Get premium membership and access revision papers, questions with answers as well as video lessons.
Math 0113: Basic Mathematics Question Paper
Math 0113: Basic Mathematics
Course:Certificate In Mathematics Bridging Course
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
CERTIFICATE IN MATHEMATICS BRIDGING COURSE
MATH 0113: BASIC MATHEMATICS
STREAMS: TIME: 2 HOURS
DAY/DATE: TUESDAY 7/8/2013 8.30 A.M. – 10.30 A.M.
INSTRUCTIONS:
Answer ALL questions in Section A and ANY THREE in Section B.
Adhere to the instructions on your answer booklet.
Do not write on the Question paper.
QUESTION ONE
(a) Classify the following numbers:
v16 [1 mark]
0.0326 [1 mark]
v(-13) [1 mark]
(b) (i) In how many ways can 9 people sit at a round table? [3 marks]
(ii) Evaluate5! + 3! – 4! [3 marks]
(c) Let ? be the preposition that “I am going to town” and q – be the preposition that “I will buy a soda.”
Express the following symbols:
‘I am going to town and ‘I won’t take a soda. [1 mark]
‘I will not both go to town or take a soda. [1 mark]
(d) If Z=3+2i, write Z in the modulus – argument form. [3 marks]
(e) Given thatf:x ? (x-2)/(3x-1) and
g:x??(1/2 (6x-1) )
Find:
fg^(-1) (1) [5 marks]
(f) Use a right-angled triangle to show that ?Sin?^2 ?+?Cos?^2 ?=1. [3 marks]
(g) How many terms of the A.P 15 + 13 + 11 + ---, are required to make a total
of-36 [3 marks]
(h) Define the following terms:
Intersection of Set A and B
Null set [2 marks]
(i) State three ways in which sets are indicated. [3 marks]
QUESTION TWO (20 MARKS)
(a) Define the following terms as used in basic mathematics:
Logics [1 mark]
Propositions [1 mark]
Tautology [1 mark]
(b) Complete the following truth table:
p q ~p ~q p?q ~(pvq) ~p?q (p?q)?~p pvq p?q
[8 marks]
(c) Show that p?(q?r) and (p?q)?(p?r) are logically equivalent. [9 marks]
QUESTION THREE (20 MARKS)
Given e={0,1,2,3,4,5,6},
A={1,2,4}and
B={2,3,5}, find
AnB [1 mark]
A?B [1 mark]
A-B [1 mark]
A'' [1 mark]
B-A [1 mark]
Use proof by contradiction to show that v2 is an irrational number. [3 marks]
Given Z_1=3-2i and Z_2=4+7i and that
Z_1/Z_2 =x+yi, determine the values of x and y. [3 marks]
Find the roots of the quadratic equation
x^2+x-2½=0 [3 marks]
In how many ways can the letters of the word ADISABABBA be arranged?
[3 marks]
Given ?8C?_6=3x-2, find the value of x. [3 marks]
QUESTION FOUR (20 MARKS)
Explain the difference between domain and range as used in functions. [2 marks]
Given the functions: f(x)=(2x-5)/3 , g(x)=5/2 x-11
determine:
f^(-1) (x) [2 marks]
f^(-1) g(x\) [2 marks]
[2 marks]
g^2 (x) [2 marks]
(i) Solve the equation 1+Cos?=2? Sin?^2 ?, for 0^( )=?=?360?^( ). [4 marks]
(ii) Prove the identity (1-Sin?+Cos?)/(1-Sin?)=(1+Sin?+Cos?)/Cos? [3 marks]
(iii) Simplify (?Cos?^2 ?)/(1+Sin?)+(?Cos?^2 ?)/(1-?Sin?^2 ?) [3 marks]
QUESTION FIVE (20 MARKS)
(i) State the difference between sequence and series. [2 marks]
(ii) Find the sum of the first eight terms of the geometrical progression
2 + 6 + 18 + … [3 marks]
(iii) What is the smallest number of terms of the geometrical progression,
8 + 24 + 72 + …, that will give a total greater than 6,000,000? [4 marks]
Show that the sum of the first n terms of the A.P with first term a and common
difference d is given by S_n=n/2 {2a+(n-1)d}. [4 marks]
Evaluate6!/(3!?(2!)?^3 ) [3 marks]
Expand ?(1-x)?^5, and hence find, correct to three places of decimals, the value of
(49/50)^5. [4 marks]
----------------------------------------------------------------------------------------------
More Question Papers
Popular Exams
Return to Question Papers