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Tutor-marked Assignment 1WUC 115/05

UNIVERSITY MATHEMATICS B

To be submitted BEST before 8 th September 2013

Evidence of plagiarism or collusion will be taken seriously and the Universityregulations will be applied fully. You are advised to be familiar with theUniversitys definitions of plagiarism and collusion.

Instructions :1. This is an individual assignment. No duplication of work will be tolerated.

Any plagiarism or collusion may result in disciplinary action in addition toZERO mark being awarded to all involved.

2. TMA 1 covers topics from Unit 1 and Unit 2.

3. No need to submit your TMAs to Turnitin.

4. Submit your TMA1 file through the Online Assignment Submission(OAS) system.

5. The total marks for TMA 1 is 100 % and it contributes 25 % towards your total grade. Marks will be awarded for correct working steps and answers.

6. TMA 1 contains five (5) questions.

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Question 1

(a). Expand and simplify the following

(i) 2 2(5 ) 2 2 ( 3 ) 5 x y x y x y x y

(ii)5 3

2 32 7( ) x y x y x y

(iii)

21 4 2 1 2

3 2 3

11 5 4

550

x y w y w x

x y w

(iv)2

2

3 95 2 25 4 p p p p

(v) 4

2

5 7

3

162

p

p p

[ 10 marks ]

(b). Evaluate the following arithmetic expressions:

(i) 3 29 2 3 8

(ii) 3

2 35 5 4 6 3 7 ( ) ( )

(iii)5 5

3 1 22 8

(iv) 3 2 1 24 4 4 4 4 4

(v)5 1 3 2 9

36 4 8 3 16

[ 10 marks ]

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Question 2

(a) Convert the following fraction to be in percentage (correct up to 2 decimal

places)

(i) 59

[2 marks]

(ii) 1335

[2 marks]

(b) (i) A 64-inch television is listed at RM7199. On the day of the 21 st

anniversary of the electrical shop, a discount of 21% is given, what is its

price after the discount? (Correct to the nearest 10 cents) [3 marks]

(ii) Patty paid RM1512 for a few electrical items at a discount of 22%,

what was the original price of the items? (Correct to the nearest 10 cents)[3 marks]

(iii) A display card on a pair of shoes showed Normal price: RM321.00;

Discounted price:RM123.00, find the percentage discount correct to 2

decimal places. [4 marks]

(c) The annual income of Jennifer in the year 2012 was RM 38,400. In 2013,

her monthly salary is RM3430.40.

(i) What is the monthly percentage increment from 2012 to 2013?

(ii) If she will receive the same rate of increment in 2014, what would be

her salary in 2014, correct to the nearest 10 cents? [ 6 marks ]

Question 3

(a) Find the domain and range of the following functions and explain briefly:

(i) ( ) 5 12 f x x

(ii)5

( )2 4

f x x

(iii) ( ) 2 6 f x x [ 6 marks ]

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(b) Given 5 2( ) , 33 x

f x x x

and ( ) 6 3 g x x . Find

(i) ( )(0) f g [2 marks]

(ii) 2( )3

f g

[3 marks]

(iii) ( 2) g f

[3 marks]

(c) A function, ( ), P x is defined as follows:

2

8 3

( ) 2 1 3 8

3 8

x

P x x x

x x

Find the following:

(i) (2) P

(ii) (5) P

(iii) (12) P [6 marks]

Question 4(a) A bicycle manufacturing company has a fixed cost of production of

RM1,200,000 per year. The production cost of bicycles is given by thefunction ( ) 82 2500 f x x where x is the number of bicycles produce in ayear. It is intended that the sale price of each bicycle is RM375.

(i) Write a cost function, ( )C x , for the company. [2 marks]

(ii) Write the gross profit function, ( ) P x , for the company. [2 marks]

(iii) Find the minimum number of bicycles the company must produce

and sell in order to make a profit. [2 marks]

(b) Suppose the value of a landed property (in thousands of RM) after t years

is given by 0.7300000 1500 t V t e . Find(i) the initial value of the property. [2 marks]

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(ii) the value of the property after 5 years, correct to the nearest

10 cents. [2 marks]

(iii) the percentage of profit gained if the owner sells the property

after 5 years.

[use e = 2.7183 or use shift e on the calculator ]

[3 marks]

(c) In manufacturing a car, the initial cost is RM 12000 and all other

additional cost is RM 42000 per unit produced. If the car is priced at

RM70000, and x units of the car is sold in the month of December 2012,

Express the cost function, C(x) (in RM); revenue function, R(x) (in RM)

and profit function P(x) (in RM) as a linear function in x . [6 marks]

Question 5

(a) Express the following in the format of 2( )a x b c where , ,a b c are

constants using completing the square method.

(i) 2 10 15 x x [2 marks]

(ii) 22 8 3 x x [3 marks]

(b) Solve the following quadratic equations by factorisation:

(i) 2 5 24 0 x x [2 marks]

(ii) 22 7 15 0 x x [2 marks]

(c) Solve the equation 22 11 7 0 x x by using formula method. [2 marks]

(d) Find the solutions for the following quadratic equations:

(i) 2 7 10 0 x x [2 marks]

(ii) 22 7 15 0 x x [2 marks]

(e) A large corporation has found out that the profit/loss of its operations can

be estimated by 2( ) 110 3000Q x x x , where x is the number of units of

the products manufactured. Determine the least number of units of the

product that is required to be produced so that the corporation can make a

profit. [5 marks]