ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
(Department of Mathematics)
WARNING
1.
2.
PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING
THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD
OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE.
SUBMITTING ASSIGNMENTS BORROWED OR STOLEN FROM
OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN
“AIOU PLAGIARISM POLICY”.
Course: Business Mathematics (1429/5405)
Level: B.A, B.Com, BBA
Total Marks: 100
Semester: Autumn, 2015
Pass Marks: 40
ASSIGNMENT No. 1
(Units 1-4)
All questions carry equal marks
Q.1 a)
b)
Q.2 a)
b)
Q.3 a)
b)
Q.4 a)
b)
Suppose two cards are selected at random from a deck of 52 cards, what is
the probability that both the selected cards are;
i.
Picture cares
ii.
Red cards
Define events in a sample space and also classify them.
Suppose that a random variable Y has normal distribution with mean 25 and
standard deviation 5. Find the probability that P(Y ≤ 25)
What do you think about the marks obtained by all the students taking the
assignment of course code 1429 Business Mathematics. Can it be represented
by continuous random variables or discrete random variables?
Solve the following quadratic equation by three different methods;
y2 – 5y + 6 =0
Solve the following system of linear equations by drawing them on the xyplane;
2x+y = 1
2x – 3y = 4
Solve the following linear inequality and represent the solution on the
number line;
|x–1| ˂ 3
Describe all the forms of a linear equation with the help of examples.
1
Q.5 Suppose the price of your bike is decreasing linearly with time and is given by:
After 3 years: Price = Rs. 80,000
After 4 years: Price = Rs. 72,000
a)
b)
Represent this data in the form of a linear equation and also draw on graph
paper.
Find the time when the bike will become worthless for you from the graph.
ASSIGNMENT No. 2
(Units 5-9)
Total Marks: 100
Pass Marks: 40
All questions carry equal marks
Q.1 a)
b)
Q.2 a)
Find the solution of the following system of equations using matrices.
x+y+z=2
3x – 4y + 2z = 17
3x + 2y + z = 2
Differentiate between Matrix and Matrices.
Find the determinant of the following matrix:
1

M = 3
1

b)
Q.3 a)
b)
Q.4 a)
b)
2
3
4
1
2

0 
Differentiate between rectangular and square matrices and write down all the
types of the square matrices.
Consider the function f(x) = x ex
Find the values of x where the function has zero slope.
Find
dy
dx
if ax2+b xy + cy2 = 0
Find gxx , gxy and gyx for the following function
g(x,y) = ax2 +b xy + cy2
You have studied the Cost and Revenue functions in this course.
Differentiate between these two functions by taking different examples from
your course book.
2
Q.5 The table given below shows the nutritional and cost information for two different
foods.
Units of Vitamins
Units of protein
Unit cost
Per unit of fish
5
10
Rs. 75
Per unit of spinach
1
3
Rs. 30
Minimum requirement
13
16
Find a diet (i.e. unit of vitamins and proteins) to meet the minimum nutritional
requirements at minimum cost.
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BUSINESS MATHEMATICS
Level: B.A/B.Com/BBA
Course Code: 1429/5405
Unit No.1
Probability Theory
Introduction, Basic Probability Theory, Definition, Laws of Probability,
Conditional Probability, Independent and Dependent Events, Applications.
Unit No.2
Random Variables
Introduction, Random Numbers and their Generation, Application of
Random Numbers, Concepts of Random Variables and their Construction,
Discrete and Continuous Random Variables.
Unit No.3
Equations
Solving Fist Degree Equations, Quadratic Equations, Solution of Quadratic
Equations by Different Methods, Inequalities, Absolute Value, Co-ordinate
System.
Unit No.4
Linear Equations
Characteristic of Linear Equations, Slope- intercept Form, Determining the
Equations, Applications.
Unit No.5
Matrices and Determinants
Matrices, Different Kinds of Matrices, Addition, Subtraction and
Multiplication of Matrices, Determinants, Application of Matrices and
Determinants.
Unit No.6
Inverse of Matrices
Expansion of Determinants, Different Properties of Determinants,
Cofactors and Minors of Elements of a Matrix, Cramer’s Rule, Solution of
System of Linear Equations by Use of Matrices.
Unit No.7
Differentiation
Derivatives, Differentiation of Explicit and Implicit Functions, Maxima
and Minima, Applications of Derivatives.
Unit No.8
Partial Derivatives
Partial Derivatives, Maxima and Minima for Functions of Multi-Variables
Applications of Partial Derivatives.
Unit No.9
Optimization
First Derivative Test. 2nd Derivative Test, Curve Sketching, Revenue, Cost
and Profit Applications in Business.
Recommended Book:1.
Applied Mathematics for Business, Economics and the Social Sciences. By Frank
S. Budnick. Mcgraw-Hill
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