Get premium membership and access revision papers, questions with answers as well as video lessons.
Math 100: General Mathematics Question Paper
Math 100: General Mathematics
Course:Bachelor Of Education Science
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATION FOR THE AWARD OF DEGREE OF
BACHELOR OF EDUCATION (SCIENCE) AND BACHELOR OF EDUCATION ARTS
MATH 100: GENERAL MATHEMATICS
STREAMS: BED (SCIE) & BED (ARTS) Y1S1 TIME: 2 HOURS
DAY/DATE: TUESDAY 13/8/2013 8.30 AM - 10.30 AM
INSTRUCTIONS:
Answer Question 1 and any other Two Questions
Adhere to the Instructions on the answer booklet
Do not write on the question paper.
Question 1 (compulsory) (30 Marks)
(a) Explain the five subsets of real numbers. [5 marks]
(b) Identify the property of real numbers being applied in each of the following:
(i) (7+10)+3=3+(7+10)
(ii) 2(12-4)=24-8
(iii) If 16-10=6 and 6=2×3 then 16-10=2×3
(iv) 1×t=t [4 marks]
(c) Solve the following equations:
(i) 1/(x-1)+3/(x+1)=2 [4 marks]
(ii) log_2??(x+2)=3+log_2?(x-5) ? [5 marks]
(d) Given that f(x)=?2x?^2-1 and g(x)=x-2
(i) Evaluate f(3) [1 mark]
(ii) Show that fog?gof [4 marks]
(iii) Find the inverse of f(x) [2 marks]
(e) Given the following distributions of marks scored by 6 students in a Mathematics C.A.T
5.5,9,13,10.5,8,5.
Determine:
(i) The range of the marks [1 mark]
(ii) The mean mark [2 marks]
(iii) The standard deviation. What information does this standard deviation represent?
[4 marks]
Question 2 (20 Marks)
(a) Evaluate the following without using a calculator.
(i) (64/0.125)^(1/3) [3 marks]
(ii) (9^(1/3) ×? 27?^((-1)/2))/(3^((-1)/6) ? × 3?^((-2)/3) ) [3 marks]
(b) Show that
(a^l/a^m )^(l+m)×(a^m/a^n )^(m+n)×(a^n/a^l )^(n+l)=1 [3 marks]
(c) (i) Using factor theorem show that 2x-1 is a factor of the polynomial
?12x?^2+ 16x^2-5x-3. [3 marks]
(ii) Confirm your result in (i) above using the long division method. [2 marks]
(iii) Hence solve ?12x?^2+?16x?^2-5x-3=0 [3 marks]
(d) Evaluate (?3(x+h)?^2-?3x?^2)/h [3 marks]
Question 3 (20 Marks)
(a) Given that f(x)=3x+2 and g(x)=x^2
Find:
(i) f(x)+3 g(x) [2 marks]
(ii) f(x) – g(2x) [2 marks]
(b) If f(x)=ax+b/x and f(2)=9 and f(3)=16. Evaluate a,b and find the values of x for which f(x)=0 [6 marks]
(c) Given that f:x?8x+4 and
g:x?x-3
Show that (fog)^(-1)=g^(-1) 0f^(-1) [6 marks]
(d) Determine the nature of the turning point of the function y=4+2x-?3x?^2. [4 marks]
Question 4 (20 Marks)
(a) Calculate dy/dx in each of the following:
(i) y=?6x?^(1/3) [1 mark]
(ii) y=vx+1/3x [2 marks]
(b) Differentiate the following using the method indicated in the bracket.
(i) y=(x^3-4)/(2x+3) (Quotient rule) [2 marks]
(ii) y=(x^2+3)^(-5) (Chain rule) [2 marks]
(iii) y=(x^2+2)(x^3-3) (Product rule) [2 marks]
(c) Differentiate from the first principle y=2-x^2 [3 marks]
(d) Classify all the turning points of the curve y=1/3 x^3-5/2 x^2+4x+1
Hence sketch the curve represented by this equation. [8 marks]
Question 5 (20 Marks)
(a) The mean marks 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]
(b) The table below shows the distribution of students waists in a class of 200 students.
Waist size (cm) 38 - 42 43 - 47 48 – 52 53 - 57 58 - 62 63 - 67 68 - 72
No. of students 6 22 30 70 50 18 4
Determine:
(i) The class width [1 mark]
(ii) The average waist size [3 marks]
(iii) The mode size [3 marks]
(iv) The interquartile range [4 marks]
(v) The median size [3 marks]
(vi) The standard deviation [3 marks]
______________________________________________________________________________
More Question Papers
Popular Exams
Return to Question Papers