Download Algebra 3 Spring 2011 Final Review

Algebra 3 Fall 2011 Final Review
Equations: Slope: m 
Name:______________________________________
y2  y1
, Slope-intercept form: y  mx  b , Point-slope form:
x2  x1
Unit 1
Determine the numbers that are found in each set:
a. Natural numbers:________________________
b. Whole numbers:_________________________
c. Integers:_______________________________
d. Rational numbers:________________________
e. Irrational numbers:_______________________
f. Real numbers:___________________________
Insert >, < or = to make the statement true.
16
a. 22 _____ 11 b.  6 _____ 6
c.
_____ 8
2
Simplify the following.
a. |-2| = _____
b. |4| = ____
a.
15
=_____
10
b.
32
=______
44
c.
56
=______
42
Perform the indicated operation. Write your answer
in lowest terms.
16 21
 =______
a.
9 8
c.
3 10
 =______
5 3
Evaluate the following for x = 1, y = -4, and z = 2
a. x  y  2
4
2
b.  2 =______
3
3
1
3
d. 5  2 =______
3
4
c. 3  x  2  12  x 
e.
a. 6  2  2  25
b.
17  5
Perform the indicated operation of real numbers:
2
25
4  1
a.     
b.   
15
6
7  7

d. 
16
8

27
45
d. 4  x  3  3  x  2
 
1
1
4 x 2  2 x  8  15 x 2  9 x  3
2
3

b. The difference of a number and five, divided by
seven. ________________________
c. The sum of a number and six subtracted from two
times a number decreased by one.
__________________
d. Five times a number less four is the same as twice
the sum of the number and three.
___________________
Solve for x:
a. 3x  9  18
b. 9 x  x  1  6( x  1)  7
c.
5  x  1
6
 2x  3
d.   5x  1  7 x  3
Solve for x. Write the answer in interval notation and
graph.
a. x  5
b. 2  x  3
c. 4  ( 6)
z3  y
Translate the following into algebraic expressions or
equations.
a. Subtract 7 x  2 from x  5 __________________
Simplify the following.
16  13  5  32
b.
x2  y  x  z
Unit 2
Simplify the following expressions.
a. 4 x  x 2  1
b. 2  x 2  3 x   5 x
c. |-5.6| =____
Write each fraction in lowest terms.
y  y1  m( x  x1 )
c. 3x  4  x
Formulas
a. Given A  l  w ; A  56, l  8 . Find w.
Find the intercepts for the following equations:
b. Solve for w: V  lwh .
Graph the following equations by plotting intercepts:
a. x  4 y  8
b. 2 x  3 y  6
4 x  5 y  20
c. Mike is trying to replace the carpet in his
bedroom. His room is rectangular and has a width of
14 feet and a length of 20 feet. How much carpet
will Mike need for his bedroom?
d. The normal body temperature for a human is 98.6
degrees Fahrenheit. Express this temperature in
9
terms of degrees Celsius. F    C  32
5
Solve the following word problems.
a. Greg gets paid $20 dollars an hour. If Greg’s
paycheck at the end of week is $700 before taxes,
how many hours did he work?
Find the slope of the following:
a. Line through (4, -2) and (2, 5)
b. Line through (2, 3) and (2, -4)
c. Line through (8, -1) and (3, -1)
Determine if the following lines are parallel,
perpendicular, or neither.
a. L1: (5, -1) and (4, 3); L2: (2, 3) and (-1, 15)
b. L1: (3, -2) and (0, -1); L2: (2, 5) and (3, 2)
b. The sum of two consecutive even numbers is 178.
What are the two numbers?
Unit 3
Graph the following using coordinate points. Find at
LEAST three points:
3x  6 y  12
c.
y  3 x  5
6x  2 y  1
Find the slope and y-intercept of the following:
a. 4 x  6 y  2
b. y  5
c. x  4
Graph the following using slope-intercept form:
a. 3 y  2 x  6
Identify the intercepts of the following graphs:
Use point-slope form to find the following equations:
a. Find an equation of the line passing through (3, 4)
1
with slope . Put in slope-intercept form.
3
b. Find an equation of the line perpendicular to the
3
line y  x  4 and goes through the point (6, -1).
2
Write the equation in slope-intercept form.
Solve the following systems. If a single answer, write
as an ordered triple:
2 x  2 y  z  1
4 x  y  2 z  5


