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ITM111S- INTRODUCTION TO MATHEMATICS -JAN 2020pdf |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
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,07BBAD,27BAGR,O7BTRM | NOF LEVEL: »
COURSE NAME: INTRODUCTION TO MATHEMATICS
(BUSINESS AND MANAGEMENT)
COURSE E CO CODE: ITM111S
SESSION: JANUARY 2020
PAPER: THEORY
DURATION: 3 HOURS
MARKS: 100
SUPPLEMENTARY/SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINERS
Ms A. SAKARIA, Ms S.Mwewa, Mr B. Obabueki
MODERATOR:
Mr G. TAPEDZESA
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. Marks will not be awarded for answers obtained without showing the necessary steps leading
To them (the answers).
4. All written work must be done in blue or black ink and sketches must be done in pencil.
5. You may not start to read the questions printed on the subsequent pages of this question
paper until instructed that you may do so by the invigilator.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
This question paper consists of 5 pages (including this cover page)
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SECTION A (Multiple choice)
Write down the letter corresponding to your best option for each question in the answer
booklet/sheet provided.
QUESTION 1 [36 Marks]
1.1 Mr. Hansen’s annual salary was N$ 282 000 in the year 2004. In 2005 his salary was increased by
12.5% and in 2006 his monthly salary increased to N$ 28 645.03 . From the information above,
determine:
1.1.1 Mr. Hansen’s monthly salary in 2005.
[3]
A. N$2 643.50
B. N$317 250.00
B. N$35 250.00
D. N$26 437.50
1.1.2 The percentage increase for 2006.
[3]
A. 8.34%
B. 1.835%
C. 0.0835%
D. 8.35%
1.1.3 His total income for the three years.
A. N$ 78 582.53
B. N$942 990.36
C. N$942 970.00
[3]
D. N$660 990.38
1.2 Simplify
77x 17° x 4923
[3]
A. 8403.5
B. 18.52
C. 47
D. 49
1.3 An amount of N$508070.00 can be expressed in standard form as:
[3]
A. N$5.08070 x 105
Cc. N$ 5080.70 x 10?
B. N$ 508.070 x x 10°
D. N$5.08070 x 1075
1.4 Evaluate and si. mplif. y 0.009999+51005-2x0+0.99001
[3]
A. 100.0009
Cc. 1
B. 0.001
D. 0.01
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1.5 If the matrix 4ix —186 ) has no inverse the value of x is:
A. 24
B. 2x
C. 2
[3]
D.
1.6 Factorize the expression y — x — xy + x?
[3]
A. (x —y)(—1x)
B.(x«-y)(x-1) C&+1)(y-~x)
D. (y—x)(-1x)
1.7 The soluti‘on of the l:inear equatio. n =5 = = —-4=-5 :is:
[3]
1
A. x=
6
B.x=—
19
Cx =-7T
1
D. x =—-T
1.8 Simplify + -[-(—2)2] + 27
[3]
3
A. -20
B. 2
C. -34
D. O
1.9 What is the sum of the series 1:3(n? + 3)
A. 128
B. 131
Cc. 240
D. 243
1.10 Which of the expressions below represents the following statement?
[3]
A.x=2y-5
B.y=2x+5
Cy=2x-5
D.x=2x+5
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QUESTION 2 [15 Marks]
2.1 It took thirty men 10 days to dig a trench. Working at the same rate, how long would it take twenty
men to dig the trench?
[3]
A. 6: days
B. 60 days
C. 15 days
D. 7 days
2.2 Determine the value of ((11260-+28-)2) +6—3(3 X 2)
[3]
A. —43.75
B. -—17
Cc. -—7
D. 17
2.3 From the Venn Diagram below, describe the shaded region.
[3]
A. AUBUC
B. ANBNC
C. (AUB)NC
D. (ANB)-C
2.4 Determine the value of n that makes the ratio n:15 the same as the ratio 36:90.
[3]
A.n = 1350
B.n=5
C.n=10
D.n=6
2.5 Mr. Titus buys x cans of cool drink at N$5.00 each and another (x +5) cans of juice at N$6.50
each. The total cost was N$ 67. How many cans of juice Mr. Titus bought?
[3]
A. 20
B.3
G. 12
D.8
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SECTION B (Clearly show all your work)
QUESTION 3 (49 MARKS)
3.1 Expand and simplify the expressions:
3.1.1 (x —xy)? — x? — x(—2xy)
[3]
3.1.2 3x(x —3)+x(x—-2)
[3]
3.2 If the universal set = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15} , set A = {2,3,4,5,6,7,8}, set B=
{5,8,9,11,14}, D = {2,3}, find:
3.2.1 ANB
[2]
3.2.2 n(ANB)
[1]
3.2.3 AUB
[4]
3.2.4 (AUB)*
[4]
3.3 Given the matrices A= [? 4 , B= ( 1 0 ) Find:
3.3.1 AA71
[6]
3.3.22A—B
[5]
3.4 Of the 60 students (S) in class, 44 can spell the word ‘Parallel’ (PA), 22 can spell ‘Pythagoras’ (PY)
and 14 can spell neither.
3.4.1 Present this information in a Venn diagram.
[5]
3.4.2 How many students can spell both words?
[4]
3.4.3 How many students can spell Parallel or Pythagoras?
[3]
3.5 Given the formula, S = 5 (2a, + (n—1)]d find the sum of the first 102 terms of the series
94+19+29+:--
[5]
3.6 Calculate the amount payable for a loan of N$ 1000 for 3 years at the rate of 10% p.a.
compounding annually.
[4]
END OF QUESTION PAPER