MODEL-1
Module I: Tools of Economic Analysis:
5 MARKS QUESTIONS:
1. What are the advantages and disadvantages of the application of mathematics in economics?
2. Explain the role of Mathematics in economics.
3. Explain the meaning of Variables, Constants and parameters in an equation.
4. What are the features of a straight line?
5. Calculate the value of y in the equation 2x2 +5x+1, When x=1, x=2.
Ans:
if x=1
2x2 +5x+1
2(1)2+5(1)+1
2+5+1=8 if x=1, y=8.
If x=2
2x2+5x+1
2(2)2+5(2)+1
8+10+1=19. if x=2, y=19
6. Find the value of x in the equation x2 +5x+6=0 by using the factorization method.
x2 +5x+6=0
x2 +3x+2x+6=0
or x(x+3)+2(x+3)=0
(x+3) (x+2)=0
or x+3=0 or x+2=0
or x=-3 or x=-2.
Thus there are two solutions to the above problem.
7. Differentiate between linear and non linear functions with examples.
8. Prepare the demand schedule for the following function D=10-2p
If P=0 (when it is a free good)
D=10-2(0) = 10
If P=1 D=10-2(1)=8
If P=2 D=10-2(2)=6
If P=3 D=10-2(3)=4
If P=4 D=10-2(4)=2
If P=5 D=10-2(5)=0
DEMAND SCHEDULE
|Price |Demand (Units) |
|(Rs.) | |
|0 |10 |
|1 |8 |
|2 |6 |
|3 |4 |
|4 |2 |
|5 |0 |
9. Prepare the supply schedule for the following equation S=2p+3
If P=0 S= 2(0) + = 3
If P=2 S= 2(1) + = 5
If P=3 S= 2(2) + = 7
If P=4 S= 2(3) + = 9
If P=5 S= 2(4) + = 11
10. In the equation y=2x+4, when x=1 and x=2 find out the value of y and graph the equation.
Ans:
y=2x+4
If x=1
Y=2x+4
Y=2(1)+4
Y=2+4
Y=6
If x=2
Y=2a+4
Y=2(2)+4
Y=4+4
Y=8
8
6
1 2
11. Distinguish between universal set and sub set with examples.
12. Explain different types of set?
13. Explain the intersections of sets with the help of a Venn diagram.
14. If A={5,7,10,15,18} = {6,10,12,13} and C={9,11,14} show A[pic](B[pic]C) = (A[pic]B)[pic]C
15. Distinguish an explicate and explicate function with a suitable example..
10 MARKS QUESTIONS:
1. Explain the advantages and disadvantage of Mathematical economics.
2. For the given information formulate the demand function by using a two point formula
|Price |Supply |
|1 |100 |
|2 |50 |
3. For the given information formulate the supply function by using a two point formula.
|Price |Supply |
|10 |50 |
|15 |100 |
4. Solve the quadratic equation X2-10+48=0 by using formula method or Sridhar Acharya Method.
5. Solve the equation 4x2 –16x+48=0 by using completing the square method.
6. Explain different types of functions.
7. Define sets, explain Various types of sets with suitable examples.
8. Graph the following function:
1. y=10-3x
2. y=2x+3
9. Solve the quadratic equation Y=2x2 +5x+10 represent it graphically.
10. When the Price of a commodity is Rs. 1, 100 units of a commodity are demanded. It the price increases to Rs. 2, 50 units are demanded. Construct a demand curve, using two-point form.
Y=price and x= quantity in units.
[pic]
[pic]
11. When the price of a commodity is Rs. 10, 15 units of a commodity are supplied. When the Price increases to Rs. 15, 100 units are supplied. Construct the supply function using two-point form.
Let y= Price
x= Quality
Ans. [pic]
[pic]
12. Find the value for x in the following function.
4x2-11x+6=0
4x2-11x-6=0 Divide this by 4
[pic]
Added half of [pic] square to both sides of the equation.
