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AAT501S - ALGEBRA AND TRIGONOMETRY - 2ND OPP - JULY 2023 |
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n Am I BI A u n IVER s I TY
OF SCIEnCE Ano TECHnOLOGY
FACULTYOF HEALTH,NATURAL RESOURCESAND APPLIEDSCIENCES
SCHOOLOF NATURALAND APPLIEDSCIENCES
DEPARTMENTOF MATHEMATICS, STATISTICSAND ACTUARIALSCIENCE
QUALIFICATION: Bachelor of science; Bachelor of science in applied mathematics and Statistics
QUALIFICATION CODE: 07BOSC; 07BSAM
COURSECODE: AATS0lS
LEVEL: 5
COURSENAME: ALGEBRAAND TRIGONOMETRY
SESSION:JULY 2023
PAPER:THEORY
DURATION: 3 HOURS
MARKS: 100
SUPPLEMENTARY/ SECOND OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER($)
MRS L. KHOA
Mr G. MBOKOMA
MODERATOR:
DR S.N. NEOSSINGUETCHUE
INSTRUCTIONS
1. Answer ALL the questions in the booklet provided.
2. Write clearly and neatly.
3. All written work must be done in blue or black ink.
PERMISSIBLE MATERIALS
1. Non-programmable calculator without a cover.
THIS QUESTION PAPERCONSISTSOF 3 PAGES{Including this front page)
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QUESTION 1 [12 Marks]
Workout the following without a calculator:
(a) i943
[2)
(b) Solve for x and y if 2i = xi(2 - 3i) - y(5 - 3i)
[5)
(c) (1 + yC"g)- 2 leave your answer in the form a+ bi
[5)
QUESTION 2 [20 Marks]
(a) State whether the following are true or false
[5)
i) (In a)k = k In a
ii) log0 ( xy) = (loga X)(loga y)
iii) If log0 6 = 4 then a6 = 4
G) iv) -In
= lnx
v) logvxxk = 2k
(b) Solve: e2x - 2ex + 1
[5]
(c) Simplify the following without a calculator:
2x2y-3z-5. 8x-ly-l
i)
4x- 3y- 4z
[3)
ii) 3v'20Q - 3v118
[3]
(d) Solve: logx 10gx=4
[4]
QUESTION 3 (30 Marks]
Solve:
(a) Jx- 2J+ 5 = 9x
[5)
(b) x 2 + ex + b = 0 by completing the square
[6]
(c) log1(x - 6) + log1(x + 1) > -3, represent the answer in interval notation [12]
2
2
(d) The product of two natural numbers is 24 and their difference is 2. What are
the numbers?
[7]
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QUESTION 4 [10 Marks]
00
(a) Evaluate if it exists
\\0
(
3
10
)n
without
a calculator
[5]
n=-2
(b) Use the binomial theorem to find the 4th term in the expansion of
(x-~)10
[5]
QUESTION 5 [12 Marks]
Decompose the following into their partial fractions:
2-x
(a) x2 (x - 4)
[6]
(b)
2
x(x 2 + 1)
[6]
QUESTION 6 [16 Marks]
(a) Solve 4 cos 0 = sec 0 for 0 in the interval [o0 , 360°]
[8]
(b) Verify: cos 30 = 4 cos3 0 - 3 cos 0
[8]
TOTAL MARKS: 100
END OF PAPER
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