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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 562 · 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.In how many different ways can the letters of the word SUN be arranged? (a) 9 (b) 3 (c) 12 (d) 6
  2. 2.A cuboid is 3 cm long, 2 cm wide and 6 cm high. What is its total surface area? (a) 144 sq cm (b) 36 sq cm (c) 73 sq cm (d) 72 sq cm
  3. 3.A canteen sells 8 kinds of sandwich and 7 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 112 (b) 64 (c) 15 (d) 56
  4. 4.What is the smallest number of children in a group that makes sure at least two of them were born in the same day of the week? (a) 15 (b) 14 (c) 7 (d) 8
  5. 5.In a class of 30 children, 24 like mangoes, 8 like bananas and 3 like neither. How many like both? (a) 2 (b) 3 (c) 27 (d) 5
  6. 6.What is the 28th term of the AP 11, 14, 17, 20, …? (a) 81 (b) 92 (c) 84 (d) 95
  7. 7.In a class of 36 children, 14 like maths, 21 like science and 9 like both. How many like only maths? (a) 14 (b) 15 (c) 5 (d) 12
  8. 8.In a class of 50 children, 26 like maths, 30 like science and 10 like both. How many like at least one of the two? (a) 56 (b) 46 (c) 36 (d) 50
  9. 9.How many prime numbers are there between 10 and 20? (a) 3 (b) 4 (c) 6 (d) 5
  10. 10.What is the sum of the first 22 odd numbers (1 + 3 + 5 + …)? (a) 484 (b) 253 (c) 43 (d) 506
  11. 11.What is the missing term in the AP 4, ?, 16, 22, 28? (a) 9 (b) 16 (c) 10 (d) 11
  12. 12.What is the sum of the first 18 odd numbers (1 + 3 + 5 + …)? (a) 342 (b) 171 (c) 35 (d) 324
  13. 13.Two straight lines cross. Two vertically opposite angles add up to 240°. What is each of the other two angles? (a) 60° (b) 61° (c) 120° (d) 59°
  14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  15. 15.What is the mean of 19, 20, 4, 5, 9 and 3? (a) 11 (b) 9 (c) 12 (d) 10
  16. 16.A canteen sells 5 kinds of sandwich and 3 kinds of juice. In how many ways can you choose one sandwich and one juice? (a) 15 (b) 8 (c) 30 (d) 20
  17. 17.In which quadrant does the point (−3, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  18. 18.Two angles of a triangle are 20° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 105° (c) 75° (d) 160°
  19. 19.7 T-shirts and 6 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 84 (b) 49 (c) 13 (d) 42
  20. 20.A fair dice is rolled once. What is the probability of getting an even number? (a) 1/3 (b) 1/6 (c) 2/3 (d) 1/2
  21. 21.7 T-shirts and 5 pairs of shorts are in a cupboard. How many different outfits of one T-shirt and one pair of shorts can be made? (a) 35 (b) 42 (c) 70 (d) 12
  22. 22.What is the prime factorisation of 144? (a) 2² × 3⁴ (b) 2⁴ × 3² (c) 2⁵ × 3² (d) 2³ × 3²
  23. 23.Which is the correct factorisation of x² + 5x + 6? (a) (x − 2)(x − 3) (b) (x + 1)(x + 4) (c) (x + 1)(x + 6) (d) (x + 2)(x + 3)
  24. 24.In a class of 48 children, 22 like maths, 18 like science and 2 like both. How many like only maths? (a) 16 (b) 20 (c) 22 (d) 30
  25. 25.What is the sum of the first 10 odd numbers (1 + 3 + 5 + …)? (a) 100 (b) 110 (c) 19 (d) 55
  26. 26.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  27. 27.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 42 (c) 14 (d) 126
  28. 28.A bag has 10 white balls and 6 black balls. Without looking, how many balls must you take out to be sure of getting 2 black balls? (a) 2 (b) 12 (c) 16 (d) 11
  29. 29.There are 6 roads from town A to town B and 2 roads from town B to town C. How many different routes go from A to C through B? (a) 24 (b) 8 (c) 12 (d) 18
  30. 30.Two angles of a triangle are 30° and 50°. What is the third angle? (a) 80° (b) 130° (c) 150° (d) 100°
  31. 31.A team of 2 players is to be chosen from 7 players. How many different teams are possible? (a) 49 (b) 21 (c) 42 (d) 14
  32. 32.What is the area of a circle of radius 28 cm? (Use π = 22/7.) (a) 9856 sq cm (b) 1232 sq cm (c) 2464 sq cm (d) 176 sq cm
  33. 33.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
  34. 34.Two angles of a triangle are 70° and 90°. What is the third angle? (a) 160° (b) 20° (c) 110° (d) 90°
  35. 35.What is the prime factorisation of 24? (a) 2² × 3 (b) 2⁴ × 3 (c) 2³ × 3 (d) 2 × 3³
  36. 36.What is the distance between the points (1, 13) and (9, 7)? (a) 100 (b) 14 (c) 10 (d) 11
  37. 37.In which quadrant does the point (−3, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.What is the prime factorisation of 45? (a) 3 × 5 (b) 3³ × 5 (c) 3 × 5² (d) 3² × 5
  39. 39.Which term of the AP 15, 19, 23, 27, … is 119? (a) 28th (b) 29th (c) 27th (d) 26th
  40. 40.What is the median of 24, 29, 11, 9 and 16? (a) 17 (b) 16 (c) 24 (d) 11

Answer key

  1. 6
  2. 72 sq cm
  3. 56
  4. 8
  5. 5
  6. 92
  7. 5
  8. 46
  9. 4
  10. 484
  11. 10
  12. 324
  13. 60°
  14. 20
  15. 10
  16. 15
  17. Third quadrant
  18. 75°
  19. 42
  20. 1/2
  21. 35
  22. 2⁴ × 3²
  23. (x + 2)(x + 3)
  24. 20
  25. 100
  26. 5
  27. 42
  28. 12
  29. 12
  30. 100°
  31. 21
  32. 2464 sq cm
  33. 7
  34. 20°
  35. 2³ × 3
  36. 10
  37. Second quadrant
  38. 3² × 5
  39. 27th
  40. 16

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