Download Algebra 3 Exam Review

Algebra 3 Fall 2015 Final Review
Equations: Slope: m 
Name:______________________________________
y2  y1
, Slope-intercept form: y  mx  b , Point-slope form:
x2  x1
Unit 1
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:___________________________
2. Insert >, < or = to make the statement true.
16
a. 22 _____ 11 b.  6 _____ 6
c.
_____ 8
2
3. Simplify the following.
a. |-2| = _____
b. |4| = ____
a.
15
=_____
10
b.
32
=______
44
c.
56
=______
42
5. Perform the indicated operation. Write your
answer in lowest terms.
a.
c.
16 21
 =______
9 8
3 10
 =______
5 3
b.
4
2
 2 =______
3
3
1
3
d. 5  2 =______
3
4
Unit 2
9. Simplify the following expressions.
a. 4 x  x 2  1
b. 2  x 2  3 x   5 x
c. 3  x  2  12  x 
e.
 
1
1
4 x 2  2 x  8  15 x 2  9 x  3
2
3
b.

10. Translate the following into algebraic
expressions or equations.
a. Subtract 7 x  2 from x  5 __________________
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.
___________________
b. 9 x  x  1  6( x  1)  7
16  13  5  32
17  5
c.
7. Perform the indicated operation of real
numbers:
2
25
4  1
a.     
b.   
15
6
7  7
c. 4  ( 6)

d. 4  x  3  3  x  2
11. Solve for x:
a. 3x  9  18
6. Simplify the following.
a. 6  2  2  25
8. Evaluate the following for x = 1, y = -4, and z = 2
x2  y  x  z
a. x  y  2
b.
z3  y
c. |-5.6| =____
4. Write each fraction in lowest terms.
y  y1  m( x  x1 )
d. 
16
8

27
45
5  x  1
6
 2x  3
d.   5x  1  7 x  3
12. Formulas
a. Given A  l  w ; A  56, l  8 . Find w.
b. Solve for w: V  lwh .
c. Mike is trying to replace the carpet in his
bedroom. His room is rectangular and has a width of
13. feet and a length of 20 feet. How much carpet
will Mike need for his bedroom?
18. Find the slope of the following:
a. Line through (4, -2) and (2, 5)
b. Line through (8, -1) and (3, -1)
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
13. 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?
b. The sum of two consecutive even numbers is 178.
What are the two numbers?
Unit 3
14. Graph the following using coordinate points.
Find at LEAST three points:
3x  6 y  12
19. 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)
c.
y  3 x  5
6x  2 y  1
20. Find the slope and y-intercept of the following:
a. 4 x  6 y  2
b. y  5
c. x  4
21. Graph the following using slope-intercept
form:
a. 3 y  2 x  6
15. Identify the intercepts of the following graphs:
16. Find the intercepts for the following equations:
a. x  4 y  8
b. 2 x  3 y  6
17. Graph the following equations by plotting
intercepts:
4 x  5 y  20
22. 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.
Unit 4
23. Solve for x. Write the answer in interval
notation and graph.
a. x  5
b. 2  x  3
28. Graph the following Systems of Linear
Inequalities:
 y  3x  2
a. 
y  x  4
c. 3x  4  x
24. Write each Compound Inequality in inequality
form and interval notation and then graph.
a. x  5  2 and 2x  3  5
x  4 y  8
b. 
x  5

b.  x  7  5 or 3x 1  13
c. 1 
x3
2
4
25. Solve the following Absolute Value Equations.
x3
 4
a. 2 x  3  5  7
b.
2
26. Solve the following Absolute Value
Inequalities. Graph the answer and write in
interval notation.
a.
2 x  3  5
b.
6 x  3
c.
x2  4
27. Graph the following Linear Inequalities.
a. y  3 x  5
b. 2 x  3 y  6
Unit 5
29. 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
30. Solve the following systems by graphing. If a
single point, write as an ordered pair:
y  x  2
a. 
 y  5 x  4
31. 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
32. 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
Unit 6
33. Determine if the following are solutions to the
given system of equations.
 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)
a. 5x 2 y  4  x3 y 2
4 x  y  2 z  5

2y  z  4
b. 
 4 x  y  3 z  10

35. Problem solving with systems:
a. The sum of three numbers is 110. The largest
number is six more than three times the smallest.
The remaining number is two more than twice the
smallest What are the three numbers?
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?
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
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?
2
 7 x  6    x  1
Unit 8
nth root rule:
39. Simplify each radical expression.
1
a. 32
b. 3
27
40. Evaluate the following expression in radical
form and simplify if possible.
a.
 27 
2
3
2
5
a. a a a
Unit 7
b. 64
1
3
41. Evaluate the following expression in rational
form and simplify if possible.
1
3
3
4
b.
x
3
y
6

1
1
3
c.
 r st 
3
4
x 
f.  5 
y 
3
4
3
b.
 2x y z  xy z 
3
3
d.
2
x y z
xy 5 z 3
e.
 2a bc 
g. 
2 4 
 15a b c 
2
3
42. Multiply/divide the following expressions.
Then simplify if possible.
2
2
2
1
2 3
2
5
c.
x 4x
x
36. Write in simplest form without zero or negative
exponents.
a. 5t 4  3t 3
c. 4x 3 z 2
b. 16  5x3 y 2
38. Perform the indicated operations and
simplify.
a.  3 x5  2 x3  x 2    3x 2  x5  x3 
34. Solve the following systems. If a single
answer, write as an ordered triple:
2 x  2 y  z  1

a.   x  y  2 z  3
x  2 y  4z  0

37. Determine the degree of the following
polynomials. Then indicate whether the
polynomial is a monomial, binomial, trinomial, or
none of these.
0
6 xy
9 xy
6 2
ab
h. 3 5
a b
a. 5a 8c  2c
4
4
c.
5 18 x3 y
2y
5
5
b.
d.
3
y5
27 x 6
2ab3  6b
43. Perform the indicated operation.
a. 2 3 24  3 3 81
b.
5 6 5
c.
d.


5 6 x 3 x  2
2
3 5


b.
3
6
9x
c.
2 3
2 3
45. Rationalize the numerator. Simplify if
possible.
24 x5
3y2
a.
b.
15  1
2
46. Solve the following radical equations. Check
for extraneous answers.
x  4  2x  5
a.
c.
3
 4  2i    7i 
b.  3  i    6  5i 
c.
 6  7i  2  4i 
d.
2  3i
2i
49. Find the powers of i.
44. Rationalize the denominator of the following.
Simplify if possible.
2
7
a.
2
Unit 9
a.
48. Perform the indicated operation. Write your
answer in the form a  bi .
b.
5x  6  1
2x  3  2  1
47. Write in terms of i.
a.
49
b.
15  10
c.
27  12
d.
8
2
a. i13
b. i 56
c. i 21