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Math 122

The document is an exam for MATH 122: Basic Mathematics. It contains 3 questions testing various math skills. Question 1 has parts testing set operations, subsets, combinations, arithmetic sequences, and inverse functions. Question 2 involves a proof using elements arguments, a Venn diagram with university student data, and set operations. Question 3 covers De Moivre's Theorem, truth tables showing logical equivalence, and proving irrationals. The exam tests a wide range of math concepts and proofs in basic algebra, sets, sequences, functions and number theory.

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1K views2 pages

Math 122

The document is an exam for MATH 122: Basic Mathematics. It contains 3 questions testing various math skills. Question 1 has parts testing set operations, subsets, combinations, arithmetic sequences, and inverse functions. Question 2 involves a proof using elements arguments, a Venn diagram with university student data, and set operations. Question 3 covers De Moivre's Theorem, truth tables showing logical equivalence, and proving irrationals. The exam tests a wide range of math concepts and proofs in basic algebra, sets, sequences, functions and number theory.

Uploaded by

Collins Bichiy
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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MATH 122

CHUKA UNIVERSITY

UNIVERSITY EXAMINATION

RESIT/SPECIAL EXAMINATIONS

EXAMINATION FOR THE AWARD OF DEGREE OF BACHELOR OF SCIENCE AND


BACHELOR OF ARTS

MATH 122: BASIC MATHEMATICS

STREAMS: TIME: 2 HOURS

DAY/DATE: WEDNESDAY 05/05/2021 8.30 A.M – 10.30 A.M

INSTRUCTIONS:

 Answer question ALL questions


 Sketch maps and diagrams may be used whenever they help to illustrate your answer
 Do not write on the question paper
 This is a closed book exam, No reference materials are allowed in the examination room
 There will be No use of mobile phones or any other unauthorized materials
 Write your answers legibly and use your time wisely
QUESTION ONE
a) A large corporation classifies its many divisions by their performance in the preceding year.
Let
P = {divisions that made a profit}
L = {divisions that had an increase in labour}
T = {divisions whose total revenue increased}
Describe symbolically the following sets:

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MATH 122

(i) {divisions that had increases in labour costs or total revenue} (2marrk)
(ii) {divisions that did not make a profit} (2marrk)
(iii) {divisions that made a profit despite an increase in labour costs} (2marrk)
(iv) {divisions that had an increase in labour costs and either were unprofitable or did not increase
their total revenue} (2marrk)
b) Let S = {1; 2; 3}. Find all the subsets of S. (4marrks)
c) How many committees of five people can be chosen from 20 men and 12 women
(i) if exactly three men must be on each committee? (3marrks)
(ii) if at least four women must be on each committee? (3marrks)

d) Prove the identity 1 + sin2θ = (sinθ + cosθ)2 (4marks)


e) The fourth term in an arithmetic sequence is -20, and the eighth term is -10. What is the
hundredth term in the sequence? (5 marks)
f) Given h(x) = 5−9x. Find ℎ−1 (x) (3marks)

QUESTION TWO: (20 MARKS)


a) Prove by the Elements Argument method that
A⋃ (B ∩ A) = (A⋃ B) ∩( A⋃ B) (4marks)
b) Each of the 100 students in Chuka university Pysical sciences Department, take at least one of
the subsidiary units: math 100, Math 122 and math 124. Given that 65 study math 100, 45 study
math 122, 42 study 124, 20 study math 100 and math 122, 25 study math
100d math 124, and 15 study math 122 and math 124.
i)Draw a venn diagram to represent the above information (4marks)
Find the number who studies:
(ii) All three subsidiary units (4marks)
(iii) Math 100 and math 122 but not math124 (4marks)
(iv) Only math 122 as a subsidiary unit. (4marks)
QUESTION THREE: (20 MARKS)
a) State the De Moivre’s Theorem, hence simplify (10marks)
b) Use truth tables to show that P ⇐⇒ Q is equivalent to (P =⇒ Q) ∧ (Q =⇒ P) (5marks)
c) Prove that is 2 not a rational number (5marks)
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