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Algebra And Business Mathematics Question Paper
Algebra And Business Mathematics
Course:Certificate In Bridging Mathematics
Institution: Kca University question papers
Exam Year:2012
1
UNIVERSITY EXAMINATIONS: 2011/2012
EXAMINATION FOR THE CERTIFICATE IN BRIDGING MATHEMATICS
MAT 101 ALGEBRA AND BUSINESS MATHEMATICS
DATE: APRIL 2012 TIME: 1½ HOURS
INSTRUCTIONS: Answer Question One and Any other Two Questions
QUESTION ONE (30 MARKS) (COMPULSORY)
a) Solve for x given the equation 2log log ( 1) log ( 2) a a a x- x- = x- (4 Marks)
b) Evaluate
1 1
6 3
1 1
4 12
8 4
32 16
×
×
(4 Marks)
c) Determine the number of terms of the following arithmetic sequence 2, -3,-8,-13,...,-58
(3 Marks)
d) Using the binomial formula, expand then simplify the terms in ascending powers of x up to and
including the term in x5 in the expression below
( )7 4 - x
Using the expansion above, estimate the value of ( )7 3.98 correct to five decimal places.
(4 Marks)
e) Rationalize the denominator 5 2 2 7
2 7 4 3
+
+
(4 Marks)
f) Juma deposited sh.16,000 in a bank which paid compound interest at 2% per annum compounded
quarterly. How much did Juma withdraw after 5 years? (5 Marks)
g) If the ratio of the sum of the first 6 terms of a G.P to the sum of the first 3 terms of the G.P is 9.
What is the common ratio of the G.P. (5 Marks)
h) Factorize 2p2q2+7pq-15 (2 Marks)
2
QUESTION TWO (15 MARKS)
a) Given that x+y= 8 and x2+y2=34 . Find the value of y.
i) x2+2xy+y2 (2 Marks)
ii) 2xy (2 Marks)
iii) x2-2xy+y2 (2 Marks)
iv) x-y (2 Marks)
v) Value of x and y (2 Marks)
b) At Maruro wholesale shop, Maureen bought 5 trays of eggs and 2 bales of maize meal for sh.1730.
Njoroge bought 7 trays of eggs and 3 bales of maize meal for sh.2530.
i) Use the matrix method to determine the cost of 1 tray of eggs and 1 bale of maize meal.
(3 Marks)
ii) How much would 2 trays of eggs and 1 bale of maize meal cost. (2 Marks)
QUESTION THREE (15 MARKS)
a) The life expectancy, E of a person varies inversely as the square of the density, d, of the drug
distributed in the body. When the density of the drug is 1g/m2, the life expectancy is 30 years.
How long will a person survive if the density of the drug is
i) 5g/m2
ii) 0.5g/m2
b) At the beginning of a certain year, Jane deposited sh.100,000 in an investment account, which
earned compound interest at 15% per annum. At the beginning of each subsequent year, he
deposited a further sh.5000 in the same account. Determine,
i) How much money he had in the account after 5 years (8 Marks)
ii) The percentage interest earned over the five years (3 Marks)
QUESTION FOUR (15 MARKS)
a) Make x the subject of the formula n 1
y b m
x
= ?? ?? -
? ?
(3 Marks)
b) Joan has some money in two denominations only: twenty shilling coins and one hundred shilling
notes. She has four times as many twenty – shillings coins as one hundred shilling notes.
3
Altogether she has sh.2160. How many one hundred shillings-notes does she have? (4 Marks)
c) The cash price of a water pump is sh.28,000. It can also be bought on hire purchase by paying a
deposit of 15% of the cash price and 20 equal installments of sh.1350.
i) How much more is the hire purchase price than the cash price? (4 Marks)
ii) If a simple interest was charged on the remaining balance after paying the deposit, calculate the
rate of simple interest charged correct to 2 d.p. (4 Marks)
QUESTION FIVE (15 MARKS)
a) A rectangular piece of paper measures 12.4cm long and 6.2cm wide. Find
i) The absolute error of the area (5 Marks)
ii) The percentage error of the area (3 Marks)
b) Consider the income tax table below
Monthly taxable pay (Ksh) Rate of tax % in each shilling
1 – 9680 10%
9,681 – 18,800 15%
18,801 – 27,920 20%
27,921 – 37,040 25%
Over 37,000 30%
Kaloki’s monthly salary is Ksh.42,000. Calculate her PAYE to be deducted if he is entitled to a
personal tax relief of sh.1,056. (7 Marks)
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