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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 309 · 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.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  2. 2.What is the sum of the first 12 terms of the AP 10, 11, 12, …? (a) 192 (b) 186 (c) 372 (d) 21
  3. 3.A bag has 2 green, 4 red and 4 yellow balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/5 (b) 4/5 (c) 1/4 (d) 1/3
  4. 4.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 265° (b) 86° (c) 85° (d) 95°
  5. 5.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 23 (c) 207 (d) 72
  6. 6.Two dice are rolled together. What is the probability that the two numbers add up to 2? (a) 1/12 (b) 1/36 (c) 1/18 (d) 1/11
  7. 7.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 44 sq cm (c) 616 sq cm (d) 77 sq cm
  8. 8.What is the smallest prime factor of 145? (a) 2 (b) 29 (c) 1 (d) 5
  9. 9.A drawer has lots of yellow, white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 3 (b) 2 (c) 4 (d) 6
  10. 10.What is the smallest prime factor of 91? (a) 13 (b) 2 (c) 1 (d) 7
  11. 11.What is the smallest prime factor of 65? (a) 1 (b) 2 (c) 13 (d) 5
  12. 12.What is the midpoint of the line joining (9, 15) and (15, 5)? (a) (24, 20) (b) (3, 5) (c) (12, 10) (d) (10, 12)
  13. 13.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
  14. 14.In a league, 14 teams each play every other team once. How many matches are played? (a) 91 (b) 105 (c) 182 (d) 196
  15. 15.In which quadrant does the point (1, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.In a class of 31 children, 14 like cricket, 22 like football and 7 like both. How many like only cricket? (a) 7 (b) 15 (c) 9 (d) 14
  17. 17.What is the 31st term of the AP 17, 26, 35, 44, …? (a) 270 (b) 296 (c) 287 (d) 279
  18. 18.In a class of 37 children, 24 like tea, 15 like coffee and 11 like both. How many like only tea? (a) 24 (b) 13 (c) 4 (d) 22
  19. 19.In a league, 7 teams each play every other team once. How many matches are played? (a) 42 (b) 28 (c) 21 (d) 49
  20. 20.How many factors does 28 have? (a) 4 (b) 7 (c) 5 (d) 6
  21. 21.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
  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 area of a circle of radius 7 cm? (Use π = 22/7.) (a) 616 sq cm (b) 154 sq cm (c) 77 sq cm (d) 44 sq cm
  24. 24.What is the mean of 19, 7, 18, 9 and 12? (a) 12 (b) 13 (c) 14 (d) 15
  25. 25.What is the sum of the roots of x² − 8x + 15 = 0? (a) 9 (b) 8 (c) 7 (d) 15
  26. 26.In a class of 40 children, 22 like tea, 20 like coffee and 2 like neither. How many like both? (a) 5 (b) 4 (c) 2 (d) 38
  27. 27.Two straight lines cross. One of the angles is 35°. What is the angle next to it on the same straight line? (a) 35° (b) 55° (c) 145° (d) 325°
  28. 28.If a + b = 14 and ab = 24, what is a² + b²? (a) 148 (b) 196 (c) 244 (d) 172
  29. 29.A bag has 6 red, 6 blue and 8 white balls. One ball is taken out without looking. What is the probability that it is not red? (a) 3/4 (b) 1/3 (c) 3/10 (d) 7/10
  30. 30.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 sq cm (b) 9856 sq cm (c) 1232 sq cm (d) 176 sq cm
  31. 31.Two straight lines cross. Two vertically opposite angles add up to 260°. What is each of the other two angles? (a) 50° (b) 100° (c) 130° (d) 51°
  32. 32.Two coins are tossed together. What is the probability of getting exactly one head? (a) 1/3 (b) 1/2 (c) 1/4 (d) 2/3
  33. 33.Which term of the AP 20, 25, 30, 35, … is 200? (a) 38th (b) 40th (c) 37th (d) 36th
  34. 34.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 32 (c) 31 (d) 22
  35. 35.What is the prime factorisation of 240? (a) 2⁴ × 3 × 5 (b) 2⁵ × 3 × 5 (c) 2 × 3 × 5⁴ (d) 2³ × 3 × 5
  36. 36.A bag has 8 red balls and 9 white balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 17 (b) 2 (c) 10 (d) 9
  37. 37.What is the sum of the first 12 odd numbers (1 + 3 + 5 + …)? (a) 156 (b) 78 (c) 23 (d) 144
  38. 38.What is the mean of 18, 18, 6 and 18? (a) 16 (b) 20 (c) 12 (d) 15
  39. 39.What is the smallest prime factor of 169? (a) 2 (b) 3 (c) 1 (d) 13
  40. 40.In a league, 10 teams each play every other team once. How many matches are played? (a) 100 (b) 90 (c) 55 (d) 45

Answer key

  1. 13
  2. 186
  3. 1/5
  4. 85°
  5. 69
  6. 1/36
  7. 154 sq cm
  8. 5
  9. 4
  10. 7
  11. 5
  12. (12, 10)
  13. 1/9
  14. 91
  15. Fourth quadrant
  16. 7
  17. 287
  18. 13
  19. 21
  20. 6
  21. 7/8
  22. 66
  23. 154 sq cm
  24. 13
  25. 8
  26. 4
  27. 145°
  28. 148
  29. 7/10
  30. 2464 sq cm
  31. 50°
  32. 1/2
  33. 37th
  34. 31
  35. 2⁴ × 3 × 5
  36. 10
  37. 144
  38. 15
  39. 13
  40. 45

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