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Math 0012: Basic Calculus Question Paper

Math 0012: Basic Calculus

Course:Certificate In Mathematics Bridging Course

Institution: Chuka University question papers

Exam Year:2013

CHUKA

UNIVERSITY

UNIVERSITY EXAMINATIONS

EXAMINATION FOR THE AWARD OF
CERTIFICATE IN MATHEMATICS BRIDGING COURSE

MATH 0012: BASIC CALCULUS

STREAMS: CERT. (BRIDING) TIME: 2 HOURS

DAY/DATE: THURSDAY 8/8/2013 11.30 A.M. – 1.30 P.M.
INSTRUCTIONS:

Answer Question 1 (Compulsory) and any other THREE questions.
Do not write on the question paper.

QUESTION 1 (SECTION I) COMPULSORY (30 MARKS)

Distinguish the following terms:

An independent variable and dependent variable in a function. [2 marks]

Limit of a function and derivative of a function. [2 marks]

Find the equation of a line passing through the point (2, 3) and is perpendicular
to the line Y=3x+2. [4 marks]

Evaluate the following limits

[2 marks]

[2 marks]

[3 marks]

Calculate in each of the following

y=?4x?^3+3x+1 [1 mark]

y=5x+1/5x [3 marks]

Identify and state the nature of the turning point of the curve presented by
y=?2x?^2-12x+4. [4 marks]

Given that f(x)=?2x?^3-x+5and g(x)=x^3-4x+1.
Evaluate (i) f(3) [2 marks]

(ii) 3f(x)-g(x) [2 marks]

Calculate the area of the shaded region in the figure below.

[3 marks]

SECTION II

2. (a) Copy and complete the table.

x 2.9 2.99 2.999 3.001 3.0 3.1
y

Hence use the table above to determine

[3 marks]

(b) Differentiate the following using the most appropriate method.

[2 marks]
[3 marks]

[2 marks]

3. (a) Use the long division method to divide the following

(i) x^5-?3x?^2+2x-24byx-2 [2 marks]

(ii) x^3byx-3 [2 marks]

(b) Given that f(x)=2x-4 and g(x)=x+1.

Find: (i) f^(-1) (x) [1 mark]

(ii) g^(-1) (x) [1 mark]

Hence show that [4 marks]

4. (a) Using the first principle of differentiation, find dy/dx if y=x^2+5.
[4 marks]

(b) Find and classify all the turning points of the curve

?y=2x?^3-6x+4 [6 marks]

5. (a) A farmer has 10,000m of fencing wire with which to fence three sides of his
rectangular farm, the fourth side being an existing fence of his neighbour. Find
inmetres(m) the dimension of the field of the largest possible area that can be enclosed. [4 marks]

(b) A particle is 5 metres from its starting point O after t seconds where

S=?8t?^3-?6t?^2-12t+30

Find (i) The expression of velocity and acceleration of the particle after t
seconds. [2 marks]

The value of S where the particle realizes its maximum distance.
[4 marks]

6. (a) Calculate [4 marks]

(b) (i) Calculate the area between the curve y=?3x-x?^2 and the x-axis
between the points x=1 and x=5. [6 marks]

OR

(ii) Use the trapezoidal rule with n=6 to estimate the area enclosed by the lines x=2,x=5, the x-axis and the curve y=x^3+3x+1.
[6 marks]

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Math 0012: Basic Calculus Question Paper

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