 |
AAT501S - ALGEBRA AND TRIGONOMETRY - 1ST OPP - JUNE 2023 |
|
|
1 Page 1 |
▲back to top |
nAmlBIA un1VERSITY
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 LEVEL: 5
COURSE CODE: AAT501S
COURSE NAME: ALGEBRAAND TRIGONOMETRY
SESSION: JUNE 2023
PAPER: THEORY
DURATION: 3 HOURS
MARKS: 100
FIRST OPPORTUNITY EXAMINATION QUESTION PAPER
EXAMINER(S}
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 PAPER CONSISTS OF 3 PAGES (Including this front page)
|
|
2 Page 2 |
▲back to top |
QUESTION 1 [12 Marks]
Workout the following without a calculator:
(a) i925
[2]
(b) Solve for x and y if x - y + (x + y)i = 2x - 2 + (y + 5)i
[4]
(c)
1-
--
1
+
i
i
+
-3--
2-
2i
9i
leave your
answer
in the
form a + bi
[6]
QUESTION 2 [20 Marks]
(a) State whether the following are true or false
[5]
i) 2x + 2x = 2x+l
ii) log(a - b) = -log a
logb
iii) log(l + 2 + 3) = log 1 + log 2 + log 3
iv) a log0 a.0 = a
v) (loga,b2)(log1ia3) = 6
(b) Solve: log3 y - 2 logy 3 = 1
[6]
(c) Solve: log x + log(x + 3) = 1
[6]
(d) Solve: 102:c- 3 = - 1-
[3]
100
QUESTION 3 [30 Marks]
Solve:
(a) 2 - 4x < 13+ 5xl represent the solution on a number line
[5]
(b) cx2 + ax = 0 by completing the square
[6]
(c) z2 < 3z and represent your answer in interval notation as well as on a
number line
[8]
(d) -1 + -1 = -- 3 and -1 - -1 = -- 7
[6]
Xy
10
Xy
10
(e) For what value(s) of p does the equation 4x2 - (p - 2)x + 1 = 0 have equal
roots?
[5]
1
|
|
3 Page 3 |
▲back to top |
QUESTION 4 (11 Marks]
55
(a) Evaluate 3n without a calculator
[5]
n=O
(x'~r (b) Use the binomial theorem to find the coefficients of x in the expansion of
+
[6]
QUESTION 5 [11 Marks]
Decompose the following into their partial fractions:
x+3
(a) x(x 2 - 1)
[7]
(b) (x+l~x-2)
[4]
QUESTION 6 [16 Marks]
(a) Prove the following 1\\'igonometric identitities:
i) 1 + sin20 = (sin0 + cos0) 2
[3]
ii) sin 0 = 2 sin cos
[2]
(b) Solve the following trigonometric equations for x in the interval [0°, 360°]
i) 3 sin x - 4 = 5 sin x - 3
[4]
ii) 4 cos2 x - l = 0
[7]
TOTAL MARKS: 100
END OF PAPER
2