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Math 0011: Basic Algebra Question Paper
Math 0011: Basic Algebra
Course:Certificate In Bridging Mathematics
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
EXAMINATIONS FOR THE AWARD OF CERTIFICATE IN MATHEMATICS BRIDGING COURSE
MATH 0011: BASIC ALGEBRA
STREAMS: CERT (BRIDGING) TIME: 2 HOURS
DAY/DATE: FRIDAY 19/4/2013 11.30 AM – 1.30 PM
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 QUESTIONS PAPER.
SECTION A: (30 MARKS)
1. (a) Classify the following according to the number type:
(i) -2.651
(ii) v11
(iii) v(-81)
(iv) 22/7
(v) 3 [5 Marks]
(b) Solve for x in the equations that follow:
(i) 4^(x+1)=32 [3 Marks]
(ii) ?log ???(15-5x)-1=log??(3x-2)? ? [3 Marks]
(iii) ?16?^(x^2 )=8^(4x-3) [3 Marks]
(c) Solve the following equations:
(i) x-(x+2)/3=2 [2 Marks]
(ii) |y-11|=2 [2 Marks]
(d) (i) Evaluate the value of 7!/4! [2 Marks]
(ii) Demonstrate with examples for the letters XYZ the difference between
permutations and combinations. [2 Marks]
(e) (i) Classify the type of sequences below:
(I) 6, -6, 6, -6, --------
(II) 15, 12, 9, 6, 3, 0, -3. [2 Marks]
(ii) Find the number of terms in the sequence below:
-3, 0, 3, . . . . . . , 54 [2 Marks]
(f) (i) Define the term singular matrix. [1 Mark]
(ii) Determine the possible values of x if the matrix below is singular.
(¦(-1&-9@5&?5x?^2 )) [3 Marks]
SECTION B: ANSWER ANY THREE QUESTIONS ONLY.
2. (a) Use a calculator to evaluate ?log?_5^13 [2 Marks]
(b) Solve the inequalities /equations below.
(i) 5> (x-3)/(x+1) [2 Marks]
(ii) 4^2y-?3×2?^(2y+2)+2^5=0 [6 Marks]
3. (a) Solve the simultaneous equations below using the matrix method:
6x-2y=10
2y=4-x [3 Marks]
(b) Reduce the following matrix to echelon form.
(¦(1&1&1@1&2&3@1&3&4)) [7 Marks]
4. (a) State the difference between sequence and series. [2 Marks]
(b) Find the 12th term of the AP below and determine the sum of the first 12 terms.
[3 Marks]
(c) Find the least number of terms of the GP 1 + 3 + 9 + 27 + ---------- that must be
taken in order that the sum exceeds 1.4×?10?^5 [5 Marks]
5. (a) Find x given 7P_3=x [4 Marks]
(b) (i) Obtain the first four terms of the expansion of (1+1/2 x)^10 in ascending powers of x. [3 Marks]
(ii) Hence find the value of (1.005)^10, correct to four decimal places.
[3 Marks]
6. (a) Simplify
(i) (x^(a+b) )^2· (x^(b+c) )^2· (x^(c+a) )^2 [3 Marks]
(ii) (?27?^(-1/2)×9^(1/3))/(3^(-2/3)×3^(-1/6) ) [3 Marks]
(b) Show that:
(2(3^(n+1) )+7(3^(n-1) ))/(3^(n+2)-2(3^(n-1) ) )=1 [4 Marks]
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