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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 420 · 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.Two dice are rolled together. What is the probability that the two numbers add up to 4? (a) 3/11 (b) 1/12 (c) 1/9 (d) 1/11
  2. 2.What is the median of 26, 37, 28, 20, 3, 5 and 39? (a) 28 (b) 27 (c) 26 (d) 20
  3. 3.What is the smallest prime factor of 55? (a) 2 (b) 5 (c) 11 (d) 1
  4. 4.What is the sum of the first 10 terms of the AP 7, 13, 19, …? (a) 370 (b) 61 (c) 340 (d) 680
  5. 5.A bag has 5 red balls and 6 blue balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 11 (c) 2 (d) 6
  6. 6.In a class of 36 children, 12 like maths, 26 like science and 9 like both. How many like at least one of the two? (a) 38 (b) 36 (c) 29 (d) 20
  7. 7.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2² × 5 × 7 (c) 2³ × 5 × 7 (d) 2 × 5 × 7
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 20 (d) 19
  9. 9.Two angles of a triangle are 50° and 80°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 230° (d) 100°
  10. 10.What is the mean of 14, 9, 6 and 3? (a) 9 (b) 8 (c) 7 (d) 10
  11. 11.In a class of 31 children, 23 like tea, 10 like coffee and 3 like neither. How many like both? (a) 3 (b) 5 (c) 2 (d) 28
  12. 12.How many factors does 69 have? (a) 5 (b) 2 (c) 4 (d) 3
  13. 13.Three coins are tossed together. What is the probability of getting at least one head? (a) 1/8 (b) 7/8 (c) 3/8 (d) 1/4
  14. 14.A canteen sells 6 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 9 (b) 24 (c) 18 (d) 36
  15. 15.What is the distance between the points (9, 12) and (15, 4)? (a) 100 (b) 14 (c) 10 (d) 11
  16. 16.Using (a + b)² = a² + 2ab + b², what is 34²? (a) 1166 (b) 1156 (c) 916 (d) 676
  17. 17.What is the 33rd term of the AP 6, 15, 24, 33, …? (a) 288 (b) 297 (c) 294 (d) 303
  18. 18.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 616 sq cm (b) 44 sq cm (c) 77 sq cm (d) 154 sq cm
  19. 19.In a class of 35 children, 15 like mangoes, 18 like bananas and 7 like both. How many like at least one of the two? (a) 35 (b) 19 (c) 26 (d) 33
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 5 (c) 10 (d) 3
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  22. 22.A bag has 9 red, 5 white and 2 green balls. One ball is taken out without looking. What is the probability that it is red? (a) 1/3 (b) 5/8 (c) 9/16 (d) 7/16
  23. 23.What is the circumference of a circle of radius 28 cm? (Use π = 22/7.) (a) 352 cm (b) 176 cm (c) 2464 cm (d) 88 cm
  24. 24.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
  25. 25.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  26. 26.How many prime numbers are there between 40 and 60? (a) 4 (b) 5 (c) 6 (d) 7
  27. 27.What is the sum of all the whole numbers from 1 to 14? (a) 91 (b) 105 (c) 98 (d) 210
  28. 28.Which is the correct factorisation of x² + 11x + 30? (a) (x + 1)(x + 10) (b) (x − 5)(x − 6) (c) (x + 1)(x + 30) (d) (x + 5)(x + 6)
  29. 29.What are the roots of x² − 14x + 48 = 0? (a) 1 and 13 (b) 1 and 48 (c) 6 and 8 (d) 2 and 24
  30. 30.In a league, 13 teams each play every other team once. How many matches are played? (a) 169 (b) 78 (c) 91 (d) 156
  31. 31.What is the missing term in the AP 2, 5, ?, 11, 14? (a) 7 (b) 11 (c) 9 (d) 8
  32. 32.A drawer has lots of yellow, red, blue and green 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) 2 (c) 5 (d) 8
  33. 33.In a class of 35 children, 15 like dance, 14 like music and 2 like both. How many like only dance? (a) 12 (b) 21 (c) 15 (d) 13
  34. 34.If a + b = 19 and ab = 90, what is (a − b)²? (a) 181 (b) 361 (c) 271 (d) 1
  35. 35.How many factors does 14 have? (a) 5 (b) 2 (c) 3 (d) 4
  36. 36.Two angles of a triangle are 45° and 90°. What is the exterior angle at the third corner? (a) 135° (b) 90° (c) 45° (d) 225°
  37. 37.Which term of the AP 1, 6, 11, 16, … is 136? (a) 27th (b) 30th (c) 29th (d) 28th
  38. 38.A bag has 10 yellow balls and 8 red balls. Without looking, how many balls must you take out to be sure of getting 2 red balls? (a) 11 (b) 2 (c) 18 (d) 12
  39. 39.Two dice are rolled together. What is the probability that the two numbers add up to 9? (a) 1/11 (b) 1/9 (c) 5/36 (d) 4/11
  40. 40.If a + b = 14 and ab = 24, what is a² + b²? (a) 196 (b) 244 (c) 172 (d) 148

Answer key

  1. 1/12
  2. 26
  3. 5
  4. 340
  5. 7
  6. 29
  7. 2² × 5 × 7
  8. 19
  9. 130°
  10. 8
  11. 5
  12. 4
  13. 7/8
  14. 18
  15. 10
  16. 1156
  17. 294
  18. 154 sq cm
  19. 26
  20. 4
  21. 9
  22. 9/16
  23. 176 cm
  24. 1/2
  25. 15
  26. 5
  27. 105
  28. (x + 5)(x + 6)
  29. 6 and 8
  30. 78
  31. 8
  32. 5
  33. 13
  34. 1
  35. 4
  36. 135°
  37. 28th
  38. 12
  39. 1/9
  40. 148

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