MAT 111 2009 Exam Questions with Solved Answers

UNIVERSITY OF BOTSWANA

2009/2010 – EXAMINATIONS


FRONT PAGE


COURSE NUMBER MAT111 DURATION 2 hrs DATE NOV 2009
TITLE OF PAPER INTRODUCTORY MATHEMATICS I
SUBJECT MATHEMATICS TITLE OF EXAMINATION BSc I


MORNING/AFTERNOON

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INSTRUCTIONS:


ANSWER ALL QUESTIONS IN SECTION A AND ANY TWO(2)
QUESTIONS FROM SECTION B.


• ALL MARKS ARE INDICATED IN BRACKETS [ ].




NUMBER OF PAGES INCLUDING COVER PAGE:



DO NOT OPEN THIS PAGE UNTIL YOU HAVE BEEN TOLD
TO DO SO BY THE SUPERVISOR.

, Section A
Answer All Questions: Each Question carries 10 Marks

Question 1

(a) Write 0.513 in the form pq, where p, q ∈ Z and q /= 0. [3]

(b) Solve the equation, 22x4x+1 = 32 [3]

(c) Solve the equation, 4x−1 = 3x+1 [4]

Question 2
Solve the following inequalities.
3 1
(a) | x − 1| ≤ . [4]
4 2
(b) x(x + 1) > −2(2x + 3). [6]

Question 3

1
(a) Given that f (x) = , g(x) = 3x find (g ◦ f )(x) and state its domain
x
and range. [6]

(b) Find the equation of the line passing through (−1, −2) and perpendicular
to 2x − y + 1 = 0 [4]

Question 4

(a) Find the value of k if the remainder, when the polynomial

P (x) = 2x4 + kx3 − 11x2 + 4x + 12

is divided by x − 3, is 60. [5]

√ine the polar form of the following complex number
(b) Determ
−1 − 3 i [5]