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AAT501S - ALGEBRA AND TRIGONOMETRY - 1st OPP - JUNE 2022 |
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A
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
DATE: JUNE 2022
PAPER: THEORY
DURATION: 3 HOURS
MARKS: 100
EXAMINER
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
MIRS. 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)
[2]
(b) Solve for x and y if 2(3 — 7?) + y(8 — 73) =i
[4]
(c) (1+ 2i)~? leave your answer in the form a + bi.
[6]
QUESTION 2 [21 Marks|
(a) Solve 102"° — 10°-* =0
[5]
b) Solve WS" = (e2# . e-t)—4
(b) Solve faa
e
[55]
(c) Solve for x: (log x)? — log x? = 3
[6]
(d) Rationalize the denominators of the following:
Ia
2]
ii) | Twil i
[3]
QUESTION 3 [30 Marks]
Solve:
(a) |2+=432|-8
[6]
(b) 2? +4 = —5zx by completing the square
[6]
(c) logi(z + 1) < logi(x + 8) — log:(x — 4) and write the answer in interval
notation.
:
[14]
(d) fe+VeFll=11
[4]
QUESTION 4 [11 Marks]
(a) Use the binomial theorem to find the coefficients of z, x? and x* in the
expansion of (2 — 2)’
[6]
(b) State whether the following series exist or not
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ii) Yo 10 (2)'
k—0
QUESTION 5 [12 Marks]
Decompose the following into their partial fractions:
(a)
ox+ 7
v8 — 72 — 27
QUESTION 6 [14 Marks]
(a) Prove the following Trigonometric identitities:
i) sinzcotzsecxz = 1
ii) tan? @ — sin? 0 = sin* 6 sec? 0
(b) Solve the following trigonometric equation for x in the interval [0°, 360°]
2cos?xz+3sinz = 3
TOTAL MARKS: 100
END OF PAPER