Algebra B
Second Semester Final Review
Name ______________________________________________
1
Period ________
To prepare for the final exam, focus your work on the learning targets listed below, and use this checklist to determine
which concepts you should practice the most. You will be provided with the notes on the back of this sheet on the final
exam. You will not be allowed to use any other notes, and you cannot retake the final exam.
Learning Target
1.11.3
1.6
I can solve equations (multi-step, use the distributive property)
4.1
I can add and subtract polynomials
4.2
I can multiply polynomials
4.3
I can factor polynomials using the greatest common factor
4.4
5.1
I can factor a trinomial with a leading coefficient of 1 into a product of
binomials.
I can factor a trinomial with a leading coefficient other than 1 into a
product of binomials.
I can factor by recognizing a difference of squares or a perfect square
trinomial.
I can factor polynomials completely using a combination of factoring
methods.
I can find the zeros (roots) of a quadratic equation by factoring.
5.2
I can find the zeros (roots) of a quadratic equation using square roots.
5.3
I can use the quadratic formula to find the discriminant of a quadratic
equation and determine the number of real solutions.
I can use the quadratic formula to find the zeros (roots) of a quadratic
equation.
I can solve a quadratic equation using an appropriate method.
(factoring, square roots, quadratic formula)
Given a quadratic equation, I can complete a table of values, draw the
graph, and identify the domain, range, intercepts, vertex, and axis of
symmetry.
I can graph a quadratic function by finding the vertex, x-intercepts, yintercept, and axis of symmetry.
Given a real world situation represented by a quadratic function, I can
evaluate the function for specific values of the domain.
I can write and solve a quadratic equation for real world situation.
4.5
4.6
4.7
5.4
5.5
5.6
5.8
5.9
5.10
I can use tables, equations, and graphs
Need to
Practice
Know
Well
Help!
Algebra B
Second Semester Final Review
2
PROVIDED TEST NOTES
Sets of Numbers:
Order of Operations:
P
E
M
D
A
S
Some perfect squares:
4
9
16
25
36
49
parenthesis and other grouping symbols
exponents
multiplication
Multiply and divide from left to right.
division
addition
Add and subtract from left to right.
subtraction
64
81
100 121 144 169 196 225
Rules of Exponents:
Product of Powers:
Quotient of Powers:
a m  a n  a m n
am
a
n
 a mn
Power of a Power:
a 
Power of a Product:
abn  a n b n
Power of a Quotient:
an
a
   n
b
b
m n
 a mn
n
n

Negative Power:
a
Zero Power:
a0  1
1
RISE y 2  y1

RUN x 2  x1
Slope-Intercept Form:
Point-Slope Form:
Standard Form:
y  m x b
y  y1  m( x  x1 )
Ax  By  C
General Exponential Form:
an
Quadratic Formula:
If ax2 +bx + c = 0 and a
Slope 
Growth/Decay Formula:
0 then
for
A  P (1  r ) t
y = ax2 + bx + c
Axis of symmetry
x=
discriminant: b2 – 4ac
y  ab x
Vertex
(x, y)
𝒙=
−𝒃
𝟐𝒂
Algebra B
Second Semester Final Review
3
To prepare for the final, begin by completing the following practice problems. Then be sure to spend extra time
reviewing learning targets with scores below proficiency
LT 1.1-1.3
Solve each equation. State your answers in exact form. (no decimal approximations)
#1 8 – 10h = 7 – 5h + 16
#2 9m + 15 = 4 + 5m – 5
#4
x
-1 = 7
2
#5 -3d + 7 + d = – (2d – 3) + 4
#7 2(5 + z) + 3 = 13 – (4z – 6z)
#8 3x – 3 + 3x = 8 – 2(-2x + 1)
LT 1.6
#9 Write an equation to represent each of the table of values, and draw the graphs.
a)
x
y
-4
-8
-2
-4
0
0
2
4
4
8
6
12
8
16
6
-4
4
-3
2
-2
0
-1
-2
0
-4
1
Equation:
b)
x
y
8
-5
Equation:
#10 Write the equation in slope-intercept form and draw the graph.
3x + 2y = 8
#3 -2x + 8 – 6x = -3x + 5
#6 3(a + 3) – a = 13 + 3a – 4
Algebra B
Second Semester Final Review
4
#11 Create a table of values and write an equation to represent the graph.
Equation ____________________________
x
y
-3
0
#12 Write the equation in slope-intercept form of each line graphed.
A) ______________
B)________________ C)_______________
Unit 4: Polynomials
Find each sum or difference. Write your answer in standard form.
