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AAT501S - ALGEBRA AND TRIGONOMETRY - 2ND OPP - JANUARY 2025 |
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nAmlBIA un1VERSITY
OF SCIEnCEAnDTECHnOLOGY
FacultoyfHealthN, atural
ResourceasndApplied
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Schoool f Natural andApplied
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Departmentof Mathematics,
StatisticsandActuariaSl cience
13JacksoKnaujeuaStreet T: +264612072913
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E: msas@nust.na
Windhoek
W: www.nust.na
NAMIBIA
QUALIFICATIONS: BACHELOR OF SCIENCE
QUALIFICATION CODE: 07BOSC
LEVEL: 5
COURSE: ALGEBRA AND TRIGONOMETRY
COURSECODE: AATS01S
DATE: JANUARY 2025
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
SECONDOPPORTUNITY/SUPPLEMENTARYE: XAMINATION QUESTION PAPER
EXAMINER:
MODERATOR:
MR GABRIELS MBOKOMA
DRS.N NEOSSINGUETCHUE
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.
PERMISSIBLEMATERIALS:
Non-Programmable Calculator
This paper consists of 3 pages including this front page.
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Question 1 (37 marks]
Without using a calculator.
1.1 Simplify the followings:
a) i943.
[2]
b) (1+ A)- 2 leave your answer in the form a+ bi
[6]
,h5 - ./x7
c)
[6]
2v'x3-x,/x
1.2 Find the value of x and y if, 2i = xi(2 - 3i) - y(5 - 3i)
[5]
1.3 Solve the following equations:
= a) lQY X 52v- 2 X 4v- 1 1
[5]
b) log3 (28 - 3x) = i 0g2( 3-x)
[8]
= c)
2
X3
-
I
X3 -
6
Q
[5]
Question 2 (38 marks]
2.1) Find the value(s) of>. for which >.x2 + 2x + 1 has a real and distinct roots.
[5]
2.2) Solve the inequalities:
a) Ix+ 51- x :s;5
[6]
b) log1 (9x - 4) :s;log1 (2x2 )
[6]
2
2
2.3) Given the geometric series: 8x 2 + 4x 3 + 2x4 + ...
a) Determine the n th term of the series.
[2]
b) What value(s) of x will the series converge?
[4]
f c) Calculate the sum of the series to infinity if x =
[4]
2.4) Without expanding, evaluate
[5]
2.5) Solve: -3 + -4 = -5 and -5 - -3 = -7 by elimination method.
[6]
Xy 2
Xy 4
Question 3 [25 marks]
20
3.1) Find the coefficient of x 2 in the expansion of ( x - ~)
[7]
1
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3·2) Decompose -x-(-2-xx-21 -x) into its partial fractions.
[8]
3.3) Show that -2--c-o-s2xsin-x secx = cot 2x
[5]
3.4) Solve the following trigonometric equations
2cosx - 1 = 0
[5]
2