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Math 0012: Basic Calculus Question Paper

Math 0012: Basic Calculus

Course:Certificate In Bridging Mathematics

Institution: Chuka University question papers

Exam Year:2013

CHUKA

UNIVERSITY

UNIVERSITY EXAMINATIONS
EXAMINATIONS FOR THE AWARD OF CERTIFICATE IN MATHEMATICS BRIDGING COURSE
MATH 0012: BASIC CALCULUS
STREAMS: CERT (BRIDGING) TIME: 2 HOURS
DAY/DATE: THURSDAY 18/4/2013 11.30 AM – 1.30 PM
INSTRUCTIONS:

ANSWER ALL QUESTIONS IN SECTION A AND ANY THREE IN SECTION B
ADHERE TO ALL INSTRUCTIONS ON YOUR ANSWER BOOKLET
DO NOT WRITE ON THE QUESTION PAPER.

SECTION A: (30 MARKS)

1. (a) (i) Define the term function giving an example. [1 Mark]

(ii) Given f (x)=(?2x?^3-?5x?^2+x-10)/(x-2),evaluate f(-1) [2 Marks]

(iii) if f(x)=x^5 ?-3x?^2+2x-24 and g(x)=x-2,find f(x)/g(x) [3 Marks]

(b) (i) Evaluate lim-(x?3)?((x^2-9)/(x-3)) [3 Marks]

(ii) Evaluate dy/(dx ) from first principle given y=?2x?^2-1 [3 Marks]

(c) Determine dy/dx for the functions indicated below.
(i) y=vx+1/3x [2 Marks]
(ii) y=x^2/(x+1) [3 Marks]

(iii) y=(?2x?^2-1)^3 [2 Marks]

(d) Find all the turning points of the function ?2x?^3+?9x?^2-24x-1 and distinguish between them. [7 Marks]

(e) (i) Evaluate ?_0^2¦(5x-x^2 ) dx [2 Marks]

(ii) Evaluate ?¦(x+2) (x-2)dx [2 Marks]

SECTION B: ANSWER ANY THREE QUESTIONS

2. (a) If f(x)=ax+b/x and if f(2)=9 and f(3)=16 evaluate a and b and find the values of x for which f(x)=0. [5 Marks]

(b) Given f(x)=x^2+1 and g(x)=1/(x ) evaluate f.g(-3) [3 Marks]

(c) Evaluate lim-(x?0)?[(x^3+5x)/x] [2 Marks]

3. A particle moves in a straight line such that its distance (S metres) from a point is given by s=45t+?11t?^2-t^3.

(i) Find an expression for its velocity v in terms of t. [1 Mark]

(ii) Find an expression for the acceleration a in terms of t. [1 Mark]

(iii) Find both the velocity and acceleration when t = 3 seconds. [4 Marks]

(iv) Show that the particle will come to rest after 9 seconds. [4 Marks]

4. (a) Calculate the area between the curve y=3x-x^2 and the x- axis between x = 0
and x = 3. [5 Marks]

(b) Use the trapezoidal rule with 4 subdivisions to estimate the area beneath the curve
y=x^2+2 from x=1 to x=5. [5 Marks]

5. (a) Differentiate from first principles y=x^2+3x-5. [3 Marks]

(b) Find the equations of the tangent and normal to the curve y=x^3-8x+6 at the
point where x = 2. [5 Marks]

(c) Given y=(x^2+3)(?3x?^2-5),determine dy/dx [2 Marks]

6. (a) Determine the turning points of the curve y=?2x?^3-6x+4 [4 Marks]

(b) Distinguish between the turning points in 6(a) above using the second derivative.
[3 Marks]

(c) Sketch the curve. [3 Marks]

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Math 0012: Basic Calculus Question Paper

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