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ITM111S - INTRODUCTION TO MATHEMATICS - 2ND OPP - JANUARY 2024 |
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nAml BIA UnlVERSITY
OF SCIEnCE AnOTECHnOLOGY
FacultyofHealthN, atural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
Statisticsand ActuarialScience
13JacksonKaujeuaStreet T: +264612072913
PrivateBag13388
E: msas@nust.na
Windhoek
W: www.nust.na
NAMIBIA
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,078PSM,04CIPM,07BRAR,07BENT
LEVEL:5
COURSE: INTRODUCTION TO MATHEMATICS
(BUSINESSAND MANAGEMENT}
COURSECODE: ITMlllS
DATE: JANUARY 2024
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
SUPPLEMENTARY/ SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER: Ms A. SAKARIA, Ms K. DAVID, Ms P. NGHISHIDIVALI, Ms Y. NKALLE
MODERATOR: Mr I. NDADI
INSTRUCTIONS
1. Answer ALL the 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 Expand and simplify the expression ( x-3)2 -x 2 +6x
[3]
A. 12x+9
B. -12x+9
C. 12x-9
D. 9
1.2 Evaluate log 2 16 + log3 27 + log 1 .
A. 4
B. 3
C.7
½4 1.3 Simplify x 2 x .jy x
I
x y2.
[3]
D. 8
[3]
A.y.Jx
I
B. xy2
I
C. xy"i
=~.) 1.4 Find the determinant of the matrix, (
A. -6
B.I
C. 7
D. x 4 y
[3]
D.-1
1.5 What is the Lowest Common Multiple (LCM) of 30 and 42?
A. 6
B. 210
c. 420
1.6 The values of P, Q and R in the Venn diagram below are:
S=S60
[3]
D. 1260
[3]
R
A. P = 160,Q = 200 and R = 200
C. P = 90, Q = 11 o and R = 200
B. P = 130,Q = 200 and R = 320
D. P = 90, Q = 11o and R = 320
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1.7 The prime decomposition of 1287 is:
A. 33x3xl3
B. 99x13
l. 1.8 Factorize the expression -2x 3 -4x 4 + x2
2
[3}
D. 9xllx13
[3}
= 1.9 The equation, x 2 - x-12 0 has the solutions:
A. x=4,x=-3 B. x=-4,x=-3
c. x=-2,x=-6
[3}
D. x=6,x=-2
L3
1.10 Determine the sum of the series 2i.
n=I
A. 48
B. 24
C. 6
[3}
D. 12
QUESTION 2 (10 MARKS]
Indicate whether the given mathematical statements are true (T) or false (F)
½. 2.1 The expression J.neN simplifies to x
[2]
2.2 The expression 16p 4 -8lq
8
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 =O is negative.
[2]
2.5 If A is a 2x3 matrix and Bis a 3x 2 matrix, then we can calculate AB .
[2]
QUESTION 3 (60 MARKS) (Clearly show all your work)
3.1 Use Cramer's rule to solve for x and y the following: 2x+ y = -Land 4x-3y=8. [7]
3.2 Solve the inequality -4x>-x-2<2x+l and represent your solution on a number
line.
[6]
3.3
S.imp 1I·yf t he expressi.on -X-2'2y'---x3~-x4-y4
[5]
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3.4 Mr. Goagoseb has 48 goats and Mrs Namises has 60 goats. They decide to share
1296 kg of animal feed between them, in the ratio of the numbers of their animals.
How many kilograms of animal feed does Mrs. Namises get?
[3]
3.5 The value of the letters, a and b in the matrices given below are:
2(-a4)-a(2S)=(-144)
[6]
a3
4 -b
-4 9
3.6
J Given the
matrices
X
=(
4
-1
3
2
1] y --( -2
3
-1
find:
3.6.1 2X-Y
[4]
3.6.2 XY
[4]
3.7 Given S ={a,b,c,d,e,f}, A= {a,c,d,e} , B= {a,b,e} find:
3.7.l Be uAc
[4]
3.7.2 AuB
[3]
3.8 Of the 60 students(S) in class, 44 can spell the word 'Parallel' (PA), 22 can spell
'Pythagoras' (PY) and 14 can spell neither.
3.8.1 Present this information in a Venn diagram.
[4]
3.8.2 How many students can spell both words?
[2]
3.8.3 How many students can spell Parallel or Pythagoras?
[2]
3.9 Given the progression; 4;12;36;108; ...
3.9.1 Find the seventh term of the progression above.
[3]
3.9.2 The sum of the first 5th terms of the progression above.
[4)
3.10 Calculate the amount payable for a loan of N$2000 for 3 years at the rate of
10% p.a. compounded semi-annually.
[SJ
END OF EXAMINATION QUESTION PAPER
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