Cba0112:Basic Business Mathematics Question Paper
Cba0112:Basic Business Mathematics
Course:Certificate In Bridging Mathematics
Institution: Meru University Of Science And Technology question papers
Exam Year:2010
QUESTION ONE (30 MARKS)
(a) Solve for p given that log2 2?? + 3 - 2 = log2 ?? - 2 (3 Marks)
(b) Expand 1 + 2?? 10 up to the term in ??3. Use your expansion to estimate 0.95 10 correct to 3 d.p (4 Marks)
(c) The average of the first and fourth terms of a G.P is 140. Given that the first term is 64, find the common ration. (3 Marks)
(d) Determine the values of ?? for which 4??2 - 4???? + ?? + 20 is a perfect square. (3 Marks)
(e) (i) Work out the exact values of
003130.0003146.0 1 ? ?R (2 Marks)
(ii) Calculate the percentage error introduced in the value of R in (i) above if each of the decimals in the denominator is first rounded off to 5 d.p. (4 Marks)
(f) Calculate the interest earned when Ksh.4500 is deposited in a bank which earns compound interest of 12% for 2 years. (3 Marks)
2
(g) Solve for ?? in 9?? + 32?? - 4 = 50 (3 Marks)
(h) Find the number of ways in which 5 green balls and 7 red balls can be arranged so that as the 7red balls are together. (3 Marks)
(i) Factorize 4 9 2 ? x (2 Marks)
QUESTION TWO (10 MARKS)
(a) A farmer bought some sheep for Sh.27,000. Two of them died and he decided to sell the rest at Sh.300 per head more than what he paid for each on the whole, he gained 10% profits. Given that the original number of sheep bought was x: I. Write an expression in x for: (i) Original cost of each sheep. (1 Mark) (ii) Selling price of each sheep. (1 Mark) II. (i) Form an equation in x and simplify it to the lowest form. (2 Marks) (iii)Solve the equation in II(i) hence find the number of sheep bought. (3 Marks) (b) Simplify 2×13! 9!6! + 13! 10!7! (3 Marks)
QUESTION THREE (10 MARKS)
(a) The nth term of a sequence is given by 3??+1 - 2??. Find the 5th term of the sequence. (2 Marks) (b) A man deposits money in a savings bank on monthly basis. Each deposit exceeds the previous one by Sh.750. If he started by depositing Sh.1500, how much will he have deposited in 12 months? (3 Marks) (c) Given that the roots of the equation 0 356 2 ? ?? xx are ?? and ??, find the following (without calculating the values of p and q) (i) ?? + ?? (2 Marks) (ii) ???? (1 Mark)
(iii)
q
p
1
1 ?
(2 Marks)
3
QUESTION FOUR (10 MARKS)
(a) The cash price of a T.V set is Ksh25000. A customer paid a deposit of Ksh.3750. He paid the amount owing in 24 equal monthly installments. If he was charged simple interest at the rate of 40% p.a, how much was each installment? (5 Marks)
(b) Peter paid Sh180 for a shirt after getting a discount of 10%. The shopkeeper made a profit of 20% on the sale of this shirt. What percentage profit would the shopkeeper have made if no discount was allowed? (3 Marks)
(c) Simplify :
q
qq
1
)1(33 ? ??? (2 Marks)
QUESTION FIVE (10 MARKS)
(a) A Salesman earns a basic salary of Ksh.1500 per week. In addition, he is paid commission per week as follows
Sales up to Ksh.50000 0% Above 50000: for the first Ksh.25000 2% For the next Sh.25000 2 ½ % Any amount above Sh100000 5%
During that week, he sold goods worth Ksh.115000. What was his total pay? (4 Marks) (b) The sum of two numbers is 24. The difference of their squares is 144. What are the two numbers? (3 Marks) (c) Find the value of ?? in ? ? 243 81 27 1 1 ? ?? ? ? ? ? ? ? m (3 Marks)
4
QUESTION SIX (10 MARKS)
(a) Use quadratic formula to solve the equation 4??2 - 6?? - 32 = 0. (3 Marks)
(b) Calculate the net monthly salary of Kamau (to the nearest 10 cents) if his basic salary was 5520 per annum when the rates of P.A.Y.E were as below:
0 2300 2 2301 4600 3 4601 6900 5 Over 6900 8
He claimed a personal relief of sh220 per month. Every month, sh.120 was deducted towards a pension scheme and sh.100 towards service charges. (7 Marks)
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