2y  z  4
a.   x  y  2 z  3
b. 
x  2 y  4z  0
 4 x  y  3 z  10


Unit 4
Determine if the following are solutions to the given
system of linear equations:
2 x  y  1
a. 
1) (3, -5)
2) (-1, 3)
3x  y  0
Problem solving with systems:
a. The sum of two numbers is 62. The first number
is six less than three times the second. What are the
two numbers?
Solve the following systems by graphing. If a single
point, write as an ordered pair:
b. A jewelry maker spends $1650 on operating costs
and $35 for each necklace made. The necklaces are
then sold for $85 each. How many necklaces does
the jewelry maker need to sell in order to break even?
c. John buys 3 pairs of jeans and 4 shirts for $195.
Nathan buys 2 pairs of jeans and 5 shirts for $165 on
the same day. How much does a pair of jeans cost?
How much does a shirt cost?
y  x  2
a. 
 y  5 x  4
Unit 6
Write in simplest form without zero or negative exponents.
a. 5t 4  3t 3
Solve the following systems by substitution. If a
single point, write as an ordered pair:
1
4 x  2 y  5
 x y 3
a. 
b.  2
2 x  y  4
 x  6  2 y
Solve the following systems by elimination. If a
single point, write as an ordered pair:
3x  y  5
2 x  3 y  0
a. 
b. 
6 x  y  4
4 x  6 y  3
c.

r 3 st 4
 x3 
f.  5 
y 

3
4
 x  y  z  1

a. 4 x  y  2 z  7
2 x  2 y  5 z  7

1) (5, -2, 4)
2) (3, -3, 1)
 2x y z  xy z 
d.
x3 y 2 z
xy 5 z 3
3
2
 2a 5bc 2 
g. 
2 4 
 15a b c 
2 3
e.
6 xy 2
9 xy
h.
a 6b 2
a 3b5
0
Determine the degree of the following polynomials.
Then indicate whether the polynomial is a monomial,
binomial, trinomial, or none of these.
a. 5x 2 y  4  x3 y 2
Unit 5
Determine if the following are solutions to the given
system of equations.
b.
b. 16  5x3 y 2
c. 4x 3 z 2
Perform the indicated operations and simplify.
a.  3 x5  2 x3  x 2    3x 2  x5  x3 
b.  4 xy  3  2 x 2 y    7 x 2 y  2 y 2  6 xy 
c.
 3x  4   x 2  5 x  2 
d.
x
2
 7 x  6    x  1
Unit 7
Factor using Greatest Common Factor.
3
2
a. 4c  18c  8c
b. x 4 y 3 z  2 x 2 y 2 z 3  4 x3 y 2 z
Factor by grouping. Remember GCF!
a. x3  5 x 2  x  5
b. 3x 2  6 x  7 x  14
Factor the following trinomials. Remember GCF!
a. x 2  5 x  6
b. 2 x 2  8 x  6
c. 2 x 2  x  10
d. 6 x 2  15 x  36
Factor the following differences of squares. Remember
GCF!
2
a. x  1
2
b. 25 x  36
2
c. 9 x  100
Unit 8
Factor the sums/differences of cubes. Remember GCF!
3
a. 8 x3  27
c. 125 x3  1
b. 3x  24
Divide the rational expressions. Write your answer in
simplest form.
3x3 6 x5

5 y 2 5 y3
c.
x3
x2  9

x 2  x  12 x 2  7 x  12
c. 12 x  27 x  0
d. x  6 x  7  0
2
Unit 9
Simplify each rational expression.
a.
x2  4
2
b. x  6 x  8
ax 2 y
ax 2 z
x 2  5 x  24
c. 2
x  7 x  30
x2  4
2
d. x  9 x  14
Multiply the rational expressions. Write your answer in
simplest form.
5 x3 y y 3
a. 2 2 
x y 15x 2
c.
12
x2 1

x2  x 4 x  2
x2  4 x  1

b. 2
x 1 x2  2x
d.
2 x 2  6 x 9 x  81

x 2  18 x  81 x 2  9
b.
Add the rational expressions. Write your answer in
simplest form.
a.
15 5

4x 4x
x
2x
 2
x2 x 4
b.
x
18
 2
c. x  3 x  9
12
3

d. x  5 x  24 x  3
2
Subtract the rational expressions. Write your answer in
simplest form.
a.
2x 1 2x  7

3x
3
b.
c.
4x2
1

2x 1 2x 1
d. x  4  x  6
Solve by factoring. Remember GCF!
a. x 2  5 x  4  0
b. 3 x 2  8 x  5  0
3
3 y  12 6 y  24

2y  4 4y 8
a.
5x 1
3x

x  7 x  12 x  3
2
3
1
Solve the rational equations. Label the extraneous
solutions.
3x
x
1
a. 4  3  12
c.
x
3
3
 
x3 2 x3
b. x  5 
d. x 
6
x
14
2x
 4
x 1
x 1