Mathematics, 04.12.2021 14:00 munch1239
1
KISII UNIVERSITY
TAKEAWAY CAT 1
15/11/2021
COURSE CODE: MATH 112 COURSE TITLE: BASIC MATHEMATICS
SEP-DEC 2021
Instructions
a) Do not write anything on this question paper.
b) Answer questions ALL the Questions.
QUESTION ONE (COMPULSORY)
a) i) Distinguish between a tautology and a contradiction.
(2 marks)
ii) Write the negation of the statement βIf I recover from my illness, I will go to Church.β
(2 marks)
b) Find the power set of
*
+
(4 marks)
c) Given
*
+
* +
*
+ and
*
+. Show that
(5 marks)
d) i) A basket contains 4 apples, 5 oranges and 8 bananas. How many ways can 2 apples, 1
orange and 2 bananas be chosen?
(4 marks)
ii) In how many ways can an even number greater than 2 000 be formed from the digits
1,2,3,4?
(4 marks)
e) Let
and
, find
i)
(2 marks)
ii)
(3 marks)
f) i)
ii)
Determine the number of ways a basketball coach can select five players from a team
of twelve players to participate in a match.
(3 marks)
g) Determine the inverse function of the following function
(3 marks)
Question Two (20 marks)
a) Given ( )
and ( )
i)
Find
( )
(3 marks)
ii)
Find (
) ( )
(3 marks)
iii)
Evaluate
(
)
(2 marks)
b) Let
*
+ and
*
+ find
(2 marks)
c) Prove that β is not a rational number.
(8 marks)
d) State the domain and range of the funct
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1
KISII UNIVERSITY
TAKEAWAY CAT 1
15/11/2021
COURSE CODE: MATH 11...
TAKEAWAY CAT 1
15/11/2021
COURSE CODE: MATH 11...
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