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Math 100: General Mathematics Question Paper

Math 100: General Mathematics

Course:Bachelor Of Education

Institution: Chuka University question papers

Exam Year:2013

CHUKA

UNIVERSITY

UNIVERSITY EXAMINATIONS

MATH 100: GENERAL MATHEMATICS

STREAMS: SCHOOL BASED TIME: 2 HOURS

DAY/DATE: TUESDAY 13/8/2013 8.30 A.M. – 10.30 A.M.
INSTRUCTIONS:

Answer question ONE (Compulsory) and any other two questions.
Adhere to the instructions on the answer booklet.
Do not write on the question paper.

QUESTION ONE (COMPULSORY) 30 MARKS

Classify each of the numbers below:

0.327

v(5/2)

v9

v(-81)
[4 marks]
Use an example to explain each of the following properties of real number.

Reflexive property
Substitutive property
Transive property [3 marks]

Find the mean of the data below.

x 2.0 2.1 2.3 2.7 3.2
f 2 3 5 7 3
[3 marks]
Evaluate [3 marks]

Solve for x in the equations below.

4^(x+2)+2^(2x+3)=96. [3 marks]

(ii) log ?(2x-11)??- ?log?_2=?log?_3-logx. [3 marks]

Given f(x)=(3x-5)/2, determine f^(-1) (x). [2 marks]

Use the long division to determine the remainder when ?5x?^5+x-9 is divided
by(x+1). [3 marks]

Given the function ?y=(?3x?^2+2)?^6,
determinedy/dx. [3 marks]

Factorise completely the cubic expression:

x^3+?2x?^2-5x-6 [3 marks]

QUESTION TWO (20 MARKS)

The mean mark of 100 students was found to be 40. Later on it was discovered that a mark 53 was misread as 83. Find the correct mean mark. [3 marks]

Calculate the mean, median and mode of the data below.

Mid-values
(x) 5 10 15 20 25 30
Frequency 5 15 25 30 15 10

[8 marks]

Find the absolute mean deviation of the following data:

31, 35, 29, 63, 55, 72, 37. What does your answer tell us? [4 marks]
Calculate the standard deviation of the numbers below:

3 5 9 19 17 23 27 4 1

[5 marks]

QUESTION THREE (20 MARKS)

Differentiate the functions below using the indicted techniques/methods.

(i) y=?(x+2)(x?^3+3) (Product rule). [3 marks]

y=x^4/(x^2+5) (Quotient rule). [3 marks]

?y=(2+vx)?^4 (Chain rule). [3 marks]

Determine the value of dy/dx for the function

? y=2x?^2+1from first principles. [3 marks]

Find all the turning points of the curve ?y=5+24x-9x?^2 ?-2x?^3
and distinguish between them. [8 marks]

QUESTION FOUR (20 MARKS)

Simplify

(i)

(ii) [3 marks]

State the remainder theorem and use it to determine the remainder when

?2x?^3+x^2-13x+9 is divided by (x-2). [3 marks]

Given f(x)=4x+7 and ?g(x)=x?^2+2,

(i) Evaluate:

(f+g)(-2) [2 marks]
fg(x) [2 marks]
(ii) Determine g^(-1) (x) [2 marks]

Evaluate using a calculator. [3 marks]

Musa added 16 to a certain number instead of taking it away. If he got 36, what
was the correct answer? [3 mark]

QUESTION FIVE (20 MARKS)

Investigate the nature of the stationary point of the function y=x^4-?4x?^3
aty=0. [5 marks]

Find the equation of the tangent and normal to the curve y=4/x^2 at x=-2.
[5 marks]

Determine dy/dx given the function y=vx+1/5x. [3 marks]

Sketch the curve represented by the function

y=x^3+?3x?^2-9x-4. [7 marks]

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Math 100: General Mathematics Question Paper

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