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CAPE Applied Mathematics Unit 2 · 2011 · Paper 2

38 questions and parts from this paper. Open one to see it in full, then practise it on Quelpr and get it marked against the mark scheme.

Practise this paper
  1. 1(a)5 marksConstruct a truth table to show that the proposition (~ p ˅ ~ q) ⇒ (p ˄ ~ q) ALWAYS takes the value of p.
  2. 1(b)4 marksWrite the Boolean expression for the given logic circuit.
  3. 1(c)4 marksDraw a switching circuit to represent the expression (a ˄ b) ˅ [a ˄ (~ b ˅ c)].
  4. 1(d)(i)a)2 marksExpress the statement 'If there is a west wind then we shall have rain' in logic form using the connectives ~ and ⇒.
  5. 1(d)(i)b)2 marksExpress the statement 'If there is no rain then the west wind does not blow' in logic form using the connectives ~ and ⇒.
  6. 1(d)(ii)4 marksConstruct a truth table to prove that the statements in parts (d)(i)a) and (d)(i)b) are equivalent.
  7. 1(e)4 marksUse de Morgan's laws to prove that ~ [(p ˄ q) ˅ ~ p] = ~ q ˄ p.
  8. 2(a)7 marksFour persons, A, B, C and D, are assigned to run a 4 x 400 relay. The average times in seconds are given. Use the Hungarian Algorithm to allocate runners to a position so as to minimize the sum of the average times.
  9. 2(b)(i)5 marksConstruct an activity network for the project.
  10. 2(b)(ii)10 marksCopy and complete the table of Earliest Start Time, Latest Start Time, and Float for activities A to E.
  11. 2(b)(iii)a)2 marksHence, determine the critical path.
  12. 2(b)(iii)b)1 markHence, determine the MINIMUM completion time of the project.
  13. 3(a)(i)2 marksDetermine the number of different arrangements of the letters of the word MAXIMUM if there are no restrictions.
  14. 3(a)(ii)3 marksDetermine the number of different arrangements of the letters of the word MAXIMUM if the last letter is a vowel.
  15. 3(a)(iii)3 marksDetermine the number of different arrangements of the letters of the word MAXIMUM if the 3 M's must be together.
  16. 3(b)4 marksA committee of four is to be chosen from 6 men and 4 women. Determine the number of ways that the committee can be chosen so as to contain AT MOST 3 women.
  17. 3(c)(i)2 marksIdentify the distribution of X and state its parameter(s).
  18. 3(c)(ii)a)3 marksDetermine the probability that it takes EXACTLY 2 attempts to obtain a green ball.
  19. 3(c)(ii)b)3 marksDetermine the probability that it takes at LEAST 3 attempts to obtain the first green ball.
  20. 3(c)(ii)c)3 marksDetermine the probability that it takes LESS than 4 attempts to obtain the first green ball.
  21. 3(d)2 marksDetermine E(X).
  22. 4(a)(i)3 marksOn a particular stretch of road, there are on average 3 accidents per week. Find the probability that no accidents occur in a particular week.
  23. 4(a)(ii)3 marksFind the probability that MORE than 3 accidents occur in a particular week.
  24. 4(a)(iii)3 marksFind the probability that EXACTLY 6 accidents occur in a particular fortnight.
  25. 4(b)5 marksThe probability that a student is awarded a pass in the statistics examination is 0.84. Find the probability that in a group of 12 students, MORE than two-thirds pass the statistics examination.
  26. 4(c)(i)3 marksCalculate the probability that the marbles, in the order drawn, will be coloured white, black and red.
  27. 4(c)(ii)4 marksCalculate the probability that one marble of EACH colour will be drawn.
  28. 4(c)(iii)4 marksCalculate the probability that the THIRD marble will be white.
  29. 5(a)(i)4 marksDraw a diagram showing the forces acting on the car.
  30. 5(a)(ii)a)4 marksCalculate the acceleration of the car.
  31. 5(a)(ii)b)5 marksCalculate the tractive force of the car.
  32. 5(a)(ii)c)4 marksCalculate the maximum power developed in kW.
  33. 5(b)(i)5 marksDetermine the acceleration of motion.
  34. 5(b)(ii)3 marksDetermine the tension in the string.
  35. 6(a)(i)4 marksSketch a velocity-time graph for the motion of the train.
  36. 6(a)(ii)10 marksUsing the graph, determine the initial uniform acceleration of the train, if the time taken for the whole journey is 6 minutes.
  37. 6(b)(i)4 marksCalculate the work done.
  38. 6(b)(ii)7 marksIf the block is of mass 70 kg and there is a frictional force opposing the motion of the block, find the magnitude of the frictional force.

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