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Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 476 · 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 mode of 1, 3, 3, 4, 1, 3 and 15? (a) 15 (b) 1 (c) 3 (d) 4
  2. 2.Which is the correct factorisation of x² + 10x + 24? (a) (x + 1)(x + 24) (b) (x + 4)(x + 6) (c) (x − 4)(x − 6) (d) (x + 1)(x + 9)
  3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
  4. 4.Two angles of a triangle are 70° and 30°. What is the exterior angle at the third corner? (a) 110° (b) 80° (c) 150° (d) 100°
  5. 5.What is the distance between the points (2, 3) and (14, 12)? (a) 21 (b) 15 (c) 16 (d) 225
  6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  7. 7.What is the area of a circle of radius 21 cm? (Use π = 22/7.) (a) 5544 sq cm (b) 693 sq cm (c) 1386 sq cm (d) 132 sq cm
  8. 8.Two angles of a triangle are 20° and 95°. What is the third angle? (a) 85° (b) 65° (c) 115° (d) 160°
  9. 9.What is the 36th term of the AP 20, 22, 24, 26, …? (a) 92 (b) 70 (c) 72 (d) 90
  10. 10.In how many different ways can the letters of the word CHAIR be arranged? (a) 20 (b) 240 (c) 25 (d) 120
  11. 11.Two angles of a triangle are 80° and 30°. What is the third angle? (a) 100° (b) 70° (c) 150° (d) 110°
  12. 12.Two angles of a triangle are 50° and 65°. What is the third angle? (a) 130° (b) 65° (c) 115° (d) 245°
  13. 13.In how many different ways can the letters of the word CAT be arranged? (a) 9 (b) 12 (c) 3 (d) 6
  14. 14.If every edge of a cube is made 2 times as long, how many times as big does its surface area become? (a) 8 times (b) 5 times (c) 2 times (d) 4 times
  15. 15.Using (a − b)² = a² − 2ab + b², what is 69²? (a) 4761 (b) 5041 (c) 4899 (d) 4771
  16. 16.What is the smallest number of children in a group that makes sure at least two of them were born in the same month? (a) 24 (b) 13 (c) 25 (d) 12
  17. 17.Two angles of a triangle are 55° and 110°. What is the third angle? (a) 70° (b) 165° (c) 125° (d) 15°
  18. 18.What is the median of 8, 14, 20, 3 and 17? (a) 20 (b) 17 (c) 14 (d) 8
  19. 19.A cuboid is 11 cm long, 6 cm wide and 8 cm high. What is its volume? (a) 404 cu cm (b) 66 cu cm (c) 25 cu cm (d) 528 cu cm
  20. 20.A drawer has lots of black, yellow, red 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) 5 (b) 2 (c) 8 (d) 4
  21. 21.What is the smallest number of children in a group that makes sure at least four of them were born in the same month? (a) 49 (b) 37 (c) 48 (d) 36
  22. 22.What is the sum of the first 10 terms of the AP 5, 7, 9, …? (a) 140 (b) 280 (c) 150 (d) 23
  23. 23.What is the 21st term of the AP 5, 7, 9, 11, …? (a) 42 (b) 40 (c) 47 (d) 45
  24. 24.What is the distance between the points (9, 13) and (15, 5)? (a) 100 (b) 14 (c) 11 (d) 10
  25. 25.There are 5 roads from town A to town B and 6 roads from town B to town C. How many different routes go from A to C through B? (a) 35 (b) 11 (c) 60 (d) 30
  26. 26.Two angles of a triangle are 55° and 90°. What is the third angle? (a) 125° (b) 90° (c) 145° (d) 35°
  27. 27.Two angles of a triangle are 40° and 130°. What is the third angle? (a) 10° (b) 50° (c) 170° (d) 140°
  28. 28.In how many different ways can the letters of the word STAR be arranged? (a) 24 (b) 48 (c) 12 (d) 16
  29. 29.What is the midpoint of the line joining (10, 4) and (12, 0)? (a) (2, 11) (b) (11, 2) (c) (1, 2) (d) (22, 4)
  30. 30.Two coins are tossed together. What is the probability of getting a head on every coin? (a) 1/4 (b) 1/2 (c) 3/4 (d) 1/3
  31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  32. 32.What is the midpoint of the line joining (7, 5) and (19, 11)? (a) (6, 3) (b) (13, 8) (c) (8, 13) (d) (26, 16)
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  34. 34.The mean of 8 numbers is 29. When the number 2 is added to them, what is the new mean? (a) 27 (b) 25 (c) 26 (d) 29
  35. 35.Two angles of a triangle are 70° and 40°. What is the exterior angle at the third corner? (a) 110° (b) 140° (c) 250° (d) 70°
  36. 36.Using (a − b)² = a² − 2ab + b², what is 55²? (a) 3575 (b) 3025 (c) 4225 (d) 3035
  37. 37.How many factors does 113 have? (a) 2 (b) 4 (c) 3 (d) 1
  38. 38.The mean of 8 numbers is 18. When the number 36 is added to them, what is the new mean? (a) 20 (b) 18 (c) 27 (d) 21
  39. 39.There are 7 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) 9 (b) 14 (c) 21 (d) 28
  40. 40.How many prime numbers are there between 90 and 100? (a) 0 (b) 2 (c) 1 (d) 3

Answer key

  1. 3
  2. (x + 4)(x + 6)
  3. 10
  4. 100°
  5. 15
  6. 25
  7. 1386 sq cm
  8. 65°
  9. 90
  10. 120
  11. 70°
  12. 65°
  13. 6
  14. 4 times
  15. 4761
  16. 13
  17. 15°
  18. 14
  19. 528 cu cm
  20. 5
  21. 37
  22. 140
  23. 45
  24. 10
  25. 30
  26. 35°
  27. 10°
  28. 24
  29. (11, 2)
  30. 1/4
  31. 5
  32. (13, 8)
  33. 9
  34. 26
  35. 110°
  36. 3025
  37. 2
  38. 20
  39. 14
  40. 1

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