[pic]
It is in the form of (a-b)2
When we take the positive sign we get, [pic]
When we take negative sign we get [pic]
[pic]
[pic]
13. Solve the quadratic equation
[pic]
Solution: here x=1 b: -16 and c=48
Formula=[pic]
[pic]
When we take the positive sign
[pic]
When we take the negative sign
[pic]
Therefore solutions are 12 & 14
TWO MARKS:
1. What is a function?
The relationship between two or more variable is called a function. For example D=f(P) is a demand function. /also Qd =f(P) is a demand function where Qd is quantity demanded and P is price.
2.what is a constant?
A constant is a quantity, which does not change its value throughout a set. In mathematical operations usually constants are denoted be a,b,c,(,(,(, 10 etc
3.what is arbitrary constant?
Arbitrary constants are those constants, which have one value throughout one problem, but may change from one problem to another. They are also called Parameters.
4.what are absolute constants?
Absolute constants take on the same value in all situation and is represented by a number, therefore, it is called a numerical constant
5.What is a Variable?
A variable is one which changes . For example Price, Demand, supply etc. In the demand function Qd=10-2p, Qd and P are Variables.
6.What is a dependent variable?
Dependent variable is one, which, depends on some other variable.
7.What is an independent variable?
Independent variable is one, which is not influenced by any other variable
8.what is a discrete variable?
Discrete variable is one which takes on only integral values.
For example: no. of students in a college , no. of hospitals in a town, no. of children in different families etc. A discrete value does not take fractional values.
9.What is a continuous variable?
If a variable can take any value with in the given range of value it is called continuous variable.
10.What is a co-efficient?
When a variable is multiplied by a constant that constant is called the co-efficient of the variable. In 2x, 2 is the co-efficient of the variable x.
11.What is mapping?
The assigning of output values to corresponding input values is often referred as mapping.
12.What does domain of a function represent?
Domain of a function represents all inputs values.
13.What does a range of a function?
Range of a function is a set of all possible output values.
14.Identify the dependent variable and independent variable in the function y = f(x).
y is the dependent variable and x is the independent variable.
15.What is a constant function?
A constant function is one whose range consists of only one element .For example y = f (x) = a is a constant function, where’ a ‘ is a constant.
16. Give an example for a constant function.
Fixed cost is a constant function. For example p =10 where, p is production is a constant function.
17.What is a linear function?
A linear function is one, which is of the form Ax + By + C = 0. Here x and y are variables, A, B, C are constants .There is always proportionate relationship between dependent and independent variables in a linear function. For example Qd = 10 – P is a linear demand function. Here price P changes by 1 unit the quantity demanded changes by 1 unit. The change
in dependent variable as a result of change in independent variable is given by the slope of the straight line, which is a constant.
18.In a demand function D + 2P- 10 = 0 if P= 4 What is the value of D?
D = 2
19.Give two economic examples for linear function and indicate their slope.
1.Qd = 10 –2p
2. Qs = 10 +3p
in the first linear function –2 is the slope in the second linear function +3 is the slope
20. Mention the two-point formula of the straight line?
y-y1 = [pic]
21. What is a slope of a curve?
Slope of a curve shows the direction in which the curve is moving or slope expresses the rate of change of a dependent variable with respect to the change in the independent variables.
22. What is a Y intercept on a graph?
The point at which the line cuts the Y axis is called Y intercept.
23.What is a X intercept on a graph?
The point at which the line cuts the X axis is called X intercept.
24. Name the four types of straight line?
1.parallel to ox axis
2.parallel to oy axis
3.falling from left to right
4.rising from left to right
25. In the equation Y=mx + c, x and y are variables and what are ‘m’ and ‘c’?
‘m’ is the slope ‘c’ is the constant.
26. What is a non-linear function?
If the power of the variable is more than one it is a non- linear function.
