PreCalculus Unit 1 (Section P.7 – 1.9) Review
Section P.7
*
linear equations:
form is
0,
0
ax b
a
+ =
≠
(largest power on variable is 1)
*
solve linear equations by isolating x on one side of the equation.
*
equations involving rational equations
eliminate the denominators by multiplying
each
side by the LCD
remember to note restrictions on the variable
*
domain
of a rational expression (what ‘x’ can be)
*
domain restriction
of a rational expression (what ‘x’ cannot be)
*
solving formulas for a specified variable
*
quadratic equations:
form is
2
0,
0
ax
bx
c
a
+
+ =
≠
(largest power on variable is 2)
*
be able to solve by following
4 methods
:
factoring, square root method,
completing the square, or quadratic formula:
a
ac
b
b
x
2
4
2

±

=
Memorize!!
*
the factoring and quadratic formula method requires that we have a zero on one
side of the quadratic equation
* discriminant is
2
4
b
ac

If discriminant is positive: 2 real solutions
If discriminant is zero: 1 real solution
If discriminant is negative: No real solutions (both answers are imaginary)
*
solving radical equations by isolating the radical on one side
of the equal sign and
then squaring each side.
REMEMBER TO CHECK SOLUTIONS.
*
equations involving absolute value
isolate the absolute value on one side; set up
two
equations if you have the
absolute value equal to a positive real number
Section P.8
* application problems; be able to set up the equations and solve
* cost function:
cost = fixed cost + variable cost
* Pythagorean Theorem:
2
2
2
c
b
a
=
+
(‘c’ must be the hypotenuse)
Memorize!!
Section P.9
*
interval notation
*
B
A
∩
(A intersection B; Think ‘And’);
B
A
∪
(A union B; Think ‘Or’)
*
linear inequalities – remember to
flip
the direction of the inequality when
multiplying or dividing each side of the inequality by a negative number
*
absolute value inequalities – two cases…
(c is a positive number) (B. box P.171)
1.
The inequality,
c
<
expression
is written without the absolute value signs
as
c
c
<
<

expression
.
This means
c
<
expression
AND
c

expression
.
2.
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 Fall '08
 Mcbride,V
 Calculus, PreCalculus, Linear Equations, Equations, Quadratic equation

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