 |
ITM111S - INTRODUCTION TO MATHEMATICS - 2ND OPP - JULY 2023 |
|
|
1 Page 1 |
▲back to top |
nAmlBIA UnlVERSITY
OF SCI En CE Ano TECH n OLOGY
FACULTYOF HEALTH,NATURALRESOURCESAND APPLIEDSCIENCES
SCHOOLOF NATURALAND APPLIEDSCIENCES
DEPARTMENTOF MATHEMATICS, STATISTICSAND ACTUARIALSCIENCE
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 NAME: INTRODUCTIONTO MATHEMATICS
(BUSINESSAND MANAGEMENT}
COURSE CODE: ITM111S
SESSION: JULY 2023
PAPER: THEORY
DURATION: 3 HOURS
MARKS: 100
SUPPLEMENTARY/ SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER(S}
Ms A. SAKARIA, Ms K. DAVID, Ms P. NGHISHIDIVALI, Ms R. KATALE,
Mr A. MPUGULU, Mr F. NDINODIVA, Mr B. OBABUEKI
MODERATOR: Mr T. KAENANDUNGE
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}
II Page
|
|
2 Page 2 |
▲back to top |
QUESTION 1 [30 MARKS)
Write down the letter corresponding to the best option for each question in the answer
booklet/sheet provided.
1.1 Evaluate: log2 16+ log3 27 + log 1.
[3]
A. 3
B. 3
C. 7
D. 8
1.2 What statement does the shaded region represent?
CT>
A. Ac nB
B. AnBc
C. AuBc
[3]
D. AcuB
1.3 Find the Lowest Common Multiple {LCM) of the numbers 255,105and 90.
[3]
A. 5355
B. 255
C. 1025
D. 10710
I
2
1.4 Simplify ( )-
[3]
A.- 1
B. 2
C.
2
1.5 Given vector A = (-2 9) , find 2A,
D.- 1
16
[3]
A. (-4 -9)
B.(4 18)
C. (-4 18)
D. (-18 -4)
2-Jsf 29 1.6 If (3+
=+
then, what is the value of k?
[3]
A. 12
B. 29
C. 6
1.7 Expressthe statement "5 more than the product of 3 and a number" in terms if x. [3]
A. 5x-3
B. 3x + 5
C. 3 - 5x
D. 3x(5)
21Page
|
|
3 Page 3 |
▲back to top |
1.8 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. Work out
the length of the trench 1 worker could dig in 1 day?
[3]
A.4m
B. 3m
C. 0.33m
D.6m
1.9 Let sets A= {l, 2, 3} and B ={3,4, 5} . Find the symmetric difference A tfJB.
[3]
A. {1,2}
B. {1,2,4,5}
C. {4,3}
D. {2,5,1,4,3}
L( n). 5
1.10 Determine the sum of the series
1+
n=I
A. 6
B. I 7
C. 20
[3]
D. 25
QUESTION 2 (10 MARKS]
Indicate whether the given mathematical statements are true (T) or false {F)
2.1 The number 0.5lxl0- 3 is in standard form.
[2]
3
2.2 The expression Inell simplifies to x 2 .
[2]
2.3 The expression 16p 4 -8 lq8 can be factorised fully as 4p 2 -9q 4
[2]
2.4
[2]
2.5 log(x2 )=(1ogx)2
[2]
QUESTION 3 (60 MARKS] (Clearly show all your work)
3.1 Use Cramer's Rule to solve the following linear equations:
[S]
x+2y=-11 and -2x+y=-13
J ~l] ~ll 3.2 If matrices M =[_:
N =[ and P =[~4
find.
3.2.1 MN
[4]
3.2.2 p- 1 (The inverse of P)
[6]
3.2.3 M-7P
[4]
31Page
|
|
4 Page 4 |
▲back to top |
3.3 Among the 133 students {S) at a school, 44 take Geography {G), 48 take Biology (B),
32 take Mathematics (M), 8 take Geography and Biology, 9 take Geography and
Mathematics, 7 take Biology and Mathematics. 30 students take none of the three
subjects while 3 take all three subjects.
3.3.1 Use a Venn diagram to present the information given above.
(5)
3.3.2 Find the number of students who take geography or biology.
(2)
3.3.3 Find the number of students who take only Mathematics.
(2)
3.3.4 Find the number of students who take mathematics but not geography.
(2)
3.4 Given that the first term of the geometric progression is 5 and the sixth term is 1215:
3.4.1 What is the common ratio?
(4)
3.4.2 Find the 10th term.
(5)
3.5 How many terms are there in the progression, 42;35; 28; 2 l ... ;-336?
(6)
3.6 Timo wishes to take a loan at an annual simple interest rate of 14.5% for 7 months. He is
told that he will have to pay back the sum of N$5422.92 at the end of the 7th month.
Calculate the loan Timo wishes to take?
(5)
3.7 EvaIuate t he foIIowi.ng wi.t hout us.ing a caIcuIator,
(6)
2-v3
2x2 -2x X 2 -X
3.8 Simplify the algebraic fraction completely ----
(4)
2x + 2 x+l
END OF EXAMINATION QUESTION PAPER
41Page