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CAPE Applied Mathematics Unit 2 · 2014 · Paper 2

42 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)3 marksState the contrapositive of p ⇒ ~q.
  2. 1(b)5 marksConstruct a truth table for the inverse of p ⇒ ~q.
  3. 1(c)(i)5 marksConstruct a truth table for (p → q) ˅ (q → r).
  4. 1(c)(ii)2 marksHence, state with reason, whether (c)(i) is a tautology or a contradiction.
  5. 1(d)4 marksDetermine the Boolean expression for the given logic circuit.
  6. 1(e)(i)3 marksDraw a switching circuit for the Boolean expression A ˅ (B ˄ C).
  7. 1(e)(ii)3 marksUse the distributive law to expand the Boolean expression A ˅ (B ˄ C).
  8. 2(a)(i)12 marksUsing the algorithm method, or otherwise, construct the activity network for these activities.
  9. 2(a)(ii)4 marksCopy and complete the table, giving the earliest start time, latest start time and float time for EACH activity.
  10. 2(a)(iii)2 marksHence, obtain the critical path(s).
  11. 2(b)(i)3 marksRepresent the circuit as a Boolean expression.
  12. 2(b)(ii)4 marksConstruct its truth table.
  13. 3(a)4 marksCalculate P(A' ∩ B').
  14. 3(b)(i)a)4 marksDetermine the probability that two sing soprano and one sings tenor.
  15. 3(b)(i)b)4 marksDetermine the probability that one soprano, one tenor and one bass are chosen.
  16. 3(b)(i)c)5 marksDetermine the probability that three tenors are chosen given that the three persons all sing the SAME part.
  17. 3(b)(ii)4 marksA committee of 9 is to be drawn from the members of the choir. Determine the probability that the committee contains EXACTLY 2 basses and 3 tenors.
  18. 3(b)(iii)4 marksThe 6 tenors and 5 basses are to be seated at a circular table so that two tenors are next to each other, and the remainder sit alternately. In how many ways can this be done?
  19. 4(a)(i)3 marksFind the probability that there are EXACTLY 4 faults in a 15-metre length of cloth.
  20. 4(a)(ii)3 marksCalculate the probability of AT LEAST 2 faults in a 60-metre length of cloth.
  21. 4(b)(i)4 marksCalculate the probability that the mass is less than 60 g.
  22. 4(b)(ii)4 marksCalculate the probability that the mass is between 61 g and 64 g.
  23. 4(c)(i)2 marksCalculate P(X + Y = 3).
  24. 4(c)(ii)a)1 markEvaluate E(X).
  25. 4(c)(ii)b)1 markEvaluate Var(X).
  26. 4(c)(ii)c)1 markEvaluate E(Y).
  27. 4(c)(ii)d)1 markEvaluate Var(Y).
  28. 4(c)(iii)a)2 marksHence, determine E(3X – 2Y).
  29. 4(c)(iii)b)3 marksHence, determine Var(3X – 2Y).
  30. 5(a)(i)4 marksOn the answer sheet provided as an insert, draw a displacement time graph for 0 ≤ t ≤ 8.
  31. 5(a)(ii)a)3 marksFrom your graph calculate the total distance travelled in the period 0 ≤ t ≤ 5.
  32. 5(a)(ii)b)3 marksFrom your graph calculate the average velocity over the period 0 ≤ t ≤ 5.
  33. 5(a)(ii)c)2 marksFrom your graph calculate the time at which the velocity is zero.
  34. 5(b)(i)4 marksDraw a force diagram to illustrate this information.
  35. 5(b)(ii)7 marksFind the LEAST value of P and the value of α when P is least.
  36. 5(b)(iii)2 marksDetermine the LEAST value of P in terms of m when α = 30°.
  37. 6(a)4 marksFormulate the equation of the trajectory of a projectile.
  38. 6(b)(i)2 marksShow that 20 tan² α – 90 tan α + 16 = 0.
  39. 6(b)(ii)5 marksHence, find to the nearest degree, the TWO possible values of α.
  40. 6(b)(iii)3 marksFind, to the nearest second, the MINIMUM possible time of flight from A to B.
  41. 6(c)6 marksFind the value of T.
  42. 6(d)5 marksFind the velocity of the particle when s = 3.

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