Chapter 5 – Linear Functions
y y 
A. Be able to calculate the slope of a line m   2 1  , Section 5-1 page 296 exercises 19, 21)
 x2  x1 
1. Find the slope of the line that passes through the points (2, 5) and (6, 13).
2. Find the slope of the line that passes through the points (7, -3) and (3, 9).
3. Find the slope of the line that passes through the points (-3, 4) and (6, 1).
B. Be able to convert an equation of the line in slope-intercept form (y = mx + b) to Standard Form (Ax
+ By = C; remember A, B, and C must be integers and A must be positive) (Section 5-5 page 322problem 4, page 324-exercise 31)
1.) Write the equation y 
1
x  4 in Standard Form
5
2.) Write the equation y  
1
x  7 in Standard Form
2
3.) Write the equation y 
1
x  3 in Standard Form
4
C. Be able to find the x- and y- intercepts of a given line page 320 – problem 1, page 324 exercise 11)
Find the x-intercept and y-intercept of each line. Make sure your intercepts are ORDERED PAIRS!
1. 6x  4y  24
2. 8x  4y  32
3.
3x  5y  15
1
D. Be able to write the equation of a line that has a given slope and contains a given point. (Section 5-4
page 314-problem 1, page 316-exercise 9)
1.) Write the equation of the line that has a slope of 2 and contains the point (5, 3).
2.) Write the equation of the line that has a slope of -3 and contains the point (3, 4).
3.) Write the equation of the line that has a slope of
1
and contains the point (2, -4)
2
E. Be able to write the equation of a given graphed line( Section 5-4 page 315 – problem 3, page 316
exercise 17)
What is the equation of the lines shown in the graphs below?
1.)
2.)
The equation of the line is ___________________
A.) y 
1
x4
3
1
3
C.) y   x  4
B.) y  
1
x3
4
D.) y  3x  4
2
F. Given the equation of a line you should be able to identify a line perpendicular to the given line –
-1
(remember perpendicular lines have slopes that are negative reciprocals 3 and
are negative
3
reciprocals) and parallel to the given line (remember parallel lines have the same slope). (Section
5-6 page 331-exercises13, 15, & 17)
1.) Find the equation of the line that is perpendicular to
3
y  x  1and contains the point (3, -2)
4
4
4
A. y   x  1
B. y   x  2
3
3
C.
y
3
x2
4
D.
y
2.) A line perpendicular to a line that
passes through the points (3, -2) and
(-1, 5) will have what slope?
4
x6
3
3.) Which line is parallel to 12x  6y  32 ?
1
x5
A. y 
B. y  2x 17
2
1
C. y  2 x  23
D. y  x  18
2
4.) Given the line: 6x  2y  8 a line
perpendicular to the given line will
have a slope of m = _________ and a
line parallel to the given line will have
a slope of m = ________
3
Chapter 6 – Systems of Equations and Inequalities
A. Be able to determine is a graphed system of linear equations is consistent and independent, consistent
and dependent, or inconsistent and independent.
B. Be able to determine if a system of linear equations has 1, 0, or infinite (Section 6-2 page 370
problem 4)
1.) If you solved a system of equations and your solution is 5 = 0 your system has ___________ solutions.
2.) If you solved a system of equations and your solution is 4=4 your system has ___________ solutions.
C. Be able to determine the solution of a graphed system of equations (Section 6-1 page 360-problem 1)
Using the graphs below find the solution to the system of equations
1.) The solution is _____________
2.) The solution is __________
4
D. Know how solve a system of equations using substitution (Section 6-2 page 370-problem 1, page
371-exercise 13) or elimination (Section 6-3 page 376, problem 3 page 378 exercises 9, 11)
Solve the following systems of equations using either substitution or elimination
1.)
4.)
x  3y  13
3x  y  11
4x  15y  10
3x  10y  5
2.)
5.)
y  x  4
y  4x  5
y  3x  7
y  4x  14
3.)
6.)
2x  5y  14
6x  7y  10
6x  18y  60
9x  2y  32
E. Know how to solve a word problem using systems of equations (Section 6-4 page 384-problem 1,
page 386-exercise 7)
A fashion designer makes and sells hats. The material for each hat costs $5.40. The hats sell for $15.40
each. The designer spends $1500 to start her business. How many hats must the designer sell in order to
break-even?
.
5
F.) Know how to write the equation of a graphed linear inequality (Section 6-5 page 393 problem 5, page
394-exercise 33)
Write an inequality for each graphed inequality
A. y 
C.
y
1
x 1
2
B. y 
1
x 1
2
D.
y
1
x 1
2
The equation of the inequality is
______________________________
1
x 1
2
G. Know how to write the equations for a system of inequalities represented by a given graph (Section 66 page-problem 2, page 399-exercise. Write a system of inequalities for each of the inequality systems
graphed
A.
3
y   x3
2
1
y   x  3
3
3
y x3
2
C.
1
y x3
3
3
y x3
2
B.
1
y x3
3
3
y x3
2
D.
1
y x3
3
The system of inequalities is:
6
Chapter 7 – Exponents & Exponential Functions

Know how to simplify negative exponents (Section 7-1 page 417-exercise 36, page 418-exercise 43)
Rewrite each of the following expressions using positive exponents only
1.)
x 2 y
=
x 3 y4
2.)
82
=
8 4
4.)
a5 (b1 )2 
Evaluate the expressions when a = -2 and b = 8
3.)

