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Math 0011: Basic Algebra Question Paper

Math 0011: Basic Algebra

Course:Certificate In Mathematics Bridging Course

Institution: Chuka University question papers

Exam Year:2013

CHUKA

UNIVERSITY

UNIVERSITY EXAMINATIONS

EXAMINATION FOR THE AWARD OF
CERTIFICATE IN MATHEMATICS BRIDGING COURSE

MATH 0011: BASIC ALGEBRA

STREAMS: CERT. (BRIDGING) TIME: 2 HOURS

DAY/DATE: TUESDAY 7/8/2013 11.30 A.M. – 1.30 P.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.

SECTION A: (30 MARKS)

(a) Classify the following according to number type:

v144 [1 mark]

?2.543×10?^(-3) [1 mark]

v(-21) [1 mark]

v27 [1 mark]

(b) Solve for x in the equations below:

?49?^(x+1)+7^2x=350 [3 marks]

4^(?2x?^2 )=8^(4x-3) [3 marks]

(??log?_3 x)?^2-½?log?_(3^x )= [4 marks]

(c) Solve the pair of simultaneous equations below using the matrix method:

x+2y=4
3x-y=5 [3 marks]

(d) (i) Evaluate 6! + 3! – 5!

(ii) In how many ways can the letters of the word AMBASSADORIAL be arranged? [2 marks]

(e) A boy added eleven to a certain number instead of taking it away. He got thirty two. What should have been the correct answer? [3 marks]

(f) Find the sum of the first ten terms of the series

log?x+?logx?^2+log?x^4+?logx?^8+? [3 marks]

(g) Use Pascal’s triangle to obtain the first four terms of the expansion
?(1+ ?^. [3 marks]

SECTION B: ANSWER ANY THREE QUESTIONS ONLY.

(a) (i) Draw a Venn diagram that shows how Natural numbers (N), Complex
numbers (C), Integers (Z) and rational numbers Q relate in the number system. [2 marks]

(ii) Evaluate ??log?_3?^21 using a calculator. [2 marks]

(iii) Show that (?2(3?^(n+1))+?7(3?^(n-1)))/(3^(n+2)-?2(3?^(n-1)))=1 [3 marks]

(b) Solve for x given

4^(x+1)=32 [3 marks]

(a) (i) Determine the possible values of x that makes the matrix below
to be singular.

(¦(-1&-3@9&?3x?^2 )) [3 marks]

(ii) Solve for x given

(2x-1)x^5 P_3=63 [3 marks]

(b) Solve for xgiven ?6x?^2+23x+20=0. [4 marks]

(a) Solve for x given
7(x+2)>5x-4 [3 marks]

(b) (i) State the difference between sequence and series. [2 marks]

(ii) Find the least number of terms of the G.P 1+3+9+27+?
that must be taken in order that the sum exceeds 1.4 x?10?^5. [5 marks]

(a) Expand ?(1-x)?^5, and hence find, correct to three places of decimals, the
value of ?(49/50)?^5. [5 marks]

(b) Given A = and B = ,

Determine:

AB + B-1A [5 marks]

(a) Reduce the matrix below to echelon form.

[6 marks]

(b) A mixed hockey team containing 5 men and 6 women is to be chosen from 7 men and 9 women. In how many ways can this be done? [4 marks]

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Math 0011: Basic Algebra Question Paper

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