Applications of Linear
and Quadratic Equations
Revenue (R) =
Selling price per
unit (P)
Variable cost
Cost
= per unit
(C)
(V. cost)
Profit
=
No. of
units (x)
No. of
Fixed
units + cost
(x)
(F. Cost)
Revenue (R)
Cost (C)
Ex. It costs a manufacturer $ 2000 t
CHAPTER ( 1 )
Equations
Equations in one variable
Degree of equation :
Degree of equation dependent on the highest
power of equation.
e.g:
3x5
Power ( 1 ) first degree
1st
3 x2 1
Power ( 2 ) second degree 2nd
2x3 + 2x  10 Power ( 3 ) third degree
3rd
x4
CHAPTER ( 4 )
MATRICES
Matrix Algebra:
A matrix is a square or a rectangular array of
real numbers which is enclosed in large brackets [ ]
or ( ).
If a matrix has (m) Rows and (n) Columns then
it is said to be the size (m x n).
Types of Matrices:
(1) Rect
CHAPTER ( 3 )
DETERMINANTS
A determinant is a square array of real
numbers which is enclosed in vertical bars   where
No. of Rows = No. of Columns
A determinant of order (2)
a1
b1
a2
b2
D = a 1 b2 a2 b1
Ex.: Evaluate the determinants
a)
3
2
0
4
b)
2
3
CHAPTER ( 2 )
Inequalities
linear inequality in one variable
C any Real No.
1) a > b
a + c
>
b + c
a  c
>
b  c
2) a > b
C positive
ac > bc
a
b
>
c
c
3) a > b
C negative
ac < bc
a
b
<
c
c
Linear inequality
xs
constants
left
right
hand
hand
side
side
Ex.:
Straight lines and linear equations.
Find the slopeintercept
Linear Cost Model
y =
mx
slope
Where:
y : Total cost.
m : V. cost per unit.
x : No. of units.
b : F. cost.
+
b
Yintercept
Ex. Given the linear equation 3x 4 y = 12. Find the
slop and yinterce
Chapter (5)
The differentiation
Rules of the derivative:
y = constant
dy
dx
= Zero
y = 6
dy
dx
= Zero
dy
dx
= Zero
dy
dx
=
y =
3
2
y = x
y
= x
y
= 5x
dy
dx
dy
dx
1
=1
=5(1)=5
y =
dy
dx
xn
= n xn1
power formula
y =
x7
dy
dx
=7 x6
y =
x3
dy
dx
=3x2
dy
dx
=
(7) Find
1
0
0
1
1
2
2
1
0
0
1
1
2
1
1
2
3
0
0
1
+
+ 3
0
1
1
2
(7)
0
1
1
13
Inverse of a square Matrix by determinants (A1):
(1) Find D D : non zero
(2) Find Cofactor of Matrix A [Aij] by Cancel Row and
Column with signs +

+
(3) Find ad joint of Ma