Back by popular demand
Honors Algebra II Summer Assignment
Pinkston 2015
Possible online Resources if you don’t remember or know how to do a problem.


www.purplemath.com
http://www.khanacademy.org/
The first chapter of the textbook we will be using contains a review of basic Algebra concepts. Instead of
using class time to discuss these topics, I am assigning problems to you for the summer!  In the past, I
copied the first six sections of the text. This year, I have decided to compile various problems from multiple
sites. Your textbook: Holt McDougal (Algebra II) Larson
DIRECTIONS:




You are to complete all the following problems contained in this packet.
You must show all of your work in the space provided in the packet. (If you need to use a
separate sheet of paper, be sure to use a separate sheet for ALL PROBLEMS, clearly identify
the page number/problem number, and attach the work to the packet.)
Be sure all problems are neatly organized and all writing is legible.
This assignment will be worth 30-50 total points. I strongly suggest that you pace yourself
and do not wait until the last two weeks of summer to begin working. If you spread out your
work sessions, you are more likely to retain the information better.
 Once again, this assignment is due, completed with quality, on the FIRST
DAY that all students attend school (grades 9-12) and our class period
meets. You will hand it in that day.
On the FIRST DAY OF SCHOOL, I will collect the assignment and grade it for completion only. I will then hand
back the assignment (the next class period?) and we will take (45 – 90 minutes), one class, to discuss the
problems that were the most challenging. (NOT EVERY SINGLE PROBLEM). You will then have a test on the
Summer Assignment. I will notify you of the date. On the day of the test, I will collect your summer
assignment again and select random problems to grade. This time, I will be looking for the correct solutions.
Please show as much work as possible when necessary. Just a list of all answers will not be acceptable.
Turning the assignment in late will not be acceptable. There will be severe late penalties. 
Supplies:
 It is strongly suggested that you purchase a graphing calculator for the upcoming year. Check your
local office supply store/on line. There are several on the market, however, the Texas Instruments: TI
–84 and TI-84plus “family” of calculators are the preferred choice here at Brandywine. A few
Honors Algebra II 2015 Summer Assignment
calculators that may NOT be used on tests and quizzes are the TI-Nspire CAS, TI – 89 and the TI-92 (Or
any Casio, Hewlett-Packard, etc. equivalent).

Please purchase a three – ring binder, 2.5 to 3 inch. A one- inch binder will not be large enough to
last throughout the entire school year. Your notebook will be graded. Information on requirements
will be distributed at the beginning of the school year.
I may check my school email every 2-3 weeks during the summer in case you have any concerns:
mary.pinkston@bsd.k12.de.us
(Please forgive any typos.)
Have a wonderful summer and I will see you at the end of August! Miss Pinkston 
Summer Assignment Problems:
I. Order of Operations (PEMDAS)
 Parentheses and other grouping symbols.
 Exponential expressions.
 Multiplication, Division, (from left to right)
 Addition & Subtraction.
Simplify each numerical/algebraic expression. Show all work! Only use a calculator to check.
1) 6 + 2 x 8 – 12 + 9  3
3)
2) 25 – (23 + 5 x 2 – 3)
2  (30)  0.5  20
4)
4 6
2
2
5) 4(2  3)
7) 47  36  8  2
15  [8  (2  5)]
18  52
6)
8) 4( x  2)  3 x
Honors Algebra II 2015 Summer Assignment
3( 4  11)
10  3  3
9) 3(2 x  5)  (5  3x)
II. Evaluating Algebraic Expressions
To evaluate an algebraic expression:
 Substitute the given value(s) of the variable(s).
 Use order of operations to find the value of the resulting numerical expression.
Evaluate.
y

1
 3z 2   2x if x  , y  4, z  2
2

2


1) x 
3)
b  b 2  4ac
2a
if a  1, b  4, c  21
3(x  y )  2(x  y )
5)
5x  y
2) 12a – 4a2 + 7a3
if a = -3
4) 1.2(3)x if x = 3
x
if
x = 3 and y = 4
1
6) 2   if x  2
3
 
III. Simplifying Radicals
An expression under a radical sign is in simplest radical form when:
1) there is no integer under the radical sign with a perfect square factor,
2) there are no fractions under the radical sign,
3) there are no radicals in the denominator
Express the following in simplest radical form.
1)
50
2)
24
Honors Algebra II 2015 Summer Assignment
3)
192
4)
169
5)
147
IV. Properties of Exponents – Complete the example problems.
PROPERTY
Product of Powers
am  an = am + n
Power of a Power
(am)n = am  n
Power of a Product
(ab)m = ambm
Negative Power
a-n =
Zero Power
Quotient of Powers
1
an
a0 = 1
a
= am – n
an
m
am
a
  = m
b
b
m
Power of Quotient
EXAMPLE
x4

