MAT093 FINAL EXAMINATION – Sept 2013

QUESTION 1

a) Solve the equation

.

(3 marks) a) Find the value of x which satisfies the equation

.

(5 marks)

c) Given that and . Find

i) A – 2B if possible, otherwise state the reason. ii) ABT.

(3 marks)

d) Write the following system of linear equations in matrix form, AX = B, then solve for x, y and z by the Inverse Matrix method.

(9 marks)

QUESTION 2

a) Factorize the polynomial expression completely. Hence, find the

roots of the equation and determine whether they are real or

otherwise. (7 marks)

b) Given , where a and b are constants. Find the values of a and b

if P(x) is divisible by and gives 40 as the remainder when divided by

(4 marks)

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c) The functions f and g are defined as and

i) Sketch the graph of f(x). Hence, state the domain and range of f(x).

ii) Find .

iii) If find the value of x.

(10 marks)

QUESTION 3

a) Evaluate

(4 marks)

b) Find the derivative of by method of first principles.

(5 marks)

c) Find the derivative for each of the following functions:

i)

ii)

(6 marks)

d) Find for the implicit function .

(5 marks)

QUESTION 4

a) If the radius of a sphere is increasing at the constant rate of 0.3 cms -1, how fast is the volume of the sphere changing when the surface area is 10 cm2?

(Hint: surface area of sphere A = and volume of sphere

(5 marks)b) Consider the function

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Findi) the intervals on which f(x) is increasing and decreasing.

ii) the maximum and minimum points.

iii) the intervals where the function is concave down and concave up.(10 marks)

c) A and B are two events of an experiment such that and

i) Find .

ii) If event C is independent of event A and find P(C).

(5 marks)QUESTION 5

a) Student’s self-learning time is an integral part in the design of a new curriculum for courses in the Centre of Foundation Studies, UiTM. The Mathematics Unit for the Centre wants some idea as to how the learning time is fulfilled among the students. A simple survey was carried out among a random sample of 120 students for a particular topic where a minimum of 25 hours of learning time was allocated. The data pertaining to the survey is as follows:

Learning time(hours), x

5 – 10 10 – 15 15 – 20 20 – 25 25 – 30 30 – 35 35 – 40

Number of students, f

5 16 29 22 34 10 4

Based on the given data,

i) draw a frequency polygon.

ii) calculate the median and the mode. Give your answer correct to 3 significant figures.

iii) calculate the mean and the standard deviation by using the data summary

and

iv) find the Pearson’s Coefficient of Skewness.

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v) estimate the percentage of students failed to fulfill the time allocated.(14 marks)

b) The table below shows the number of students in a particular class who own a tablet computer (Samdung or Applet) or otherwise.

TabletGender

Samdung (S) Applet (A) Does not own any of these (N)

Male (M) 6 10 12

Female (F) 5 13 14

If a student is selected at random, find the probability that

i) the student does not own a Samdung or Applet table computer.ii) the student is a female given that she owns an Applet tablet computer.

(3 marks)

c) Nine persons in a room are wearing badges marked 1 through 9. Three persons are chosen at random and are assigned special tasks. What is the probability that those given these tasks wear badge numbers less than 6?

(2 marks)

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