BT 1120, Homework I BT 1120, Homework I

Please write your College ID and the course number (BT1120) clearly on the top of each sheet you submit. Remember that marks are awarded for method as well as correct answers. This homework is to be handed in at the lecture to be given on the 20/1/1999.

Question 1
Simplify the following as far as possible, using cancellation where appropriate: (i)

x+1
x
 - x+1
x+2
(5 marks)
(ii)
x
x+3
x2+2x
(x+3)(x+2)
(5 marks)

Question 2
Find the slope/intercept form of the following linear equations:
(i) y +9x = 27(5 marks)
(ii) 17x+ 8y = 37 (5 marks)

Question 3
(a) Derive the equation of the straight line passing through the point (3,8) with slope -7.(5 marks)
(b) Find the slope of the line through the points (2,17) and (3,20).
(5 marks)

Question 4
Use Gaussian elimination to solve the following sets of simultaneous equations. If a unique solution does not exist, comment on the nature of the two lines.
(a) x-y = -1 and x-2y = -5 (5 marks)
(b) 2x+2y = 4 and -12x = 12y-24 (5 marks)
(c) 3x-7y = 2 and x+4y = 11(5 marks)
(d) y = x+4 and -2x+2y = 10(5 marks)
Question 5
The demand and supply functions of a good are given by

P+2QD
=
60
P -QS
=
30.
(i) Use Gaussian elimination to solve this system of linear equations and find the equilibrium price and quantity. (5 marks)
(ii) Verify your answer to (i) using the graphical method. (Don't forget that all graphs should be drawn on graph paper). (5 marks)

Question 6
Find the roots of the following quadratic functions:
(i) y = x2-x-6
(ii) y = 6x2 +24x-24 (10 marks)

Question 7
Sketch the graphs of the following quadratic functions:
(i) y = x2 + 2x-15
(ii) y = -3x2 - 3x +36 (20 marks)

Question 8
The total revenue received from the sale of Q goods at the price P is given by TR = P×Q.
(a) Given the demand function P = 75-3Q, express TR as a function of Q.
(b) For what values of Q is TR zero?
(c) What is the maximum value of TR and at what value of Q does it occur?
(10 marks)

File translated from TEX by TTH, version 2.10.
On 6 May 1999, 15:36.