(x4)2
x2
=x
=x
6
8
3
(2x)3 = 8x
1
x3
(a  0)
x-3 =
(a  0)
40 = 1
x3
1
=x  x
2
x
(a  0)
3
x
x3
  = 3
y
y
 
(b  0)
Simplify each expression. Answers should be written using positive exponents.
1)
g5  g11 __________
2)
(b6)3 __________
3)
w-7
__________
4)
y 12
__________
y8
5)
(3x7)(-5x-3) __________
6)
(-4a-5b0c)2 __________
8)
 4x9 

 __________
4 
 12 x 
7)
15x 7y 2
25x 9y 5
3
__________
IV. Solving Linear Equations
To solve linear equations, first simplify both sides of the equation. If the equation contains fractions,
multiply the equation by the LCD to clear the equation of fractions. Use the addition and
subtraction properties of equality to get variables on one side and constants on the other side of
the equal sign. Use the multiplication and division properties of equality to solve for the variable.
Express all answers as fractions in lowest terms.
Examples:
a) 3(x + 5) + 4(x + 2) = 21
3x + 15 + 4x + 8 = 21
7x + 23= 21
7x = -2
x=-
2
7
Honors Algebra II 2015 Summer Assignment
b) 2(5x - 4) - lOx = 6x + 3(2x - 5)
lOx - 8 - lOx = 6x + 6x - 15
8 = 12x - 15
7 = 12x
7
12
=x
c)
2
x  5  6x 
3
3
4
2
3
12  x  5  6x  
3
4 

8x  60  72x  9
69  64x
69
x
64
Solve for the indicated variable:
1)
3n + 1 = 7n – 5
2) 2[x + 3(x – 1)] = 18
3)
6(y + 2) - 4 = -10
*4) 2x2 = 50
5)
5 + 2(k + 4) = 5(k - 3) + 10
7)
-3x + 4 = 11
9)
8x – 24 = -6 + 18
11)
2
x + 6 = 18
3
13)
-5 +
15)
b
=7
4
4t + 7 + 6t = -33
Honors Algebra II 2015 Summer Assignment
6) 6 + 2x(x – 3) = 2x2
8)
1
x- 8 = 3
2
10) -6 + x – 4 = 7x + 2
12) 6 – x – 5 = -4x – 3 – x
14)
16)
4.2m +4 = 25
6 = -z – 4
17) 4m + 2.3 = 9.7
19)
18) 2a + 5 = 9a – 16
1 4
2
+ y=
3 6
3
20) 6(y – 2) = 8 – 2y
m
= 2.7
12
21) n + 3(n – 2) 10.4
22)
23) -4.7 = 3x + 1.3
24) 3w + 2 – w = -4
25) A taxicab company charges each person a flat fee of $1.85 plus an additional $.40 per
quarter mile.
A. Write a formula to find the cost for each fare.
B. Use the formula to find the cost for 1 person to travel 8 mi.
26.) Find the dimensions of the rectangle given the area = 164 sq. ft.
3x+5
4
Honors Algebra II 2015 Summer Assignment
V. Operations With Polynomials
To add or subtract polynomials, just combine like terms.
To multiply polynomials, multiply the numerical coefficients and apply the rules for exponents for
variables.
Perform the indicated operations and simplify:
1) (7x2 + 4x - 3) - (-5x2 - 3x + 2)
2)
3) (4x + 5)(5x + 4)
4) (n2 + 5n + 3) + (2n2 + 8n + 8)
5) (5x2 - 4) – 2(3x2 + 8x + 4)
6) -2x(5x + 11)
7) (2m + 6)(2m + 6)
8) (5x – 6)2
9)
3x – 4 + 7x – 8 – 10x – 2
10)
4x + 2(x + 5)
11)
3(x + 5) – 4(x – 6)
12)
5x3 + 2x2 -7x – x3 + 5x2 – 18
Honors Algebra II 2015 Summer Assignment
(7x - 3)(3x + 7)
13)
(5x2 + x – 4) – (9x2 – 4x – 11)
14)
12x3(x4 – 5x2 + 2)
VI. Linear Equations in Two Variables (We will revisit these topics in Chapter 2.)
Examples:
a) Find the slope of the line passing through the points (-1, 2) and (3, 5).
slope = m =
b) Graph y 
y2 - y1
x2 - x1

m=
5-2
3 - (-1)

