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AAT501S - ALGEBRA AND TRIGONOMETRY -2ND OPP - JULY 2022 |
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NAMIBIA UNIVERSITY
OF SCIENCE AND TECHNOLOGY
FACULTY OF HEALTH, APPLIED SCIENCES AND NATURAL RESOURCES
DEPARTMENT OF MATHEMATICS AND STATISTICS
QUALIFICATION: Bachelor of science ; Bachelor of science in Applied Mathematics and Statistics
QUALIFICATION CODE: 07BOSC; 07BSAM
LEVEL: 5
COURSE CODE: AAT501S
COURSE NAME: ALGEBRA AND TRIGONOMETRY
SESSION: JULY 2022
DURATION: 3 HOURS
PAPER: THEORY
MARKS: 100
SECOND OPPORTUNITY/ SUPPLEMENTARY EXAMINATION QUESTION PAPER
EXAMINER
MRS L. KHOA
MODERATOR:
MR G. TAPEDZESA
DR S.N. NEOSSI NGUETCHUE
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
2. Show clearly all the steps used in the calculations.
3. All written work must be done in blue or black ink and sketches must
be done in pencil.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPER CONSISTS OF 3 PAGES (Including this front page)
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QUESTION 1 [12 Marks]
Workout the following without a calculator:
(a)
(b) Solve for a and 6 if a— 3bi = (1+7%)7!
(c) i2 + L - +24“ leave your answer in the form a + bi.
QUESTION 2 [21 Marks]
(a) Work out the following without a calculator:
pl2\\ tf p9\\73
i) Simplify ~ (=) (-F] (¢2~*)
ii) 67 -1-—6!-” =0
(e8@t1)2 _ 10
iii) a
(b) Using the laws of logarithms:
i) show that log, a -log.b = log.a
ii) solve log7(logy x”) = 0
QUESTION 3 [30 Marks]
Solve:
(a) ) 22 —5|)+x2=2
( b) 327+ 36 = 31z by completing the square
(6)
(c) ) log,(a% + 3) + log.(x — 3) < 4 and write the answer in interval notation. [12|
(d) c+ Vr—4=4
[5]
QUESTION 4 [14 Marks]
Given the following sequences:
a) 9,14,19,24,...
b) 1024, 512, 256, 128,...
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Determine:
(i) whether the sequence is arithmetic or geometric
(ii) dorr
(iii) formula for a,
(iv) ag5
(v) S30
QUESTION 5 [10 Marks]
Decompose the following into their partial fractions:
v7 +1
(a) aa — (e+)
4
(D) (c — 2)(x +2)
QUESTION 6 [13 Marks]
(a) Prove that tan? 2+ 1 = sec? x
(b) Solve cosx = cosxtanz for x in the interval [0°, 360°]
TOTAL MARKS: 100
END OF PAPER