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ITM511C-INTRODUCATION TO MATHEMATICS 1A-2ND OPP- NOV 2024 |
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nAmlBIA
UnlVERSITY
OF SCIEnCE
TECHnOLOGY
HP-GSB
HAROLDPUPKEWITZ
GraduateSchoolof Business
FACULTY OF COMMERCE; HUMAN SCIENCES AND EDUCATION
HAROLD PUPKEWITZ GRADUATE SCHOOL OF BUSINESS
QUALIFICATION : DIPLOMA IN BUSINESS PROCESS MANAGEMENT
QUALIFICATION CODE: 06DBPM LEVEL: 6
COURSE CODE: ITM511 C
COURSE NAME: INTRODUCTION TO
MATHEMATICS IA
·SESSION: NOVEMBER 2024
DURATION: 3 HOURS
PAPER: SESSION 2
MARKS: 100
SECOND OPPORTUNITY EXAMINATION -QUESTION PAPER
EXAMINER(S) Ms. H.Y. NKALLE
MODERATOR: Ms. A.N. SAKARIA
INSTRUCTIONS
1. Answer ALL the questions.
2. Write clearly and neatly.
3. Number the answers clearly.
PERMISSIBLE MATERIALS
1. Examination paper
2. Examination script
3. Non-Programmable Calculator
THIS QUESTION PAPER CONSISTS OF 4 PAGES (INCLUDING THIS FRONT
PAGE)
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SECTIONA
Question 1 (45 Marks, each question 3 Marks)
1.1 The highest Common Factor of 255, 105 and 90 is:
A. 45
B.3
C.5
D.15
1.2 The factors of the expression -ai + 2x 2 - aix + 2x are:
A. (2x - ai)(x + 1) B. (x - 1)(2x + ai) C. ai(2x 2 - 2x - 1)
D. (x - 1)(2x - ai)
1.3 Three friends, Alex, Brenda and Charles decided to buy a house. Alex pays! of the cost,
3
Brenda
pays
2
5
of
the
cost
and
Charles pays the
rest.
1.3.1 What fraction of the cost does Charles pay?
A.~
B.2.
c.~
12
12
15
1.3.2 Charles pays N$ 8380 less than Brenda. Calculate the cost of the house.
A. N$ 20950
B. N$ 628500
C. N$ 46090
D. N$ 62850
1.4 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 pace.
1.4.1 Determine the length of the trench 1 worker could dig in 1 day.
A. 4m
B. 3m
C. 0.33m
D.6m
1.4.2 A group of workers digs 12 meters in 1 day. How may workers are in this group?
A. 3 workers
B. 2 workers
C. 4 workers
D. 6 workers
6x- 4 2x 3
1.5 The expression ax-3 Simplifies to:
A.
3
-4
2x
B.--12sxx--
12
3
c.-2x23
D.-3x 2
2
1.6 The average of two number is 7, and three times the difference between them is 18.
What are the numbers.
A. 52 and 24
B. 7 and 7
C. 10 and 4
D. 8 and 6
1.7 Express
a-lx
1
4-y,:a:.-, 8
.
in
the form
ax.
C. a3
D. a'Vs.
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1.8 Expand and simplify the expression (x - xy) 2 - x 2 - x(-2xy).
C. X - xy
1.9 If x and x 2 + x are the first two terms of the Geometric Progression (GP}, determine the
common ratio of the progression.
A. x+ 1
B. -3
C.x-1
D. x 2 + 1
1.10 Given that of 380 students, 210 play soccer and golf, 260 play soccer and 60 play
none of the two sports. How many students play golf?
A. 270
B.60
C.120
D. 210
= 1.11 The solution of the quadratic equation 4x 2 - 1 0 are:
= = = = A. (2x + 1)(2x - 1) B. x 0 or x 1 C. x 4 or x 1
D. x = 1/2 or x = -1/2
1.12 Find x if the determinant of[~
A. x = 1
B. x = 5
~] is equal to 5.
C. X = 4
D. X = 12
+ 1.13 Simplify (log 12 18 - log 12 3) log 12 2
A. 1.079
B.log 12 6
C. 1
D. log 12 9
SECTION B
QUESTION 2 [32 Marks)
2.1 Out of 600 students (S} taking the course, Introduction to Mathematics 1A (ITM511C}, it
was found that there are 220 male students (M}. It was further found that 20x students
qualified to write the June examination(E} of which Sx students are male. Only 5 female
students do not qualify to write the June Examination.
2.1.1 Show the information as given above on a Venn diagram.
[S]
2.1.2 Find the value of x.
[3]
2.1.3 Find the number of female students who qualified to write the June examination. [3]
2.2 Solve the following equations without using a calculator:
x = 4X
2.2.1
32
[S]
8
2
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= 2.2.2 log 2 x 2 4
[3]
2.3 Factorise the following expressions completely:
2.3.1 Sx2 - 5
[3]
2.3.2 xa - 2xb + ya - 2yb
[4]
2.4 Simplify the expression below:
-x-+-2--- x 2 -4
2x-3 · 2x 2 -3x
[6]
QUESTION 3 [23 Marks)
! [! !], 3.1 Given the two matrices A= [~ 1] and B = 1
Find (A+ B)2.
[6]
3.2 Find the values of the letters in the matrix equation below:
[41
o][n
m -2
P]= [2012]
0 -1 q
[4]
3.3 The common difference in an Arithmetic Progression {AP) is 3. The 24th term is 74. What
is the first term?
[3]
3.4 If x + 2; 3x + 1 and 4x - 3 are the first three terms of an Arithmetic Progression, Find
the value of x.
[5]
+ 3.5 Evaluate log 5 ( 11/s) log11 3-yr;1--1;;. Show all your workin. gs.
[5]
END OF QUESTION PAPER
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