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ITM111S - INTRODUCTION TO MATHEMATICS - 2ND OPP - JANUARY 2025 |
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nAmlBIA UnlVERSITY
OF SCIEnCEAno
FacultyofHealthN, atural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuarialScience
13JacksonKaujeuaStreet
PrivateBag13388
Windhoek
NAMIBIA
T: +264612072913
E: msas@nust.na
W: www.nust.na
QUALIFICATION: Bachelor of Agriculture, Bachelor of Business Management, Bachelor of
Horticulture, Bachelor of Marketing, Bachelor of Natural Resources Management,
Bachelor of Entrepreneurship, Bachelor Regional and Rural Development, Bachelor of
Public Management, Bachelor of Procurement and Supply Chain Management, Bachelor
of Transport Management, Bachelor of Human Resources Management
QUALIFICATION CODE: 07BAGA, 07BBMN, 07BHOR,07BMAK,
07BNRS,07BOEN, 07BORR, O7BPMA, 07BPSM, 07BRAR,
07BTRA, 07HRM
LEVEL:5
COURSE:INTRODUCTION TO MATHEMATICS (BUSINESS AND
MANAGEMENT)
COURSECODE: ITM111S
DATE: JANUARY 2025
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
SECOND OPPORTUNITY/SUPPLEMENTARY EXAMINATION: QUESTION PAPER
EXAMINER: Ms K. DAVID, Ms Y. NKALLE,Ms H. WILHELM, Ms P. NGHISHIDIVALI
MODERATOR: Ms A. SAKARIA
INSTRUCTIONS:
1. Answer ALL 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. No books, notes and other additional aids are allowed.
5. Mark all answers clearly with their respective question numbers.
PERMISSIBLE MATERIALS:
1. Non-Programmable Calculator
This paper consists of 4 pages including this front page.
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SECTION A: MULTIPLE CHOICE AND TRUE/ FALSE
[30 MARKS]
QUESTION 1: MULTIPLE CHOICE
[20 MARKS]
Write down the letter corresponding to the best option for each question in the answer
booklet/sheet provided.
1.1. Which of the following numbers is NOT a composite number?
[2]
A. 6
B. 7
C. 8
D. 9
1.2. The product of two consecutive even numbers is 12 more than the square of the
smaller number. Find the smaller number.
[2]
A. 8
B.6
C.12
D.4
1.3. A proper fraction is recognized by:
[2]
A. A numerically smaller numerator and larger denominator
B. A numerically lager numerator and smaller denominator
C. A numerator equals to the denominator
D. All of the above
1.4. Find the Highest Common Factor {HCF}of the numbers 255, 105 and 90.
[2]
A. 45
B.3
C.5
+ - 1.5.
Simplify the expression - -y42 - -y4 - -y12
3
y
D. 15
[2]
A.
---y-52
1
y
-5-7
B.-2y-
y
C. 2y
D.--y-21-2y
1.6. Which of the following is a linear equation
A. 3x 2 + 4
B. 2x - -5 = 3
2
C. -1+ 7 = 4x
X
[2]
D. x(x + 2)
1.7. Which of the following surds is in its simplest form?
[2]
A. 2m
B.v16
c.-/98
D. 3v'12
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.
[2]
A. 4m
B. 3m
C. 0.33m
D. 6m
Introduction to Mathematics (ITM111S)
2nd Opportunity Examination January 2025
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1.9. Determine the value of x that makes the ratio x: 9 the same as the ratio 15: 45. [2]
A. X = 3
B. X = 5
C. X = 6
D. X = 9
1.10. The shaded region on the venn diagram below represents:
[2]
A. AU C
B. (An C) - B
C. (Au C)C
D. (Ancy
QUESTION 2: TRUE/FALSE
[10 MARKS)
Evaluate the statements and select whether the statement is True (T) or False (F). Write the
correct answer next to the corresponding number on your ANSWER SHEET.
2.1. Any negative number raised to a power of a positive even number is negative. [2]
2.2. loga (x + y) = logax + logay
[2]
2.3. The expression (x + y) 2 is equivalent to x 2 + y 2
[2]
= 2.4. Given two sets A and B, A EBB (A - B) u (B - A)
[2]
= = 2.5. If A and Bare matrices of which B A- 1 , then AB BA
[2]
SECTION B: STRUCTURED QUESTIONS
QUESTION 3:
[70 MARKS]
3.1. Evaluate the following expressions without using a calculator:
3.1.1.
2
5
of
5
6
+
83 X
2
1
3
[5]
3.1.2. 4--/2 + 5.../98+ 3-v'SO
[5]
3.1.3. log 5 25 - log 25 5 + log 10 1
[5]
3.2. Round the following numbers to the nearest value indicated in brackets:
3.2.1. 0.3757
(to 3 decimal places}
[1]
3.2.2. 4195.0124
(to 2 significant figures}
[1]
Introduction to Mathematics {ITM111S)
2nd Opportunity Examination January 2025
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3.3. Solve the following simultaneous equations using the elimination method.
[4]
3x - 2y = 14
Sx - 2y = 6
3.4. Factorize the following expressions:
3.4.1. 3xy + 6x + 2y + 4
[4]
3.4.2. 25a 4 - 49b 2
[3]
3.5.
3.5.1.
3.5.2.
3.5.3.
A survey was conducted among 250 people (S} regarding their preferences for three
sports: football (F}, basketball (B), and tennis (T}. The results showed: 120 people like
football. 90 people like basketball. 100 people like tennis. 40 people like both football
and basketball. 30 people like both basketball and tennis. 50 people like both football
and tennis. 20 people like all three sports.
Draw a Venn diagram to represent the information given above.
[6]
Find how many people like only football, basketball only and tennis only.
[3]
Find how many people do not like any of these sports.
[2]
3.6. Use Cramer's rule to find the values of x and y in the following system of linear
equations:
[5]
3x + 2y = 7 and Sx - 4y = -3
3.7. Determine the value of x,y, and z in the following matrix equation:
[5]
!], -2] 3.8. Let A=[~ and B= [~ 3 I
3.8.1. A- 1
[4]
3.8.2. AB
[4]
3.9. An arithmetic progression is given by 4m, (4m + 6), (4m + 12), .... If the 8th term is
58, find the value of m.
[SJ
3.10.
Bank Windhoek offers 10% interest on a savings account. If Tom deposits N$20 000
in the account, calculate the interest and the total amount in the account after 3 years
if interests are compounded semi-annually.
[4]
3.11. Determine the sum of the following series:
3.11.1. Ii=s 2k
[2]
3.11.2.
"'2
L.,m=l--
(-l)m
m
[2]
END OF QUESTION PAPER
Introduction to Mathematics (ITM111S)
2nd Opportunity Examination January 2025
4