**UNIVERSITY EXAMINATIONS: 2016/2017**

**EXAMINATION FOR THE CERTIFICATE IN BRIDGING MATHEMATICS**

**MAT105 GRAPHS**

**DATE: AUGUST, 2017 TIME: 2 HOURS**

**INSTRUCTIONS: Answer Question One & ANY OTHER TWO questions.**

**QUESTION ONE [30 MARKS] – COMPULSORY**

a) Given f(x)= x2

-2x+1 , find f(6) using a graph. [6 Marks]

b) Graph the following functions:

i. f(x)= |x|

ii. f(x)= x+2 [6 Marks]

c) Solve the simultaneous equations below using graphical method and determine the gradient of

each line:

3x-6y=10

2x+5y=4 [4 Marks]

d) Discuss three uses of graphs in the information and communication technology

[4 Marks]

e) A calculator company produces a scientific calculator and a graphing calculator. Long-term

projections indicate an expected demand of at least 100 scientific and 80 graphing calculators

each day. Because of limitations on production capacity, no more than 200 scientific and 170

graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200

calculators much be shipped each day.

If each scientific calculator sold results in a $2 loss, but each graphing calculator pro- duces a

$5 profit, how many of each type should be made daily to maximize net prof- its? [6 Marks]

f) Explain the meaning of the following terms as used in graphs [4 Marks]

i. Y intercept

ii. Gradient

iii. Parabola simultaneous

iv. gradient

**QUESTION TWO**

a) Find the equation of as straight line passing through a point A(2,0) and perpendicular to

another line y=4x+1 [6 Marks]

b) The table below shows the time and distance covered by a car.

i. Draw a graph for the above information using a scale of 1cm to represent 1 min and 2 cm to

represent 1km.

ii. From your graph , estimate (by drawing a tangent) the speed of the train in km/min when the

train has traveled 6km. [10 Marks]

c) Differentiate between functions and equations. [4 Marks]

**QUESTION THREE**

a) Solve the equation y=(3x+1)(2x-5)for the domain- -4 ≤x ≤4 [6 Marks]

b) A company invests in particular project and it has been estimated tht after x months of

running the cumulative profit (Sh. 000) from the project is given by the function 31.5x-3×2

-60

where x represent time in months. The project can run for a maximum 9 months.

i. Draw a graph which represents the profit function [6 Marks]

ii. Calculate the breakeven time points for the project [4 Marks]

iii. What is the initial cost of the project [2 Marks]

iv. Use the graph to estimate the best time to end the project. [2 Marks]

**QUESTION FOUR**

3

a) Draw the graph of

y =sin x

y =cos x

**QUESTION FIVE**

a) Discuss the following terms [8 Marks]

i) Cartesian plane

ii) Line of symmetry

iii) Quadratic equations and cubic equations

iv) Polynomial equations

b) A furniture factory manufactures two types of coffee table, A and B. Each table goes through two

distinct stages, assembly and finishing. The maximum capacity for assembly is 195 hours and for

finishing is 165hours. Each A table requires 4 hours assembly and 3 hours finishing while a B table

requires 1 hour for assembly and 2 hours for finishing. Calculate the number of A and B tables to be

produced to ensure that the maximum capacity available is utilized. [12 Marks