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Math 102: Foundations Of Mathematics Second Trimester 2017 Question Paper
Math 102: Foundations Of Mathematics Second Trimester 2017
Course:Bachelor Of Business Information Technology
Institution: Kenya Methodist University question papers
Exam Year:2017
KENYA METHODIST UNIVERSITY
END OF SECOND TRIMESTER 2017 EXAMINATION
COURSE CODE : MATH 102 PT
COURSE TITLE : FOUNDATION OF MATHEMATICS
TIME : 2 HOURS
Answer question ONE and TWO others
QUESTION ONE 30 Marks (Compulsory)
a) Given the universal set as and
Find
i). (A )c (2 mark)
ii). A B c (2 marks)
iii). A-B (2 marks)
b) Solve 2 lnx = 6.04 (3 marks)
c) Solve each of the following quadratic equations
i. x2 +6x +2 =0 (2 marks)
ii. 3x2 -7x-2 =0 2 marks
d) Solve the inequality (3 marks)
e) The 6th term of an AP is 17 and the 13th term is 38. Determine the 19th term. (4 marks)
f) Find an equation of the line through the point (2,4) which is parallel to the line through the
line (-2,3) and (4,6) (4 marks)
g) Construct the truth table of the compound statement:
(6 marks)
QUESTION TWO (20 marks)
a) Determine the value of x for which the following form an AP. ( 3 marks)
2x+2, 4x+8, 8x+10
b) Find the domain and the range of the following function.
(3 marks)
c) Solve the value of x given: 72x =343 ( 3 marks)
d) Construct truth tables for the following propositions
and comment on this type of proposition. 5 marks
e) Give reason whether the function f(x)= x2 from a set of integers to a set of integers is onto.
2 marks
f) Determine the value of the following composite function g o f(2) given that
, (4 marks)
QUESTION THREE (20 marks)
a) Determine the following function f o g and g o f given that
i. f(x)= , g(x) = 3x2 (4 marks)
b) Determine the inverse of the following function
i. ( 3 marks)
c) Find the equation of the line though the points (1,6) which is perpendicular to the line through the points (-4,6) and (8,4) ( 3 marks)
d) Find the sum of the first ten terms in the following sequence:
4, 12, 36… (4 marks)
e) Suppose that X varies directly as Y and inversely as the cube of Z. Give the relationship if X=8, when Y=3 and Z=5. Find Z when X=10 and Y=4. 3 marks
f) Given that sets A= {1, 2, 3} and B = {a, b, c}, determine the Cartesian product A x B.
3 marks
QUESTION FOUR (20 marks)
a) Solve each of the following logarithmic equation
Log3 (x+2) –log3 (x-1) =2 (3 marks)
b) The first term of a G.P. is 5, and the common ratio is -3, which term is equal to -135? (3 marks)
c) Differentiate between even and odd functions and give an example of each functions.
(4 marks)
d) A class has 120 students. The following table shows the number of students studying one or more of the following subjects.
Subjects Number of students
Mathematics 60
Physics 45
Chemistry 32
Mathematics and physics 23
Mathematics and chemistry 19
Physics and chemistry 15
Mathematic, chemistry, and physics 11
Required
i. Draw a Venn diagram and represent the above information. (3 marks)
ii. How many students are enrolled in mathematics alone, physics alone, and chemistry alone? (3 marks)
iii. Are there students who are not offered any of these subjects? (2 marks)
iv. Find the number of students who enrolled exactly one subject? ( 2 marks
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