Quelpr

CAPE Applied Mathematics Unit 2 · 2015 · Paper 2

31 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)(i)a)3 marksBy identifying the variables, formulate the profit function that needs to be solved.
  2. 1(a)(i)b)7 marksFormulate the inequalities to be used to solve this problem.
  3. 1(a)(ii)a)6 marksOn the graph sheet provided, draw the graphs of the inequalities obtained in (i) b).
  4. 1(a)(ii)b)2 marksIdentify the feasible region to solve the problem.
  5. 1(a)(iii)a)3 marksFrom your graph, determine the number of EACH type of bottle required for maximum profit.
  6. 1(a)(iii)b)2 marksDetermine the maximum profit.
  7. 1(b)2 marksDetermine the SHORTEST and LONGEST path from Town S to Town G.
  8. 2(a)(i)8 marksUse the Hungarian algorithm to determine the class to which each teacher must be assigned in order to minimize the total time.
  9. 2(a)(ii)2 marksHence, determine the total time spent in the classroom by the four teachers.
  10. 2(b)3 marksBy constructing a truth table, determine whether (p ∧ q) → p is a tautology or a contradiction.
  11. 2(c)(i)4 marksWrite down a Boolean expression for the given circuit.
  12. 2(c)(ii)8 marksSimplify the expression obtained in (c) (i) above and hence draw the corresponding circuit.
  13. 3(a)(i)4 marksDetermine the probability that in a random sample of 15 bolts, more than one is defective.
  14. 3(a)(ii)8 marksIf X represents the number of defective bolts manufactured by the factory, determine the SMALLEST value of n for which the ratio of the standard deviation of X to the mean of X is less than 0.1.
  15. 3(b)5 marksIf X ~ Bin(500, 0.005), use a suitable approximation to find P(X ≤ 2).
  16. 3(c)5 marksIf X ~ Po(20), use a suitable approximation to find P(X ≤ 25).
  17. 3(d)3 marksIf X follows a geometric distribution with probability 0.3, determine the probability that X is less than 4.
  18. 4(a)(i)10 marksShow that a = 2.2 and determine the value of b.
  19. 4(a)(ii)3 marksDetermine P(X > 0.5).
  20. 4(b)(i)3 marksDetermine the value of m and n shown in the table.
  21. 4(b)(ii)9 marksCarry out a χ² goodness-of-fit test at the 5% significance level to determine whether the data may be modelled by a normal distribution with mean 9 and standard deviation 1.
  22. 5(a)(i)3 marksDraw a force diagram to illustrate this information.
  23. 5(a)(ii)8 marksThe particle is released from rest. Determine the tension, T, in the string and the acceleration, a, of the particle.
  24. 5(a)(iii)4 marksCalculate the force exerted by the string on the pulley.
  25. 5(b)(i)2 marksFind in vector form the acceleration when t = 3.
  26. 5(b)(ii)4 marksFind in vector form the position of the particle when t = 3.
  27. 5(c)4 marksA particle of mass m falls vertically from rest through a medium with resistance to motion proportional to v, where v is its velocity at time t. Obtain a differential equation relating v and t.
  28. 6(a)3 marksA pressure washer hose delivers 10 kg of water per second horizontally, hitting a wall at a speed of 30 m s⁻¹. Assuming water does not bounce off, find the average force exerted on the wall.
  29. 6(b)6 marksA 5-tonne truck moving at 4 m s⁻¹ and a 3-tonne truck moving at 7 m s⁻¹ travel along the same road in opposite directions, collide, and couple together. Find the velocity and direction in which they continue to move.
  30. 6(c)12 marksBlock A of mass 3M kg rests on a smooth table top connected by a light inextensible string of length 1.2 m passing over a smooth pulley at the edge to block B of mass 1.5M kg hanging freely. Block A is initially held…
  31. 6(d)4 marksA string passes over a fixed, smooth, weightless pulley, with masses of 3 kg and 5 kg attached to each end. Calculate the acceleration of the system.

More CAPE Applied Mathematics Unit 2 papers