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Math 100: General Mathematics Question Paper
Math 100: General Mathematics
Course:Bachelor Of Education Arts
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATIONS FOR THE AWARD OF DEGREE IN BACHELOR OF EDUCATION (ARTS)
MATH 100: GENERAL MATHEMATICS
STREAMS: BED Y1S1 TIME: 2 HOURS
DAY/DATE: FRIDAY 19/4/2013 2.30 PM – 4.30 PM
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
(a) By giving an example in each case, explain the following properties of real numbers.
(i) Transive property
(ii) Associative property of addition
(iii) Reflexive property. [3 Marks]
(b) Classify each of the numbers below.
(i) 3.142
(ii) 2v5
(iii) v(-9) [3 Marks]
(c) (i) Solve for x given 9^x+3^2x-3=51 [3 Marks]
(ii) Given (log_3?x )^2-1/2 log_3??x=3/2,find x.? [3 Marks]
(d) Given that f:x?(x-1)/(x+2) and g(x)=5/(x+5,)
(i) Evaluate (f·g)^(-1 ) (x) [3 Marks]
(ii) Evaluate ?g·?^(-1) f^(-1) (x) [3 Marks]
(iii) Comment on your results in (d) (i) and (ii) above. [1 Mark]
(e) Find the turning points of the curve y=5+24x-?9x?^2-?2x?^3 and distinguish between
them. [5 Marks]
(f) Factorise completely the expression x^2+?2x?^2-5x-6 [3 Marks]
(g) The table below represents part of a cumulative frequency distribution table.
Height (x) metres 2 6 3 5
Cumulative frequency 11 22 30 50
Determine the mean height. [3 Marks]
QUESTION TWO (20 MARKS)
(a) Simplify
(i) ?((?27x?^3 y^9)/(x^6 y^3 )) [2 Marks]
(ii) (8^(1/6)×4^(1/3))/(?32?^(1/6)×?16?^(1/12) ) [3 Marks]
(b) Evaluate log_5?17 using a calculator. [2 Marks]
(c) When the price of an item was increased by Sh 10, I bought 2 items fewer with sh.120. What is the current price of the item? [5 Marks]
(d) Use the long division to find the remainder when ?5x?^5+x-9 is divided by the factor (x + 1) [3 Marks]
(e) Show that (2(3^(x+1) )+7(3^(1-x) )^(-1))/(3^(x+2)-2(3)^(x-1) )=1 [5 Marks]
QUESTION THREE (20 MARKS)
(a) Consider the data below which represents the marks scored by students in a C.A.T
16, 13, 24, 9, 17, 28, 11, 8, 19, 18. Determine :
(i) The mean mark
(ii) The absolute mean deviation. What does it represent? [6 Marks]
(b) The data of some observations are presented in the following frequency table.
Class 10-24 25-39 40-54 55-69 70-84 85-99
Frequency 12 15 18 25 20 10
Using a working mean of 47, determine:
(i) The mean height [3 Marks]
(ii) The median height [3 Marks]
(iii) The mode [3 Marks]
(iv) The standard deviation. [5 Marks]
QUESTION FOUR (20 MARKS)
(a) (i) Define the derivative of a function. [1 Mark]
(ii) Given that f(x)=vx+1/(3x,) determine f^1 (1) using any method. [3 Marks]
(iii) 1000m of fencing is to be used to make a rectangular enclosure. Find the greatest
possible area, and the corresponding dimensions of the enclosure fenced. [4 Marks]
(b) Differentiate the functions below using the techniques indicated.
(i) y=(x^2+3x)^(7 ) (Chain Rule) [3Marks]
(ii) y=(1-x^2)/(1+x^2 ) (Quotient Rule) [3 Marks]
(iii) y=(x^2-3) (x+1)^2 (Product Rule) [3 Marks]
(c) Differentiate y=3x+7 from first principles. [3 Marks]
QUESTION FIVE
(a) Find all the turning points of the curve y=?-x?^3+?2x?^2-x-2 and
distinguishing between them. Hence sketch the curve represented by the function
y=?-x?^3+?2x?^2-x-2 [8 Marks]
(b) Find the equation of the tangent and normal to the curve y=3/x^2 at x=-2.
[5 Marks]
(c) Investigate the nature of the stationary point of the function y=x^4-?4x?^3 at y=0
[5 Marks]
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