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ITM111S - INTRODUCTION TO MATHEMATICS - 2ND OPP - JAN 2023 |
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nAm I BI A un IVERS ITY
0 F SCIEn CE An D TECHn OLOGY
FACULTY OF HEALTH, APPLIED SCIENCESAND NATURAL RESOURCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
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,07BBAD,27BAGR,07BTRM,07BHOR
NQF LEVEL: 5
COURSE NAME: INTRODUCTION TO MATHEMATICS
(BUSINESSAND MANAGEMENT)
COURSE CODE: ITMlllS
DATE: JANUARY 2023
DURATION: 3HOURS
PAPER :THEORY
MARKS: 100
SECOND OPPORTUNITY /SUPPLEMENTARY EXAMINATION QUESTION PAPER
EXAMINER
Ms A. SAKARIAM, s Y. NKALLE, Ms P. NGHISHIDIVALI, Mr B. OBABUEKI,
Mr F. NDINODIVA
MODERATOR:
Mr I. NDADI
INSTRUCTIONS
1. Answer ALL the questions in the answer sheet.
2. 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.
3. For QUESTION 2 indicate whether the given mathematical statements
are true (T) or false (F).
4. QUESTION 3 show clearly all the steps used in the calculations.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 4 PAGES (Including this front page)
~1~
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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
ef6s61J Evaluate
[
-105
3.5
3
. and leave your answer correct to 3 significant figures. [3]
A. 27
B. 19683
C. 19700
D. 197
1.2 An AP (Arithmetic Progression) is 8, 5, 2, _ 1,... Find the 50 th term.
[3]
A. 299
B. -139
C. -380
D. 100
1.3 Find the Lowest Common Multiple (LCM) of the numbers 255,105 and 90
[3]
A. 5355
B.255
c. 1025
D.10710
1.4 A group of workers is digging a trench. When there are 6 workers, the length of the
trench they can dig is 18 meters in 1 day. All the workers dig at the same rate.
1.4.1 Work out the length of the trench 1 worker could dig in 1 day.
A.4m
B.3m
C. 0.33m
[3]
D.6m
1.4.2 A team of workers digs 12 meters in 1 day. How many workers are in this team? [3]
A. 3
B. 2
C. 4
D.6
1.5 Evaluate log 2 16 + log 3 27 + logl •
[3]
A. 4
B.3
C. 7
D. 8
1.6 Kiito earned N$1450 last month and spent of the income on food and ..!_
3
5
of the remaining amount on transport. How much did he spend on transport?
[3]
A. N$290.00
B. N$90.00
c. N$966.67
D. N$96.67
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1.7 Five years ago, a man was seven times as old as his son. In five years time, the man
will be three times as old as his son. How old are father and son now?
[ 3)
A. Father is 40 years old, and the son is 5 years old.
B. Father is 40 years old, and the son is 10 years old.
C. Father is 96 years old, and the son is 13 years old.
D. Father is 91 years old, and the son is 8 years old.
1.8 Factorize the expression xs- xt- ys +yt
[3]
A. (x+ y)(s-t)
B. (x-y)(s+t)
C. (x+ y)(s+t) D. (x-y)(s-t)
L(5
1.9 Determine the sum of the series
1+n).
n=I
A. 6
B. I 7
C. 20
[3]
D. 25
QUESTION 2 [10 MARKS]
Indicate whether each of the given mathematical statements is true (T) or false {F)
2.1 The number 0.5lxl0- 3 is in standard form.
[2]
)3 2.2 The expression ( x + 2 simplifies to x3 +23 •
[2]
2.3
log5
4
=
log 10
log10
4
5
[2]
2.4 The discriminant of the equation 2x2 -4x+9 =0 is negative.
[2]
2.5 If A and B are both 2 x 3 matrices then, we can calculate AB.
[2]
QUESTION 3 [60 MARKS] {Clearly show all your work)
3.1 Let S ={21,22,23,24,25,26,27,28,29,30,31}, A= {21,22,23,26,27,30}.
B={22,23,26,29,30}, C={23,25,27,29,30} find:
3.1.1 Bu( AnC)
[4]
3.1.2 AcnB
[4]
3.1.3 A-C
[2]
3.1.4 AffiB
[6]
3.1.5 The number of elements in the power set P(BnC)
[3]
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2), -5) (0 3.2
Let A= (-3
-1
3
B=(-3
-4
-1
and C= 1 ~) , find:
3.2.1 A-C
[4]
3.2.2 B2
[4]
3.2.3 A-I
[6]
3.3 Determine the type of solution for the quadratic equation 2x(x+ 1)+2x =42 and
then solve the equation by factorization.
[7]
3.4 Solve the inequality, 3x-3;?:x+5;?:2x-I and show the results on a number line. [6]
3.5 Copy the Venn diagram below and shade the region Ac n( BuC).
[3]
3.6 The maturity value of a loan of N$350000.00is N$402500.00. Calculate the annual
simple interest rate if the loan takes 5 years to mature.
[SJ
3.7 What sum of money will N$350.00grow to if it is invested for 5 years at 9% per
annum compounded semi-annually?
[6]
END OF EXAMINATION QUESTION PAPER