a 
2 2
b2 

2 2
Know how to simplify any base raised to the zero power ( 3ab c
5.)
  1 - Section 7.1)
0
54x 0 

Know how to recognize a number that is expressed in scientific notation (Section 7-2 – scientific
notation format is p  1 0n , where 1  p  1 0)
Write the following numbers in scientific notation:
6.) 38,567,200,000 = ____________________
7.) .0065378000 = ______________

Know how to multiply powers with the same base (Sections 7-3 page 429 exercises 17, 19)
8.) (4x 2 y 4 z 5 )(3x 3 y6 z 2 ) 

Know how to raise a power to a power (Section 7-4 page 435-problem 4, page 437-exercise 29, 31)
9.)

4a b
2
3
=
10.)
Know how to divide powers with the same base (Section 7-5 page 443-exercises 21, 23)
Simplify the expressions making sure there are only positive exponents
11.)
16x 3 y5
=
12x 4 y2
12.)
15a 5b 7

25a 2b 3
7
Chapter 8 – Polynomials & Factoring

Know how to add and subtract polynomials (Section 8-1 page 477-problem 5, page 479-exercises 45,
47)
13.)
4x
14.)
5x
15.)

3
 
4
 

 3x 3  6x  3x 3  11x 2  8x 
5a b
2 3
 

 2ab2  7a 2b  9a 2b 3 
Know how to factor out the GCF of a polynomial (Section 8-2 page 481-problem 3, page 483exercises 23, 25)
Factor the following expressions by factoring out the GCF
16.) 3x 4 y 3  12x 3 y  18x 2 y2


 3x 2  5x  x 3  11x 2  8 
17.)
15x 3  45x 2 y  20x y2
Know how to multiply binomials (Section 8-3 page 488, problem 3)
17.)
(𝑥 + 4)(𝑥 + 5) =
19.)
5x  32x  2  
18.) (𝑥 − 2)(𝑥 + 7) =
20.)
6x  24x  5  
8


Know how to factor a quadratic when a = 1 . (Section 8.5 page 500 Problems 1 – 3)
Factor
21.) 𝑥 2 + 9𝑥 + 20
22.) 𝑥 2 − 6𝑥 + 8
23.) 𝑥 2 − 3𝑥 − 18
24.) 𝑥 2 + 6𝑥 − 16
Know how to factor a quadratic when a ≠ 1 but you can factor out a GCF to make a = 1
25.) 2𝑥 2 + 2𝑥 − 40
26.) 3𝑥 2 + 6𝑥 − 9
27.) 4𝑥 2 + 20𝑥 + 24
Chapter 9 – Quadratic Functions & Equations

Know how to solve a quadratic by finding the square roots. (Section 9-3 page 549 Problem #2)
Solve each equation.
28.) 𝑥 2 − 25 = 0

29.) 5𝑥 2 − 45 = 0
Know how to solve a quadratic by factoring. (Section 9.4 page 555 Problems 1 & 2)
Solve each equation.
30.) 𝑥 2 + 2𝑥 − 15 = 0
32.) 2𝑥 2 − 20𝑥 + 48 = 0
31.) 𝑥 2 − 15𝑥 + 56 = 0
33.) 2𝑤 2 + 2𝑤 = 24
9
Chapter 10 – Radical Expressions & Equations

Know how to apply the Pythagorean Theorem(Section 10-1 page 601-problem 2, page 603-exercise
9)
1.) The length of the hypotenuse of a right triangle is 25 feet. One of the legs measures 20 feet. What is the length of
the other leg?
2.) The length of the legs of a right triangle are 20 inches and 21 inches. What is the length of the triangle’s
hypotenuse?
3.) The length of the hypotenuse of a right triangle is 37 centimeters. One of the legs measures 12 centimeters. What
is the length of the other leg?

Know how to simplify radical terms and combine like radicals (Section 10-3 page 614-problem 2,
page 616 – exercises 15, 17)
Simplify each sum or difference
4.) 4 7  63
5.)
5 18  4 32
6.) 3 20  2 45
10

Know how to multiply two radicals and simplify (Section 10-2 page 607- problem 2, page 610 exercise 29)
4ab3  12ab3 
7.)
8.)
16 x 5 y 3  4 x 3 y 
Chapter 12 – Data Analysis & Probability


Know how to calculate the mean of a given set of data (Section 12-3, problem 1- page 727 page 730exec. 9)
Know how to calculate the median of a given set of data (Section 12-3 problem 1- page 727)
9.) Find the mean and median of the data: 36, 59, 47, 56, 67
10.) Find the mean and median of the data: 23, 21, 17, 15, 12, 11

Given the mean be able to find the last data point (Section 12-3 page 727- problem 2,page 730exercise 13)
11.) Find the value of x such that the data set has the given mean
a.) 55, 60, 35, 90, x
Mean = 51
b.) 100, 112, 98, 235, x
Mean = 127
11

Know how to calculate the probability of two independent events (Section 12-8 page 766- problem 2,
page 768-exercise 17)
12.) You spin a spinner with 4 equal sections, then flip a coin, how many possible outcomes do you have?
13.) You role two number cubes, how many possible outcomes do you have?
12