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ITM511C- INTRODUCTION TO MATHEMATICS- 1ST OPP- NOV 2023 |
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nAmlBIA
UnlVERSITY
OF SCIEnCE Ano
TECHnDLOGY
HP-65B
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: ITM5 l l C
COURSE NAME: INTRODUCTION TO
MATHEMATICS
SESSION: NOVEMBER 2023
DURATION: 3 HOURS
PAPER: PAPER I
MARKS: 100
SECOND OPPORTUNITY EXAMINATION -QUESTION PAPER
EXAMINER(S) Ms. A. Sakaria
MODERATOR: Mr. I. Ndadi
INSTRUCTIONS
I. Answer ALL the questions on the separate answer sheet..
2. Write clearly and neatly.
3. Do not use the left side margin of the exam paper. This must be
allowed for the examiner.
4. 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.
5. QUESTION 2 indicate whether the given mathematical statements
are true (T) or false (F).
6. QUESTION 3 show clearly all the steps used in the calculations.
7. Number the answers clearly.
PERMISSIBLE MATERIALS
1. Non-Programmable calculator without a cover.
TillS 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 Expand and simplify the expression (x-3}2-x2 +6x
[3]
A. 12x+9
B. -12x+9
C. 12x-9
D. 9
1.2 Evaluate log2 l 6 + log3 27 +log 1 .
A. 4
B. 3
C.7
ef7 1.3 Simplify x 2 x .Jyx
I
x y2.
[3]
D. 8
[3]
I
B. .xyz
I
C. xy4
=~.) 1.4 Find the determinant of the matrix, (
A. -6
B.1
C. 7
D. x 4 y
[3]
D.-1
1.5 What is the Lowest Common Multiple {LCM} of 30 and 42?
A. 6
B. 210
c. 420
1.6 The values of P, Q and R in the Venn diagram below are:
5=560
B=130
C=200
[3]
D. 1260
[3]
R
A. P = 160,Q = 200 and R = 200
C. P = 90, Q = 11 0 and R = 200
B. P = 130,Q = 200 and R = 320
D. P = 90, Q = 11 0 and R = 320
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1.7 The prime decomposition of 128 7 is:
A. 33 x3 X 13
B. 9 9 X 1 3
1.8 Factorize the expression -2x 3 -4x 4 +-1x- ?
2
[3]
D. 9xllxl3
[3]
= 1.9 The equation, x2 -x-12 O has the solutions:
A. x=4,x=-3 B. x=-4,x=-3
C. x=-2,x=-6
[3]
D. x=6,x=-2
L3
1.10 Determine the sum of the series 2i .
n;J
A. 48
B. 24
C. 6
[3]
D. 12
QUESTION 2 (10 MARKS]
Indicate whether the given mathematical statements are true (T) or false (F)
½. 2.1 The expression lneN simplifies to x
[2]
2.2 The expression 16p 4 -8lq 8 can be factorised fully as 4p 2 -9q 4 •
[2]
2.3 (log a )(log b) is equal to log (a+ b) .
[2]
= 2.4 The discriminant of the equation 2x2 -4x+9 0 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 Use Cramer's rule to solve for x and y the following:
x=--5+3y and 7y=4x-11
[7]
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3.2 Solve the inequality -4x>-x-2<2x+ 1 and represent your solution on a number
line.
[6]
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3.3 Simplify the expression 2yx - 4Y .
[5]
x 2 -3x-4
3.4 Mr. Goagoseb has 48 goats and Mrs Namises has 60 goats. They decide to share
1296 kg of animal feed between them, in the ratio of the numbers of their animals.
How many kilograms of animal feed does Mrs. Namises get?
[3]
3.5 Matrices P, Q and R are defined by
P=5(:~ Q=(~!).R=(~ 2 1
1)
;}wherexandyarerealnumbers.
3.5.1 Given that the determinant of matrix P is 2, calculate the value of x. [3]
3.5.2 R-1
[4]
3.5.3 The value of y if matrix RQ =( 36 - 4).
[4]
24 -6
3.6 Leon left N$800000.00 in his estate account. This amount is to be invested in the
estate for 6 years at the interest rate of 12.75% p.a. compounded monthly. After 6
years the maturity value will be distributed amongst his 4 daughters in the ratio of
their age. Maria will be 15 years old, Jolene will be 22 years old, Rosewill be 28 years
old and Tina will be 8 years old.
3.6.1 Calculate the maturity value after 6 years.
[4]
3.6.2 What is the difference between Roseand Tina's amount?
[2]
3.7 Given the progression; 1;-4; 16;-64; ...
3.7.1 Find the common ratio.
[2]
3.7.2 Work out the 9th term of the progression.
[5]
3.8 Given S ={a,b,c,d,e,f}, A={a,c,d,e}, B ={a,b,e} find:
[4]
3.8.2 Au B
[3]
3.9 Of the 60 students(S) in class, 44 can spell the word 'Parallel' (PA), 22 can spell
'Pythagoras' (PY)and 14 can spell neither.
3.9.1 Present this information in a Venn diagram.
[4]
3.9.2 How many students can spell both words?
[2]
3.9.3 How many students can spell Parallel or Pythagoras?
[2]
END OF EXAMINATION QUESTION PAPER
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