27. What is a quadratic function?
If the highest power of x is 2 it is called as a quadratic function in the
form of y =f(x)
28.Name the three methods to solve quadratic equations?
1.Factorisation Method
pleting the square method and
3.Formula method
29.Which is the formula in which the solution of x is given by X=[pic]
ax2 +bx + c = 0
30.What is the formula in which the solution of x given the equation
ax2 +bx + c = 0
X=[pic]
31.What is a cubic function?
When the highest power of a variable is more than 3, it is called a cubic function.
32.What is polynomial function?
Polynomial means multi-terms. In any equation if we have more terms it is called polynomial function.
33.What is the shape of an ellipse?
It is egg shaped.
34.Explain the functional relationship with the help of an example.
S = 2p +3 this is a supply function. If expresses the relationship between price and supply
35.Differentiate between absolute constants and arbitrary constants.
Absolute constant takes on the same value in all situations, whereas arbitrary constants are those constants, which have one value through out one problem, but may change from one problem to another. Absolute constants are called numerical constants and arbitrary constants are called parameters.
36. Differentiate between dependent variable and an independent variable.
Dependent variable is one, which depends on some other variables. Whereas, independent variable is one which is not influenced by any other variable.
37. Distinguish between discrete and continuous variables.
If a variable takes only limited number of values within the interval of a given value is called discrete variable. If a variable can take any value with in the given range of value is called continuous variable.
39. Give any example for identity.
When the values of left hand side are always equal to the values of the right hand side of the equation it is called identity.
For example, 4+6[pic]5+5 or y[pic]c+s.
40) Define the slope of a curve.
Slope of a curve shows the direction in which the curve is moving.
41) Differentiate between linear and non-linear function.
If the power of a variable is only one in any equation it is called linear. If it has more than one it is a non-linear function.
42) Identify the constant and slope in the equation y=mx+c.
In this equation ‘m’ is the slope and ‘c’ is the constant.
43) Name the two-point formula of a linear function.
y-y1 = [pic]
44) Write the formula of Sridhar Acharya method.
X=[pic]
45) Give two examples for non-linear functions.
[pic]
[pic]
46) a) Write the equation of a circle.
[pic]
b) Write the equation of a hyperbola
[pic]
47) Define a set.
A set is a collection of well-defined and well-distinguished objects.
48) What is an infinite set? Give an economic example.
A set is said to be infinite if finite numbers cannot count the elements of the set.
49) What is singleton set? Give an example.
A set consisting of only one element is called singleton set. It is also called a unit set. S={2}
50) What is an equal set?
Two sets A and B are equal sets, if and only if every element of A is also an element of B and every element of B is also an element of A. it is denoted as A=B.
51) What do you mean by equivalent set?
if the elements of one set can be put into one to one correspondence with the element of another set, then the two sets are called equivalent sets.
52) What is subset?
Set A is called a subset of B if each element of A is also an element of B. it is denoted as A[pic]
53) What is a power set?
The set of all possible subsets of a set A is called a power set of A and is denoted by P(A).
54) What is a universal set?
The set, which describes the well-defined limit, is called universal set for that particular situation.
55) What do you mean by intersection of a set?
The set consisting of the elements that are common to both A and B is called their intersection. It is denoted as A[pic].
56) Show the intersection of a set by Venn diagram.[pic]
[pic]
57) What do you mean by disjoint set?
If the sets A and B have no common elements in them. Then we say, that the two sets A and B are disjoint, if the set are disjointed then A[pic]=[pic]
58) What is the union of a set?
The union of two sets A and B is the set consisting of all elements, which belong to either A, or B or both. It is denoted as A[pic]
-----------------------
|Price |Supply |
|(Rs.) |(Units) |
|0 |3 |
|1 |5 |
|2 |7 |
|3 |9 |
|4 |11 |
[pic]
[pic]
By-
Prof. K.M. Veeraiah
J.S.S. College for Women
Saraswathipuram
Mysore.
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