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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 460 · 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 34, 21, 8, 35, 16, 37 and 2? (a) 16 (b) 21 (c) 34 (d) 35
  2. 2.Two angles of a triangle are 40° and 40°. What is the exterior angle at the third corner? (a) 140° (b) 100° (c) 280° (d) 80°
  3. 3.What is the sum of the first 11 terms of the AP 3, 4, 5, …? (a) 88 (b) 13 (c) 89 (d) 176
  4. 4.A bag has 2 yellow, 7 red and 2 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 4/11 (b) 4/7 (c) 7/11 (d) 1/3
  5. 5.Two angles of a triangle are 55° and 100°. What is the third angle? (a) 155° (b) 25° (c) 80° (d) 125°
  6. 6.A team of 2 players is to be chosen from 9 players. How many different teams are possible? (a) 18 (b) 72 (c) 81 (d) 36
  7. 7.What is the 21st term of the AP 15, 23, 31, 39, …? (a) 175 (b) 183 (c) 168 (d) 160
  8. 8.Two angles of a triangle are 60° and 85°. What is the exterior angle at the third corner? (a) 95° (b) 120° (c) 35° (d) 145°
  9. 9.What is the mean of 17, 18, 13 and 20? (a) 17 (b) 16 (c) 19 (d) 18
  10. 10.What is the sum of all the whole numbers from 1 to 91? (a) 4187 (b) 4095 (c) 8372 (d) 4186
  11. 11.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 207 (c) 198 (d) 210
  12. 12.What is the distance between the points (5, 23) and (17, 7)? (a) 400 (b) 28 (c) 21 (d) 20
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 130° (b) 100° (c) 50° (d) 51°
  14. 14.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 1/3 (b) 2/3 (c) 1/2 (d) 1/4
  15. 15.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 39 (c) 117 (d) 13
  16. 16.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/8 (c) 7/8 (d) 1/7
  17. 17.A fair dice is rolled once. What is the probability of getting an even number? (a) 2/3 (b) 1/6 (c) 1/2 (d) 1/3
  18. 18.A bag has 3 green balls and 4 black balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 5 (b) 2 (c) 7 (d) 4
  19. 19.What is the area of a circle of radius 14 cm? (Use π = 22/7.) (a) 88 sq cm (b) 2464 sq cm (c) 616 sq cm (d) 308 sq cm
  20. 20.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/2 (b) 1/4 (c) 2/3 (d) 1/3
  21. 21.Two angles of a triangle are 20° and 25°. What is the third angle? (a) 135° (b) 155° (c) 160° (d) 45°
  22. 22.In how many different ways can the letters of the word MATHS be arranged? (a) 25 (b) 240 (c) 20 (d) 120
  23. 23.What is the distance between the points (2, 6) and (8, 14)? (a) 100 (b) 11 (c) 10 (d) 14
  24. 24.What is the 36th term of the AP 9, 15, 21, 27, …? (a) 225 (b) 216 (c) 219 (d) 210
  25. 25.Using (a + b)² = a² + 2ab + b², what is 63²? (a) 3979 (b) 3249 (c) 3969 (d) 3609
  26. 26.Two straight lines cross. Two vertically opposite angles add up to 60°. What is each of the other two angles? (a) 150° (b) 30° (c) 120° (d) 300°
  27. 27.What is the mean of 17, 6, 15, 14, 7 and 13? (a) 13 (b) 14 (c) 12 (d) 11
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 18 (d) 17
  29. 29.What is the missing term in the AP 15, 24, ?, 42, 51? (a) 33 (b) 42 (c) 34 (d) 32
  30. 30.What is the area of a circle of diameter 28 cm? (Use π = 22/7.) (a) 88 sq cm (b) 308 sq cm (c) 2464 sq cm (d) 616 sq cm
  31. 31.What is the mode of 19, 19, 20, 20, 6, 19 and 13? (a) 13 (b) 20 (c) 19 (d) 6
  32. 32.In how many different ways can the letters of the word MANGO be arranged? (a) 120 (b) 25 (c) 240 (d) 20
  33. 33.In a class of 48 children, 25 like maths, 25 like science and 7 like both. How many like at least one of the two? (a) 36 (b) 43 (c) 50 (d) 48
  34. 34.In a class of 42 children, 29 like mangoes, 13 like bananas and 9 like both. How many like only mangoes? (a) 29 (b) 4 (c) 9 (d) 20
  35. 35.7 T-shirts and 3 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 10 (b) 28 (c) 21 (d) 42
  36. 36.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 176 cm (b) 352 cm (c) 88 cm (d) 2464 cm
  37. 37.Using (a − b)² = a² − 2ab + b², what is 19²? (a) 371 (b) 441 (c) 399 (d) 361
  38. 38.What is the median of 26, 11, 24, 39 and 8? (a) 11 (b) 24 (c) 25 (d) 26
  39. 39.Two angles of a triangle are 60° and 30°. What is the exterior angle at the third corner? (a) 270° (b) 150° (c) 120° (d) 90°
  40. 40.If a + b = 3 and ab = 2, what is a² + b²? (a) 9 (b) 7 (c) 13 (d) 5

Answer key

  1. 21
  2. 80°
  3. 88
  4. 4/11
  5. 25°
  6. 36
  7. 175
  8. 145°
  9. 17
  10. 4186
  11. 207
  12. 20
  13. 50°
  14. 1/2
  15. 39
  16. 1/8
  17. 1/2
  18. 5
  19. 616 sq cm
  20. 1/2
  21. 135°
  22. 120
  23. 10
  24. 219
  25. 3969
  26. 150°
  27. 12
  28. 17
  29. 33
  30. 616 sq cm
  31. 19
  32. 120
  33. 43
  34. 20
  35. 21
  36. 176 cm
  37. 361
  38. 24
  39. 90°
  40. 5

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