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Math 100: General Mathematics Question Paper
Math 100: General Mathematics
Course:Bachelor Of Science In Nursing
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATION FOR THE AWARD OF
DEGREE IN BACHELOR OF SCIENCE IN NURSING (SUPPLEMENTARY )
MATH 100: GENERAL MATHEMATICS
STREAMS: BSC (NURS) TIME: 2 HOURS
DAY/DATE:
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) List the subsets of real numbers giving an example in each case. [5 marks]
(b) Identify the property of real numbers being applied in each of the following:
(i) (2+5)+3=3+(2+5)
(ii) 4+0=4
(iii) (5+9)+7=5+(9+7) [3 marks]
(c) Given f(x)=4x-3 and g(x)=x^2+2,
(i) Evaluate (f+g) (-2) [2 marks]
(ii) Evaluate f^(-1) (x) [2 marks]
(iii) Find g/f using long division. [3 marks]
(d) (i) Find the value of x given ?16?^(3x-4)=1/8 [3 marks]
(ii) If ?log?_10^( 4x-9)=?3log?_10^( 3), find x [2 marks]
(e) The following shows part of the cumulative distribution table.
Class 2 0 - 4 5 - 9 10 - 14 15 - 19
Cumulative frequency 11 22 30 47
Determine the frequency for each class. [2 marks]
(f) Determine if the graph of y=x^2-2x+1 has a maximum or minimum turning point. [3 marks]
(g) (i) Find the remainder when ?2x?^3+x^2-13x+9 is divided by the factor (x-2)
[3 marks]
(ii) Confirm your results in g(i) above using the reminder theorem. [2 marks]
Question Two (20 Marks)
(a) (i) Define the derivative of a function f(x). [1 mark]
(ii) Given f(x)=?6x?^5-?3x?^4+?2x?^3+7x-8, find dy/dx at the point (1,-3).
[3 marks]
(iii) Determine dy/dx for the function y=4x-3 from the first principles. [3 marks]
(b) Differentiate the following using the indicated techniques:
(i) y=(x-4) (x^2+2) (Product rule) [3 marks]
(ii) y=(x^2+7)/(x-5) (Quotient rule) [3 marks]
(iii) y=(4x-7)^5 (Chain rule) [3 marks]
(c) Calculate dy/dx of the function y=vx+1/2x [4 marks]
Question Three (20 Marks)
(a) Simplify
(i) (1/?4x?^6 )^(1/2) [2 marks]
(ii) ((a^(x+y) )^2×(a^(y+z) )×(a^(z+x) )^2)/(a^x. a^y.? a?^z )^4 [3 marks]
(b) (i) Using a calculator, evaluate ?log ?_11^( 37) [2 marks]
(ii) Evaluate (3^((-1)/6) × 3^((-2)/3))/9^(1/(3 )× ?27?^((-1)/2) ) without the use of a calculator. [3 marks]
(c) (i) A boy added 13 to a certain number instead of taking it away. He got 42. Find the correct answer. [4 marks]
(ii) Solve the quadratic equation x^2+9/4 x +1/2=0 [4 marks]
(iii) Factorise a^4 x^2-1 [2 marks]
Question Four (20 Marks)
(a) The mean age of 30 students in a class is 20 years. It was later discovered that while calculating the mean, the ages of two students were wrongly taken as 21 and 20 years instead of 25 and 19 years. Find the correct mean. [4 marks]
(b) Find the absolute mean deviation of the following data: 11,15,20,12,15,12,18,20. What information does your result tell us? [4 marks]
(c) Consider the distribution below.
Mid – points (x) 5 10 15 20 25 30
Frequency (f) 5 15 25 30 15 10
(i) Construct a grouped distribution table. [3 marks]
(ii) Calculate the mean [3 marks]
(iii) Determine the mode [3 marks]
(iv) Calculate the median of the distribution [3 marks]
Question Five (20 Marks)
(a) Find all the turning points of y=?2x?^3-6x+4 and classify them. [6 marks]
(b) Sketch the curve represented by y=x^3+?3x?^2-9x-4. [8 marks]
(c) Find the equation of the tangent and normal to the curve y=2/x at x=4. [6 marks]
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