3
4
2
x 4.
3
Reminder: y = mx + b is slope-intercept form where m =. slope and b = y-intercept.
Therefore, slope is 2/3 and the y-intercept is – 4.
Graph accordingly.
c) Graph 3x - 2y - 8 = 0 with slope-intercept method.
Re-write in Slope-Intercept form: y =
m = 3/2
3
x -4
2
b = -4
d) Write the equation of the line with a slope of 3 and passing through the point (2, -1)
y = mx + b
-1 = 3(2) + b
-7 = b
Equation:
y = 3x – 7
Honors Algebra II 2015 Summer Assignment
9
Calculate the slope of the line that contains each pair of points.
1)
(-3, -4) (-4, 6)
2)
(-4, -6) (-4, -8)
3)
(-5, 3) (-11, 3)
Sketch the graph of each line in the space provided.
4.
y = 2x
6.
𝑦 = 4𝑥
5
Honors Algebra II 2015 Summer Assignment
5.
y = -3x
7.
𝑦 = −3𝑥
4
10
8.
An hot air balloon is currently at an altitude of 10,000 feet. The pilot begins to
descend the balloon at a rate of 50 feet per minute.
a)
Write an equation for the altitude (a) of the balloon as a function of the time (t)
b)
Find the altitude of the balloon after:
i.
10 minutes
ii.
30 minutes
iii.
1 hour
Sketch the graph of these “special” lines in the space provided.
9.
y=6
10.
x = -4
Write an equation, in slope-intercept form using the given information
11)
Line m is perpendicular to y = 4 x  1 and passes through the origin. What is
the equation of line m?
________________________
12)
A line that passes through the point (-5,6) with a slope of 4.
13)
A line that passes through the points (4,1) and (7,-11)
14)
A line that passes through the points (2, 2) and (3, 2)
Honors Algebra II 2015 Summer Assignment
11
Find the slope and y-intercept and x-intercept of each line. Then write the equation of
each line in y = mx + b form.
15)
16)
Slope = _________
Slope = ________
y-intercept : ________
y-intercept: _________
equation: y = _________________
equation: y = ________________
x-intercept: _______
x-intercept:_______
17)
18)
Slope = _________
Slope = ________
y-intercept : ________
y-intercept: _________
equation: y = _________________
equation: y = ________________
Honors Algebra II 2015 Summer Assignment
12
y = 4x – 2
19)
20)
6x – 3y = 15
slope = _______
slope = _______
y-intercept (let x = 0) = _______
y-intercept (let x = 0) = _______
x-intercept (let y = 0) = _______
x-intercept (let y = 0) = _______
VII. Solving Systems of Equations
Solve for x and y:
x = 2y + 5
3x + 7y = 2
Solve for x and y:
3x + 5y = 1
2x + 3y = 0
Using substitution method:
Using linear combination (addition/
subtraction) method:
3(2y + 5) + 7y = 2
6y + 15 + 7y = 2
13y = -13
y = -1
x = 2(-1) + 5
x=3
Solution: (3, -1)
3(3x + 5y = 1)
-5(2x + 3y = 0)
9x + 15y = 3
-l0x - 15y = 0
-1x = 3
x = -3
2(-3) + 3y = 0
y=2
Solution: (-3, 2)
Solve each system of equations by either the substitution method or the linear
combination (addition/ subtraction) method. Write your answer as an ordered pair.
1)
y = 2x + 4
-3x + y = - 9
3) x – 2y = 5
3x – 5y = 8
Honors Algebra II 2015 Summer Assignment
2) 2x + 3y = 6
-3x + 2y = 17
4) 3x + 7y = -1
6x + 7y = 0
13
VIII. Solving Linear Inequalities
Solve each inequality. Then graph the
solution set on a number line.
1.
3( y  7)  y  5
2.
3

  x  18   6
2

3.
3(8  6t )  2(5  9t )
4.
2 x  8  14
5.
7  5z  3  z  1
Honors Algebra II 2015 Summer Assignment
-Do the same steps that you would do if there
were an equal sign. Remember if you are
multiplying or dividing by a negative number
you need to reverse the inequality symbol.
14
6.
QUESTION
m
9   3  11
2
HINT
-Be sure to perform the steps to each of the
three parts of the inequality.
7.
2
3
b  2  10 or b  5  4
3
4
-Solve each inequality, then graph on the
same number line.
IX. Solving absolute value equations and inequalities
Solve each equation. Check your solutions.
1.
2x  3  5
-Isolate the absolute value expression.
-When a  b , then a  b or a  b , so set
up both equations and solve each.
2.
6  3m  6
3.
4x  6  2
Honors Algebra II 2015 Summer Assignment