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ITM111S - INTRODUCTION TO MATHEMATICS - 1ST OPP - JUNE 2023 |
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nAm I BIA un IVE RSITY
OF SCIEnCE Ano TECHnOLOGY
FACULTYOF HEALTH,NATURAL RESOURCESAND APPLIEDSCIENCES
SCHOOLOF NATURALAND APPLIEDSCIENCES
DEPARTMENT OF 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: JUNE 2023
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
EXAMINER(S)
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
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.
II Page
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION 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 What is the solution to the following linear equation?: _!_(x+5)- 2x = O
[3]
4
3
A. 1
B. -1
C. 23
D. 3
1.2 At present John is twenty years younger than Mary. In five years' time he will be half
Mary's age. How old is John now?
[3]
A. 35years
B. 55years
C. 15years
D. 20 years
5
a3bc-,
1.3 Simplify - 1 -2
[3]
a2b3
II
C.a 2b 5
=!!), 1.4 Given A= (1 2), B = ( ~) , and C = (
which one of the following matrix
calculations is not possible?
A.BC
B.AC
C. CB
[3]
D.C 2
1.5 Determine the value of n that makes the ratio n: 15 the same as the ratio 36: 90. [3]
A. n=5
B. n = 1350
C. n=lO
D. n=6
1.6 Write the number 0.03249 in standard form to 3 significant figures.
[3]
A. 3.24x 10-1
B. 3.24 X 10-2
C. 3.25 X 10-2
D. 3.25 x 10-3
1.7 Expressthe statement "nine more than three times a number" in terms of h.
[3]
A. 3h-9
B. 3(h-9)
C. 3(h+9)
D. 3h+9
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1.8 Factorize the expression 2ab 2 - abd - 2bc + cd
A. (2b-d)(ab-c)
B. (ab-c)(ab-c)
C. (2b-d)(ab+c)
[3]
D. (2b+d)(ab-c)
1.9 Which of the following statements is false?
A. {a,b,c} ={c,a,b}
B.{0} =0
C. {a,b} c {a,b,c}
[3]
D. Ac A
5
1.10 Determine the sum of the series I(2n+3).
ll=l
A. 45
B. 90
C. 49
[3]
D. 47
QUESTION 2 (10 MARKS)
Indicate whether the given mathematical statements are true (T) or false (F)
3
2.1 The expression lneN simplifies to x 2 .
[2]
2.2 The expression
16p4 -8lq
8 can be factorised
fully
as
4p 2 -9q
4
•
[2]
2.3 (loga)(logb) is equal to 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 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 Given the system of linear equations: x- 2y =0 and x - 5 =3 (y- 5) ,use Cramer's
rule to solve for x and y .
[7]
_Ix::;; 3.2 Solve the inequality 15::; 7
21 and represent your solution on a number
5
line.
[6]
2
3.3 Simplify the expression x + Jx- l O
[5]
x2 -4
3.4 Expand and simplify (ab-a2 )2-(a4 -2a3b)
[6]
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(! 3.5 Let A = 8 ~ 5) and B = (_ l ~ 7). Find:
3.5.1 AB
[4J
3.5.2 Calculate A-' (The inverse of A).
[SJ
3.5.3 ~A
[4J
2
3.6
JsJ+ Evaluate log5 (
.ifII log 11 without using a calculator.
[SJ
3.7 In a survey of 200 households{HO) regarding the ownership of desktop(D) and laptop
(L) computers, the following information was obtained:
120 households(HO) own only desktop(D) computers, 10 households own only
laptop(L) computers, and 40 households own neither desktop(D) nor laptop(L)
computers.
3.7.1 Present the information in a Venn diagram.
[SJ
3.7.2 How many households own both desktop and laptop computers?
[3J
3.8 The common difference in an Arithmetic Progression {AP) is 3. The 24th term is 74.
What is the first term?
[4]
3.9 Determine the sum to be invested for 4 years at 8% p.a. compounded semi-annually
to amount to N$3500 at the end of the investment period.
[6J
END OF EXAMINATION QUESTION PAPER
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