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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 222 · 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.Three coins are tossed together. What is the probability of getting a head on every coin? (a) 1/7 (b) 1/8 (c) 1/4 (d) 7/8
  2. 2.In how many different ways can the letters of the word LAMP be arranged? (a) 24 (b) 12 (c) 48 (d) 16
  3. 3.In a class of 22 children, 5 like cricket, 15 like football and 2 like both. How many like neither? (a) 6 (b) 5 (c) 2 (d) 4
  4. 4.Two coins are tossed together. What is the probability of getting at least one head and at least one tail? (a) 2/3 (b) 1/4 (c) 1/3 (d) 1/2
  5. 5.A bag has 5 red balls and 4 blue balls. Without looking, how many balls must you take out to be sure of getting 2 blue balls? (a) 6 (b) 7 (c) 9 (d) 2
  6. 6.Two angles of a triangle are 35° and 80°. What is the third angle? (a) 115° (b) 145° (c) 100° (d) 65°
  7. 7.Two straight lines cross. Two vertically opposite angles add up to 330°. What is each of the other two angles? (a) 15° (b) 16° (c) 165° (d) 30°
  8. 8.What is the sum of the first 10 terms of the AP 2, 3, 4, …? (a) 70 (b) 11 (c) 130 (d) 65
  9. 9.Two dice are rolled together. What is the probability that the two numbers add up to 5? (a) 1/11 (b) 5/36 (c) 4/11 (d) 1/9
  10. 10.A cube has edges of 12 cm. What is its total surface area? (a) 576 sq cm (b) 1728 sq cm (c) 864 sq cm (d) 144 sq cm
  11. 11.What is the missing term in the AP 6, 14, ?, 30, 38? (a) 30 (b) 23 (c) 22 (d) 21
  12. 12.What is the circumference of a circle of radius 14 cm? (Use π = 22/7.) (a) 176 cm (b) 44 cm (c) 616 cm (d) 88 cm
  13. 13.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 2464 cm (b) 88 cm (c) 352 cm (d) 176 cm
  14. 14.What is the distance between the points (8, 2) and (20, 11)? (a) 21 (b) 225 (c) 16 (d) 15
  15. 15.Two angles of a triangle are 55° and 35°. What is the third angle? (a) 145° (b) 270° (c) 125° (d) 90°
  16. 16.A bag has 10 red balls and 3 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 2 (b) 11 (c) 12 (d) 13
  17. 17.Which is the correct factorisation of x² + 13x + 40? (a) (x + 1)(x + 40) (b) (x + 1)(x + 12) (c) (x + 5)(x + 8) (d) (x − 5)(x − 8)
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 3 (b) 4 (c) 5 (d) 2
  19. 19.What is the smallest prime factor of 319? (a) 29 (b) 2 (c) 11 (d) 1
  20. 20.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) 325° (d) 145°
  21. 21.How many factors does 46 have? (a) 3 (b) 4 (c) 5 (d) 2
  22. 22.Which is the correct factorisation of x² + 17x + 72? (a) (x + 1)(x + 72) (b) (x + 1)(x + 16) (c) (x + 8)(x + 9) (d) (x − 8)(x − 9)
  23. 23.What is the distance between the points (6, 6) and (18, 11)? (a) 14 (b) 169 (c) 13 (d) 17
  24. 24.How many prime numbers are there between 70 and 80? (a) 2 (b) 3 (c) 4 (d) 5
  25. 25.In a class of 40 children, 19 like tea, 19 like coffee and 4 like both. How many like at least one of the two? (a) 34 (b) 40 (c) 30 (d) 38
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 5 (b) 6 (c) 3 (d) 4
  27. 27.A bag has 8 yellow 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) 12 (b) 9 (c) 5 (d) 2
  28. 28.If a + b = 8 and ab = 7, what is a² + b²? (a) 57 (b) 78 (c) 50 (d) 64
  29. 29.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 465 (b) 59 (c) 930 (d) 900
  30. 30.In how many different ways can the letters of the word CAT be arranged? (a) 3 (b) 6 (c) 12 (d) 9
  31. 31.A drawer has lots of white, green, blue, yellow and black socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 2 (b) 6 (c) 10 (d) 5
  32. 32.A drawer has lots of red, green, black 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) 4 (b) 8 (c) 2 (d) 5
  33. 33.Using (a + b)² = a² + 2ab + b², what is 93²? (a) 7569 (b) 8649 (c) 8659 (d) 8109
  34. 34.In a league, 6 teams each play every other team once. How many matches are played? (a) 21 (b) 36 (c) 15 (d) 30
  35. 35.What is the mode of 18, 16, 16, 6, 6, 16 and 19? (a) 18 (b) 16 (c) 19 (d) 6
  36. 36.A cuboid is 8 cm long, 5 cm wide and 5 cm high. What is its volume? (a) 210 cu cm (b) 18 cu cm (c) 40 cu cm (d) 200 cu cm
  37. 37.What is the 15th term of the AP 4, 7, 10, 13, …? (a) 49 (b) 42 (c) 45 (d) 46
  38. 38.Two angles of a triangle are 50° and 20°. What is the third angle? (a) 130° (b) 110° (c) 160° (d) 70°
  39. 39.In how many different ways can the letters of the word SUN be arranged? (a) 12 (b) 9 (c) 3 (d) 6
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 17 (d) 8

Answer key

  1. 1/8
  2. 24
  3. 4
  4. 1/2
  5. 7
  6. 65°
  7. 15°
  8. 65
  9. 1/9
  10. 864 sq cm
  11. 22
  12. 88 cm
  13. 176 cm
  14. 15
  15. 90°
  16. 12
  17. (x + 5)(x + 8)
  18. 4
  19. 11
  20. 145°
  21. 4
  22. (x + 8)(x + 9)
  23. 13
  24. 3
  25. 34
  26. 5
  27. 9
  28. 50
  29. 900
  30. 6
  31. 6
  32. 5
  33. 8649
  34. 15
  35. 16
  36. 200 cu cm
  37. 46
  38. 110°
  39. 6
  40. 18

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