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Archive3: Following questions are taken from Mathematics IEB Exam Paper of Nov. 1993.

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Question 1 Given the complex numbers a) Plot both Z1 and Z2* on an Argand diagram. b) Find Z1 - Z2* c) Using rectangular form arithmetic only, find:        i) Z1Z2                  ii) give both answers in rectangular form. d) Convert Z1 and Z2 into polar form and using polar arithmetic only, find:        i) Z1Z2                  ii) give both answers in polar form. e)Find f) Find all the roots of g) The circuit below is constructed using the complex numbers Z1 and Z2 to describe the impedances.

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Question 2
A triangle can be labedded as follows.
a represents the length of the side opposite angle A.
b represents the length of the side opposite angle B.
c represents the length of the side opposite angle C.
If for a particular triangle we have,

a) Convert angle A into DMS form.
b) Calculate tan A.
c) Determine another angle
d) Calculate
e) Calculate
f) Find both possible values for the angle B in the triangle ABC
g) Determine angle C (both cases).
h) Determine length C (both cases).
i) Sketch both cases of triangle ABC.

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Question 3
a) If
b) Differentiate the following "from first principles"

c) Differentiate
d) Find the gradient of the tangent to the curve
at the point (-2,-6)
e) In the given RLC series circuit the charge build up on the capacitor over a period of time t is given by

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The voltage across the capacitor, resistor and inductor in the circuit shown are:

i)   Find the charge on the capacitor at time t = 12 milliseconds.
ii)  What is the current through the capacitor at t = 12 milliseconds.
iii)  After 12 milliseconds find the voltages across the capacitor, resistor and inductor.

Queston 4
a) Prove the identity
b) Show that
c) Simplify
d) Solve the equation

Question 5
a) Sketch the given graph for
then draw the horizontal line y = 5.
b) read the relevant values off your graph in part a) to solve the equation

Question 6
a) Express
b) Solve the equation
c) Graph the following on the same set of axes for

 

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