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
