**UNIVERSITY EXAMINATIONS: 2011/2012 **

**EXAMINATION FOR THE CERTIFICATE IN BRIDGING MATHEMATICS **

**MAT 105 GRAPHS **

**DATE: APRIL 2012 TIME: 1½ HOURS **

**INSTRUCTIONS: Answer Question One and Any other Two Questions**

**QUESTION ONE [30 MARKS]**

a) Determine the equation describing a straight line that passes thorough (-3,5) and (7,2). [3 Marks]

b) Using a suitable scale, plot the function y = 3x − 2 on the Cartesian plane . [3 Marks]

c) Plot the basic graph of 3 1 2

y = x − x + , for − 4 ≤ x ≤ 4 ,on the same axis plot f (−x) and describe the

transformation. [9 Marks]

d) Determine the feasible region described by the following inequalities

[6 Marks]

e) Given that y = sin 2x and that 0° ≤ x ≤ 360°, plot this trigonometric function on a Cartesian plane.

[9 Marks]

**QUESTION TWO [15 MARKS]**

a) A straight line whose gradient is -2 meets another straight line perpendicularly at the point

(2,3).Calculate the equations of these two straight lines hence plot them on the Cartesian plane.

[8 Marks]

b) The end of semester examination paper has twenty questions worth 100 points. The examination

consists of optional questions worth 3 points each and compulsory questions worth 11 points each.

Using graphical method, determine how many compulsory questions are on this examination.

[7 Marks]

**QUESTION THREE [15 MARKS]**

a) Given the general form of equation of a circle as x2

+ y2

– 6x + 4y + 9 = 0.

i. Find the center and radius of the circle. [3Marks]

ii. Graph the circle. [4 Marks]

b) Mr. Been invested Ksh 30000.00; part at 5% and part at 8%.The total interest rate on the investment

was Ksh 2100.Using the graphical method, find how much he invested at each rate. [8 Marks]

**QUESTION FOUR [15 MARKS]**

a) Plot the graph of 4 ( 2)

2y = x − − for the values -4≤x≤4, hence solve 0 4 2

x − x = [7 Marks]

b) The sum of two numbers is 30.Using graphical method determine the maximum product of these

two numbers. [8 Marks]

**QUESTION FIVE [15 MARKS]**

A farmer has a total of 150 tomato and cucumber plants. Each tomato plant yields 4 kg of tomatoes.

Each cucumber plant yields 6 kg of cucumbers. The total yield is 710 kg.

i) Formulate the required equations [4 Marks]

ii) Plot the equations on the same Cartesian plane [6 Marks]

iii) Using a graphs plotted determine how many cucumber plants are there? [5 Marks]