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ITM111S - INTRODUCTION TO MATHEMATICS - 1ST OPP - NOVEMBER 2024 |
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nAml BIA un IVERSITY
OF SCIEnCEAno TECHnOLOGY
FacultyofHealthN, atural
ResourceasndApplied
Sciences
Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuariaSl cience
13JacksonKaujeuaStreet
Private Bag13388
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: NOVEMBER 2024
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
1sr OPPORTUNITY 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 5 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. Prime numbers are defined as:
[2]
A. Numbers divisible by 1, 2, and themselves
B. Numbers divisible only by 1 and themselves
C. Numbers divisible by any number
D. Numbers divisible by 2 and themselves
1.2. Which of the following is an example of an irrational number?
1
A. -2
B. 3.14
C. .../2
1.3. A mixed number consists of:
A. Only a whole number
B. A whole number and a proper fraction
C. A whole number and an improper fraction
D. Only an improper fraction
[2]
D. -5
[2]
1.4. Find the HCFof the numbers 24, 36, and 60.
A. 6
B.8
1.5. si·mp l'If y t he expressi.on -sxz + -3x
X
X
A. Sx 2 + 3
B. Sx + 1
C. 12
C. Sx + 3
[2]
D. 18
[2]
D. Sx + x
1.6. Which of the following is a polynomial of degree one
A. 3x 2 + 4 = Sx
= B. 2x - -5 3
2
c.-1+ 7 = 4x
X
1.7. Which of the following is a surd?
A. ../26
B.V4
C. -..fM
[2]
D. x(x + 2) = 3
[2]
D.1/27
Introduction to Mathematics (ITM111S)
1st Opportunity Examination November 2024
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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
1.9. Determine the value of n that makes the ration: 15 the same as the ratio 36: 90. [2]
A. n = 5
B. n = 1350
C. n = 10
D. n = 6
1.10. The shaded region on the venn diagram below represents:
[2]
A. A UB
B.A nB
C. (Au BY
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 ANSWERSHEET.
2.1.1. When solving inequalities, dividing or multiplying by a negative value reverses the
direction of the inequality sign.
[2]
= 2.2. (log 2 x) 3 3log 2 x
[2]
= 2.3. The discriminant of the quadratic equation 3x 2 - 4x + 1 0 is 2.
[2]
= 2.4. Given two sets A and B, A E9B (A - B) U (B - A).
[2]
2.5. If A and Bare matrices whose determinants are not equal to zero, then
(AB)- 1 = A- 13- 1
[2]
SECTION B: STRUCTURED QUESTIONS
QUESTION 3:
3.1.
3.1.1.
3.1.2.
Evaluate the following expressions without
-1of-+-x3l- 7
1
3
48
2
2--/3 + 3127+ frill
using a calculator:
[70 MARKS]
[5]
[5]
[5]
Introduction to Mathematics (ITM111S) ist Opportunity Examination November 2024
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3.2. Round the following numbers to the nearest value indicated in brackets:
3.2.1. 2.2731
(to 3 decimal places)
[1]
3.2.2. 4090.0124
(to 2 significant figures)
[1]
3.3. Solve the following simultaneous equations using the substitution method.
[4]
y = 3x -1
2x + 4y = 10
3.4. Factorize the following expressions:
3.4.1. 6mx - 3nx + 2my - ny
[4]
3.4.2. 9x 2 - 25y 2
[3]
3.5. Three companies A, 8, and C, produce smartphones in a city. A survey of 200 people
was conducted to find out their preferences. The results showed the following: 70
people own a smartphone from Company A. 80 people own a smartphone from
Company 8. 90 people own a smartphone from Company C. 30 people own
smartphones from both Company A and Company 8. 40 people own smartphones
from both Company 8 and Company C. 20 people own smartphones from both
Company A and Company C. 10 people own smartphones from all three companies,
A, 8, and C.
3.5.1. Draw a Venn diagram to represent the information given above.
[6]
3.5.2. Calculate the number of people who own smartphones only from: Company A,
Company 8, Company C.
[3]
3.5.3. Find the number of people who do not own smartphones from the three companies.
[2]
3.6. Use Cramer's rule to find the values of x and y in the following system of linear
equations:
[5]
3x + 4y = 7and5x - 2y = 3
y, 3.7. Determine the value of x, and z in the following matrix equation:
[5]
[; ~]+ [! y:z]= [~ ~]
-1] [-1 -2] 3.8. Let A= [~ 4 3 , and B = _ 3 -4,
3.8.1. A-1
[4]
3.8.2. B2
[4]
Introduction to Mathematics {ITM111S)
1st Opportunity Examination November 2024
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3.9. A progression is given by 3m, (3m + 5), (3m + 10) ... If the 15 th term is 98, find the
value of m.
[5]
3.10.
FNB is offering 10% interest on an account. Ribelius makes an initial deposit of
N$20 000 in the account. Calculate the interest and the total amount in the account
after 5 years if the bank uses compound interest compounded quarterly.
[4]
3.11. Determine the sum of the following series:
3.11.1. L~=5l S
[2]
3 (-1)n+1
3.11.2. Ln=l-- n
[2]
END OF QUESTION PAPER
Introduction to Mathematics (ITM111S)
1st Opportunity Examination November 2024
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