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ITM111S - INTRODUCTION TO MATHEMATICS - 1ST OPP - NOVEMBER 2023 |
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fr.-UnAmlBIA UnlVERSITY
OF SCIEnCEAnOTECHnOLOGY
FacultyofHealthN, atural
ResourceasndApplied
Sciences
Schoolof NaturalandApplied
Sciences
Departmentof Mathematics,
Statisticsand ActuarialScience
13JacksonKaujeuaStreet
PrivateBag13388
Windhoek
NAMIBIA
T: •264 612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION : Bachelor of Technology: Geo-Information Technology, Bachelor of
Human Resources Management, Bachelor of Marketing, Bachelor of Transport
Management, Bachelor of Business Administration, Bachelor of Agricultural Management,
Bachelor of Horticulture
QUALIFICATION CODE: 07BGIT,07BHRM,07BMAR, 07BBMN,
27BAGA,07BTRM,07BHOR,07BPSM,04CIPM,07BRAR,07BENT
LEVEL:5
COURSE: INTRODUCTION TO MATHEMATICS
(BUSINESSAND MANAGEMENT)
COURSECODE: ITMlllS
DATE: NOVEMBER 2023
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER: Ms A. SAKARIA, Ms K. DAVID, Ms P. NGHISHIDIVALI, Ms Y. NKALLE
MODERATOR: Mr I. NDADI
INSTRUCTIONS
1. Answer ALLthe questions on the separate answer sheet.
2. Please write neatly and legibly.
3. Do not use the left side margin of the exam paper. This must be allowed for the examiner.
4. QUESTION 1 of this question paper entail multiple choice questions with options A to D.
Write down the letter corresponding to the best option for each question.
5. QUESTION 2 indicate whether the given mathematical statements are true (T) or false (F).
6. QUESTION 3 show clearly all the steps used in the calculations.
PERMISSIBLE MATERIALS:
1. Non-Programmable Calculator without a cover.
This paper consists of 4 pages including this front page
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QUESTION 1 [30 MARKS)
Write down the letter corresponding to the best option for each question in the answer
booklet/sheet provided.
1.1 Factorize the expression: xp+xq+py+qy.
[3]
A. (x+y)(p+q) B. (x+p)(q+y) C. (x-y)(p-q) D. (x- p)(q-y)
1.2 Tulonga is 3 years older than Tuma, who is 3 years older than Uveni. If their combined
Age is 15 years, how old is Uveni?
[3]
A. 15years
½r2
1.3 Simplify ( x iflli
B. 8 years
C. 2 years
D. 5years
[3]
A.4
B. 64
C. 256
D.8
1.4Givensets A={l,2,3,7,11},and B={3,5,7,ll,12} ,find (AnBr.
[3]
A.(AnBr ={1,2,5,12}
B. (AnBt ={3,7,11}
C.(AnBt = {1,2, 7,11}
D.(AnBr ={3,5,12}
1.5 The values of x, y and z in the Venn diagram below are:
[3]
1200
z
A. x = 750,y = 400 and z = 150
B. x=150,y=650 and z=l00
C. x = 320,y = 200 and z = 220
D. x=650,y=100 and z=l50
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1.6 There were a certain number of coffee mugs in the shop. Theo bought -5 of the mugs
and Johr bought -1 . Now there are 150 mugs left in the shop. How many coffee
5
Mugs did Theo buy? '
[3]
A. 150
B. 375
C. 225
D. 75
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1.7 Thefactorsfortheexpression 3x2 +14x-5 are:
A. (3x+I)(x-5) B. (3x-l)(x+5)
C. x(2x-3x-5)
[3]
D. (x-1)(3x-5)
1.8 The prime decomposition of 42 is:
A. 3x 2 x 5
B. 2 x 3 x 7
(. 3 X 14
1.9 The expressi.on-+3-+--2- 2 2 s1· mpI1T,es to:
4 553
A. -4- 5
16
B. 22-
24
C. 2~
12
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1.10 Determine the sum of the series I,{2n+3).
n~I
A.45
B. 90
C. 49
[3)
D. 2 x 21
(3)
D. 1- 1
12
[3)
D. 47
QUESTION 2 [10 MARKS]
Indicate whether the given mathematical statements are true (T) or false (F)
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2.1 The expression JneR simplifies to x2 .
[2)
2.2 The expression 16p 4 -8Iq8 can be factorised fully as 4p 2 -9q 4 •
[2)
2.3 (loga)(logb)isequalto log(a+b).
[2]
2.4 The discriminant of the equation 2x 2 -4x + 9 =0 is negative.
[2]
2.5 If A is a 2 x 3 matrix and Bis a 3 x 2 matrix, then we can calculate AB .
[2]
QUESTION 3 (60 MARKS] (Clearly show all your work)
3.1 Expand and simplify 8(3h-4)-5(h-2).
[4)
3.2 Solve the following pair of simultaneous equations using Cramer's rule.
x=--5+3y and 7y=4x-11
[6]
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3.3 After a price decrease of 8.5%, a television set costs N$2640.00. What was the price
before the decrease?
[4}
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3.4 A factory requires 42 machines to produce a given number of articles in 63 days.
How many machines would be required to produce the same number of articles in
54 days?
[4)
(--22 3.5 Let A=
~} find:
3.5.1 A2
[4]
3.5.2 Calculate A-1(The inverse of A).
[6]
3.6 Find the numerical values of the letters in the Matrices,
~s)=(: -2( p
-1
~4)-2G
:)
[7]
3.7 The progression 39;34;29;24 ... is given.
3.7.1 Identify the common difference.
[2]
3.7.2 What is the 9th term of the progression?
[3]
3.7.3 Find the sum of the pt 20 terms of the progression.
[4]
3.7.4 What term of the progression above has the value -56?
[4)
3.8 In a survey of 200 households regarding the ownership of desktop and laptop
computers, the following information was obtained:
120 households own only desktop computers, 10 households own only laptop
computers, and 40 households own neither desktop nor laptop computers.
a) Draw a Venn diagram and show the information as given above on the Venn
diagram.
[SJ
b) How many households own both desktop and laptop computers?
[3]
3.9 Find the simple interest payable on a loan of N$170000 at 6.75% p.a. at
the end of 9 years.
[4)
END OF EXAM/NATION QUESTION PAPER
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