word MANGO be arranged? (a) 20 (b) 25 (c) 240 (d) 120
  10. 10.What is the mean of 19, 6, 13 and 10? (a) 16 (b) 11 (c) 13 (d) 12
  11. 11.How many prime numbers are there between 50 and 80? (a) 6 (b) 8 (c) 9 (d) 7
  12. 12.What is the area of a circle of diameter 42 cm? (Use π = 22/7.) (a) 1386 sq cm (b) 693 sq cm (c) 5544 sq cm (d) 132 sq cm
  13. 13.What is the sum of the first 9 terms of the AP 8, 14, 20, …? (a) 288 (b) 56 (c) 315 (d) 576
  14. 14.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 130° (b) 65° (c) 245° (d) 115°
  15. 15.What is the missing term in the AP 11, 16, ?, 26, 31? (a) 21 (b) 26 (c) 22 (d) 20
  16. 16.A bag has 12 blue balls and 9 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 14 (c) 21 (d) 13
  17. 17.The mean of 5 numbers is 30. When the number 54 is added to them, what is the new mean? (a) 30 (b) 34 (c) 35 (d) 42
  18. 18.In a class of 20 children, 12 like tea, 9 like coffee and 4 like neither. How many like both? (a) 1 (b) 4 (c) 5 (d) 16
  19. 19.How many prime numbers are there between 70 and 100? (a) 7 (b) 6 (c) 5 (d) 8
  20. 20.What is the sum of the first 11 terms of the AP 1, 6, 11, …? (a) 51 (b) 286 (c) 572 (d) 291
  21. 21.If a + b = 4 and ab = 3, what is (a − b)²? (a) 4 (b) 2 (c) 16 (d) 10
  22. 22.A cube has edges of 6 cm. What is its volume? (a) 217 cu cm (b) 18 cu cm (c) 216 cu cm (d) 144 cu cm
  23. 23.If every edge of a cube is made 3 times as long, how many times as big does its surface area become? (a) 3 times (b) 27 times (c) 9 times (d) 6 times
  24. 24.How many prime numbers are there between 50 and 60? (a) 1 (b) 3 (c) 2 (d) 4
  25. 25.Using (a + b)² = a² + 2ab + b², what is 71²? (a) 5051 (b) 5041 (c) 4901 (d) 4761
  26. 26.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 79 (c) 88 (d) 70
  27. 27.A cuboid is 5 cm long, 2 cm wide and 7 cm high. What is its total surface area? (a) 236 sq cm (b) 59 sq cm (c) 118 sq cm (d) 70 sq cm
  28. 28.How many factors does 74 have? (a) 3 (b) 4 (c) 5 (d) 2
  29. 29.If a + b = 12 and ab = 27, what is a² + b²? (a) 198 (b) 90 (c) 117 (d) 144
  30. 30.If a + b = 13 and ab = 22, what is a² + b²? (a) 213 (b) 147 (c) 169 (d) 125
  31. 31.Which is the correct factorisation of x² + 11x + 24? (a) (x − 3)(x − 8) (b) (x + 1)(x + 10) (c) (x + 3)(x + 8) (d) (x + 1)(x + 24)
  32. 32.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 616 sq cm (c) 308 sq cm (d) 2464 sq cm
  33. 33.In a class of 30 children, 10 like cricket, 16 like football and 3 like both. How many like only cricket? (a) 14 (b) 7 (c) 10 (d) 13
  34. 34.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  35. 35.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 295 (b) 285 (c) 294 (d) 268
  36. 36.The mean of 3 numbers is 10. When the number 18 is added to them, what is the new mean? (a) 12 (b) 13 (c) 14 (d) 10
  37. 37.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 81 (b) 18 (c) 36 (d) 72
  38. 38.In a class of 29 children, 17 like cricket, 15 like football and 4 like neither. How many like both? (a) 7 (b) 25 (c) 3 (d) 4
  39. 39.A captain and a vice-captain are to be chosen from 8 players. In how many ways can this be done? (a) 28 (b) 16 (c) 64 (d) 56
  40. 40.Which term of the AP 10, 18, 26, 34, … is 122? (a) 15th (b) 17th (c) 16th (d) 14th

Answer key

  1. 16
  2. 5
  3. 105
  4. 25°
  5. 5
  6. 15
  7. 82 sq cm
  8. 70°
  9. 120
  10. 12
  11. 7
  12. 1386 sq cm
  13. 288
  14. 65°
  15. 21
  16. 14
  17. 34
  18. 5
  19. 6
  20. 286
  21. 4
  22. 216 cu cm
  23. 9 times
  24. 2
  25. 5041
  26. 79
  27. 118 sq cm
  28. 4
  29. 90
  30. 125
  31. (x + 3)(x + 8)
  32. 616 sq cm
  33. 7
  34. 10
  35. 294
  36. 12
  37. 36
  38. 7
  39. 56
  40. 15th

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