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Hps2231:Business Statistics Question Paper
Hps2231:Business Statistics
Course:Bachelor Of Business Information Technology
Institution: Meru University Of Science And Technology question papers
Exam Year:2011
QUESTION ONE - (30 MARKS)
a) (i) Define a set. (2 Marks) (ii) Let ?? = 1,2,3,4,…,10 ; consider the sets ?? = 2,4,6,8,10 ,?? = 0,1,2,…,11 ?????? ?? = 5 . Which of these sets are subsets of P and which ones are not and why? (3 Marks)
(iii) Use a Venn Diagram to shown ?? n ?? (3 Marks)
b) Given that ??(??) = ?? + 3 ?????? ?? ?? = 16 - ??2. Find ?? ??
?? and the Domain of
?? ??
?? . (4 Marks)
c) (i) Find ?? if log2 ?? - 2 = log2 92. (3 Marks) (ii) Solve for x without using tables or calculator. log 75 + log 9 + log 5 log 5 + log 45 (3 Marks) d) Solve the following equations i. 8?? - 3?? = 12 5?? - 2?? = 17 (3 Marks)
ii. 3 - ?? - 2??2 = 0 (3 Marks)
2
e) Solve the inequality 1 - 3?? 2
= ?? - 4 and represent the solution graphically. (3 Marks) f) Given that ?? = ??2 2-?? show that ???? ???? = 4-?? ?? 2-?? 2 (3 Marks)
QUESTION TWO – (20 MARKS)
a) (i) Derive the quadratic formula by solving the equation ????2 + ???? + ?? = 0 where ??,??,?????? ?? are real numbers and ?? ? 0. (Hint use the method of completing squares). (4 Marks) (ii) Using the formula derived above, solve the equation 2??2 + 7?? - 15 = 0. (3 Marks) b) (i) Find the inverse of the matrix ?? where ?? = 3 2 2 5 and hence solve the matrix equation ???? = ?? in which ?? = ?? ?? and C = 10 3 . (5 Marks)
(ii) Given that ?? =
2 1 1 1 2 1 3 2 2 ,?? =
2 0 -1 1 1 -1 -4 -1 3
(4 Marks)
Find ???? ?? (4 Marks)
c) Solve the inequalities below ??2-??-2 ??2-4??+3 = 0 (4 Marks)
QUESTION THREE – (20 MARKS)
a) (i) Given that ?? ?? = 5?? + 1 ?????? ?? ?? = ??2. Express the composite function ?? ° ?? and ?? ° ?? in their simplest form possible and find ??(?? -2 ) and ??(?? 3 ). (6 Marks)
(ii) Find the inverse of the function ?? = 2?? - 3 . (4 Marks)
b) The third term of a geometric sequence is 9 and the 6th term is 243. Find the first term and the common ratio. (5 Marks) c) Given = 1,2 ,3,4,5 ,?? = 2,4,6,8,10 ?? = 3,4,5,6,7 and ?? = {1,2,3,…,12}. Find i. ?? ? ??
ii. ?? n ??
3
iii. ????
iv. (?? ? ??)??
v. (?? n ??)?? (5 Marks)
QUESTION FOUR – (20 MARKS)
a) A sewing machine valued at Sh25,000 can be bought by cash at a discount of 10% or by installments whereby a deposit of Sh.3,000 is paid followed by 15 monthly installments of Sh.1,500 each. Find: i. The cash price of the machine. (1 Mark) ii. The hire purchase price of the machine (2 Marks) iii. The carrying charge. (2 Marks) iv. The interest rate of hire purchase buying. (3 Marks)
b) Evaluate i. ? ??2 + 2 + 1 ??2
???? (3 Marks)
ii. ? 1+??-4??3 ??3
???? (3 Marks)
iii. ? ??2 ?? - 1 ?? - 2 ???? -1 -2
(4 Marks)
c) List the members of the set of real numbers for which the expression 1 ??-1 ??-2 ??-3 does not exist. (2 Marks)
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