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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 259 · 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 12 odd numbers (1 + 3 + 5 + …)? (a) 23 (b) 78 (c) 156 (d) 144
  2. 2.In a class of 27 children, 7 like maths, 19 like science and 3 like both. How many like neither? (a) 4 (b) 1 (c) 7 (d) 3
  3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  4. 4.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) 21 (c) 22 (d) 28
  5. 5.In a class of 35 children, 28 like mangoes, 15 like bananas and 9 like both. How many like neither? (a) 10 (b) 2 (c) 9 (d) 1
  6. 6.Two straight lines cross. Two vertically opposite angles add up to 110°. What is each of the other two angles? (a) 250° (b) 70° (c) 55° (d) 125°
  7. 7.In a class of 36 children, 29 like cricket, 15 like football and 9 like both. How many like at least one of the two? (a) 36 (b) 26 (c) 44 (d) 35
  8. 8.In a class of 41 children, 14 like tea, 27 like coffee and 9 like both. How many like at least one of the two? (a) 23 (b) 41 (c) 33 (d) 32
  9. 9.What is the sum of the roots of x² − 13x + 36 = 0? (a) 12 (b) 13 (c) 36 (d) 14
  10. 10.What is the smallest number of children in a group that makes sure at least three of them were born in the same day of the week? (a) 14 (b) 21 (c) 22 (d) 15
  11. 11.What is the circumference of a circle of radius 7 cm? (Use π = 22/7.) (a) 22 cm (b) 88 cm (c) 154 cm (d) 44 cm
  12. 12.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/11 (c) 1/9 (d) 1/12
  13. 13.Two angles of a triangle are 50° and 75°. What is the third angle? (a) 125° (b) 55° (c) 130° (d) 105°
  14. 14.In which quadrant does the point (−4, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  15. 15.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 36 (b) 49 (c) 48 (d) 37
  16. 16.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 615 (c) 488 (d) 625
  17. 17.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  18. 18.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 15 (c) 45 (d) 48
  19. 19.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 75° (b) 160° (c) 105° (d) 125°
  20. 20.A fair dice is rolled once. What is the probability of getting a prime number? (a) 1/6 (b) 1/2 (c) 2/3 (d) 1/3
  21. 21.Two angles of a triangle are 25° and 35°. What is the third angle? (a) 155° (b) 120° (c) 60° (d) 145°
  22. 22.What is the circumference of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 cm (b) 616 cm (c) 44 cm (d) 176 cm
  23. 23.What is the mode of 2, 12, 5, 5, 3, 5 and 3? (a) 12 (b) 3 (c) 5 (d) 2
  24. 24.If a + b = 12 and ab = 11, what is a² + b²? (a) 166 (b) 133 (c) 144 (d) 122
  25. 25.If every edge of a cube is made 4 times as long, how many times as big does its volume become? (a) 16 times (b) 4 times (c) 8 times (d) 64 times
  26. 26.In a class of 28 children, 8 like dance, 23 like music and 4 like both. How many like neither? (a) 5 (b) 4 (c) 1 (d) 2
  27. 27.A cuboid is 7 cm long, 4 cm wide and 9 cm high. What is its total surface area? (a) 252 sq cm (b) 254 sq cm (c) 127 sq cm (d) 508 sq cm
  28. 28.If a + b = 9 and ab = 18, what is a² + b²? (a) 45 (b) 117 (c) 63 (d) 81
  29. 29.If a + b = 19 and ab = 88, what is a² + b²? (a) 361 (b) 537 (c) 273 (d) 185
  30. 30.Which term of the AP 10, 16, 22, 28, … is 142? (a) 22nd (b) 23rd (c) 25th (d) 24th
  31. 31.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/4 (b) 1/8 (c) 3/8 (d) 7/8
  32. 32.In how many different ways can the letters of the word KITE be arranged? (a) 12 (b) 48 (c) 16 (d) 24
  33. 33.In a class of 46 children, 29 like maths, 16 like science and 9 like both. How many like neither? (a) 9 (b) 1 (c) 19 (d) 10
  34. 34.If a + b = 12 and ab = 35, what is a² + b²? (a) 144 (b) 214 (c) 109 (d) 74
  35. 35.What is the sum of the first 12 terms of the AP 1, 5, 9, …? (a) 300 (b) 45 (c) 276 (d) 552
  36. 36.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 260° (b) 100° (c) 80° (d) 160°
  37. 37.A canteen sells 3 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 12 (b) 18 (c) 9 (d) 6
  38. 38.7 T-shirts and 2 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 28 (b) 21 (c) 14 (d) 9
  39. 39.What is the sum of the first 12 terms of the AP 9, 15, 21, …? (a) 1008 (b) 504 (c) 75 (d) 540
  40. 40.What is the distance between the points (6, 2) and (18, 11)? (a) 16 (b) 21 (c) 15 (d) 225

Answer key

  1. 144
  2. 4
  3. 10
  4. 22
  5. 1
  6. 125°
  7. 35
  8. 32
  9. 13
  10. 15
  11. 44 cm
  12. 1/12
  13. 55°
  14. Second quadrant
  15. 37
  16. 624
  17. 5
  18. 45
  19. 75°
  20. 1/2
  21. 120°
  22. 88 cm
  23. 5
  24. 122
  25. 64 times
  26. 1
  27. 254 sq cm
  28. 45
  29. 185
  30. 23rd
  31. 7/8
  32. 24
  33. 10
  34. 74
  35. 276
  36. 100°
  37. 9
  38. 14
  39. 504
  40. 15

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