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Math 0113: Basic Mathematics Question Paper
Math 0113: Basic Mathematics
Course:Diploma In Education
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
EXAMINATIONS FOR THE AWARD OF DIPLOMA IN EDUCATION
MATH 0113: BASIC MATHEMATICS
STREAMS: DIP. EDUC TIME: 2 HOURS
DAY/DATE: FRIDAY 19/4/2013 8.30 AM – 10.30 AM
INSTRUCTIONS:
Answer questions ONE (compulsory) and any other TWO questions
Adhere to the instructions on the answer booklet
Do not write on the question paper.
QUESTION ONE (COMPULSORY) (30 MARKS)
1. (a) Define the following terms as used in set theory and illustrate using an
appropriate example.
An empty set.
The intersection of sets A and B.
Equal sets. [3 Marks]
(b) (i) State the difference between a tautology and a contradiction. [2 Marks]
(ii) Show that (p?q) ?¦?~ ? p=p?~p [2 Marks]
(c) (i) Given? Z?_1=2+3i and Z_2=3-4i,determine Z_1/Z_2 in the form x + yi.
[3 Marks]
(ii) Solve the equation x^2+9=0 [2 Marks]
(d) If f(x) (x-2)/(x+5),x?-5 determine
(i) f(3) [1 Mark]
(ii) f^(-1) (2) [4 Marks]
(e) Solve for x in 0° x=360° given 2?sin?^2 x+5cosx=4 [4 Marks]
(f) Given 7?_5=3x, find the value of x. [3 Marks]
(g) (i) State the difference between sequence and series. [2 Marks]
(ii) In an arithmetic progression, the thirteenth term is 27, and the seventh
term is three times the second term. Find the first term, the common difference and the sum of the first ten terms. [4 Marks]
2. (a) Given two functions f(x)=(x+4)/5 and g(x)=(x-1)/(2 ) find
(i) (f·g)(x) [3 Marks]
(ii) (f·g)^(-1) (2) [4 Marks]
(b) Given h(x)=(x+p)/(x-3 ),x?3, where p is constant,
(i) Find the value of p if h(5)=2 1/4 [2 Marks]
(ii) Find h^(-1) (2) [3 Marks]
(iii) State the value of x for which h^(-1) (x) is undefined. [1 Mark]
(c) 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]
?^'' [1 Mark]
B-A [1 Mark]
(d) Use analytic method to show that if a?B and B?A,then A=B
[2 Marks]
3. (a) (i) Show that v(2 ) is not a rational number. [3 Marks]
(ii) Express Z=1+i in the form (r, ?) [3 Marks]
(iii) Given the complex number
Z_1=5-2i and Z_2=3-2i find the values of x and y if Z_2/Z_1 =x+yi
[4 Marks]
(b) Construct a truth table to show that ~q is logically~q ~(p?q)?p.
[ 4 Marks]
(c) In how many ways can the letters of the work BESIEGE be arranged? [3 Marks]
(d) In how many ways can 8 people sit at a round table? [3 Marks]
4. (a) (i) Solve the equation tan?=2sin?,for 0°=?=360° [5 Marks]
(ii) Prove that sin??x+sin??x?cot?^2 x=cosecx.? ? [3 Marks]
(iii) Find the exact value of cos??15°? by using 15°=60°-45° [4 Marks]
(b) Simplify (?cos?^2 ?)/(1+sin?)+(?cos?^2 ?)/(1-?sin?^2 ? ) [3 Marks]
(c) Use a right-angled triangle to prove identity ?sin?^2 ?+?cos?^2 ?=1 [5 Marks]
5. (a) Find the 12th term of the AP below and determine the sum of the first 12 terms.
5 + 11 + 17 + ……….. [4 Marks]
(b) Consider the general G.P whose first term is a and the common ration is r. If the
G.P has n terms and r > 1, show that the sum of the first n term,
S_n=a(r^(n-1)/(r-1)) [5 Marks]
(c) Determine the missing terms in the geometric sequence.
4, ____, ______, ______, ______, 128. [6 Marks]
(d) Find the least number of terms of the G.P 1 + 3 + 9 + 27 + ………. That must be
taken in order that the sum of the G.P exceeds 1.4 × ?10?^5 [5 Marks]
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