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AAT501S - ALGEBRA AND TRIGONOMETRY - 1ST OPP - NOVEMBER 2024 |
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nAml BIA UnlVERSITY
OF science Ano TeCHnOLOGY
FacultoyfHealthN, atural
ResourcaensdApplied
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Schoool f NaturalandApplied
Sciences
Departmentof Mathematics,
StatisticsandActuarialScience
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W: www.nust.na
NAMIBIA
QUALIFICATIONS: BACHELOR OF SCIENCE
QUALIFICATION CODE: 07BOSC
LEVEL:5
COURSE: ALGEBRA AND TRIGONOMETRY
COURSECODE: AAT501S
DATE: NOVEMBER 2024
SESSION: 1
DURATION: 3 HOURS
MARKS: 100
EXAMINER:
MODERATOR:
FIRST OPPORTUNITY: EXAMINATION QUESTION PAPER
MR GABRIEL S MBOKOMA
DR S.N NEOSSI-NGUETCHUE
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:
Non-Programmable Calculator
This paper consists of 3 pages including this front page.
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Question 1 [35 marks]
Without using a calculator.
1.1 Simplify the followings:
[7]
[3]
[5]
1.2 Find the value of x and y if, (x + 2i) + i(3 - i) = 3 - yi 7
[5]
1.3 Solve the following equations:
a) (2 + y2)2 = (2yJ2)2
[5]
b) !o3 [g(10)T'-3!o+Ts] 2
[5]
c) ax2 +bx+ c = 0 (using completing of squares method)
[5]
Question 2 [37 marks]
2.1) Find 0.272727(27) as a fraction?
[5]
2.2) Solve the inequalities:
a) x2 - 2x - 3 < 0
[5]
b) log1.(3x2 ) :s;log1.(2 - 5x)
[6]
3
3
2.3) Given the geometric series: 8x2 + 4x3 + 2x4 + ...
a) Determine the n th term of the series.
[2]
b) What value(s) of x will the series converge?
[4]
t c) Calculate the sum of the series to infinity if x =
[4]
2.4) Find sum of the followings, if they exists.
[5]
2.5) So1ve: -3 + -4 = -5 an d -5 - -3 = -7 by e11. m.mat1. 0n met hod .
[6]
Xy 2
Xy 4
1
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Question 3 [28 marks]
3.1) If the 2nd , 3rd and 4th terms in the expansion of (a+ bt is 240, 720 and 1080 respectively,
find the value of a, band n?
[10]
1-x
3.2) Decompose x( 2x 2 _ x) into its partial fractions.
[8]
3.3)
Show t hat
sinx - cosx
-s-i-n--x + cos x
=
-ttaa-nn-xx
-
+
1
1
[5]
3.4) Solve the following trigonometric equation
2 cos2 x - h cos x = 0
[5]
2