#13 (12𝑥 4 − 6𝑥 2 + 4𝑥 − 1) + (5𝑥 3 − 2𝑥 2 + 1)
#14 (𝑥 5 + 3𝑥 2 − 3) − (5𝑥 3 − 9𝑥 2 + 7)
#15 (−5𝑥 2 + 23𝑥 − 6) − (8𝑥 2 − 𝑥 + 7)
#16 (−12𝑥 2 − 4𝑥 6 − 3) + (18𝑥 6 + 7 + 3𝑥 2 )
Find each product
#17 −9𝑦 2 (3𝑦 2 − 𝑦 + 11)
#18 (2𝑥 + 6)(𝑥 − 10)
#19 10𝑥(𝑥 − 7)(𝑥 − 5)
#20 (−3𝑥 − 12)2
Factor each of the following completely.
#21
3𝑥 4 − 9𝑥 2 − 12𝑥
#22
2𝑥 2 + 8𝑥 + 6
#23
𝑥 2 + 11𝑥 + 28
Algebra B
Second Semester Final Review
5
#24
𝑥 2 − 10𝑥 + 25
#25
𝑥 2 + 5𝑥 − 24
#26
#27
36𝑥 2 − 81
#28
4𝑥 2 + 28𝑥 + 49
#29
3𝑥 2 + 𝑥 − 4
#31
2𝑥 4 − 4𝑥 3 − 70𝑥 2
#32
𝑥 2 + 5𝑥 − 84
#30
𝑥 3 + 2𝑥 2 − 15𝑥
𝑥 2 − 49
Unit 5: Quadratic Functions
LT 5.1 Solve by factoring.
#33 𝑥 2 + 11𝑥 + 10 = 0
#34 2𝑥 2 = 10𝑥
#35 2𝑥 2 − 36 = 21𝑥
#36
𝑥 2 − 14𝑥 = −45
LT 5.2 Solve using square roots. State your answer in simplest radical form when necessary.
#37 25𝑥 2 = 625
#38 (𝑥 + 5)2 = 20
#39 2𝑥 2 − 14 = 0
#40 −3𝑥 2 + 12 = 0
LT 5.3 For each of the following:
a) Find the value of the discriminant.
b) Determine the number of real solutions.
2
#41 𝑥 − 6𝑥 + 7 = 0
#42 𝑥 2 − 6𝑥 + 9 = 0
#43
𝑥 2 − 6𝑥 + 11 = 0
LT 5.4 Solve using the quadratic formula. When necessary state your answer in simplest radical form.
#44 −3𝑥 2 − 11𝑥 + 4 = 0
#45 2𝑥 2 − 𝑥 − 120 = 0
#46 5𝑥 2 − 47𝑥 = 156
#47
−𝑥 2 − 25 = 10𝑥
#48 𝑥 2 = −3𝑥 − 11
Algebra B
Second Semester Final Review
6
LT 5.5 Solve each quadratic equation using an appropriate method (factoring, square roots, quadratic formula)
State your answer in simplest radical form when necessary.
#49 3𝑥 2 − 48 = 0
#50 𝑥 2 − 4𝑥 = −4
#51 𝑥 2 − 8𝑥 = −16
#52 3𝑥 2 + 2𝑥 − 4 = 0
#53
−4(𝑥 + 3)2 + 64 = 0
#54
𝑥 2 + 3𝑥 = 10
LT 5.6 For each of the following quadratic functions:
a) Complete the table of values.
b) State the coordinates of the vertex.
c) State equation for the axis of symmetry.
d) State the y-intercept.
e) State the x-intercepts.
f) State the domain AND range.
g) Graph the quadratic function on graph paper.
#55
𝑦 = 𝑥2 + 4
x
-3
-2
-1
0
1
2
3
y
#56
𝑦 = −𝑥 2 − 4𝑥 + 5
x
-5
-4
-3
-2
-1
0
1
𝑦 = −2𝑥 2 + 8𝑥
#57
y
x
-1
0
1
2
3
4
5
y
#58 𝑦 = 𝑥 2 − 4𝑥 + 4
x
-1
0
1
2
3
4
5
y
LT 5.8 For each of the following:
a) Find the vertex. Show work.
b) State the equation for the axis of symmetry.
c) Find the zeros. (x-intercepts) Show work.
d) State the y-intercept.
e) State the domain AND range.
f) Graph the quadratic function on graph paper.
#59 𝑦 = 𝑥 2 − 6𝑥 − 7
#60 𝑦 = −𝑥 2 + 2𝑥 − 4
#61 𝑦 = 2𝑥 2 + 12𝑥
#62 𝑦 = −3𝑥 2 − 12𝑥 − 9
Algebra B
Second Semester Final Review
7
LT 5.9
#63 A baseball is thrown with an upward velocity of 64 ft/s. Its height h, in feet, after t seconds is given by the function:
ℎ = −16𝑡 2 + 64𝑡 + 6
a) At what time will the baseball reach its maximum height? (show work)
b) What is the baseball’s maximum height? (show work)
c) How long does it take the baseball to hit the ground? (show work)
d) When is the baseball 10ft above the ground? (show work)
e) What is the baseball’s height at 0.5 seconds? (show work)
f) Use the answers from parts a through d to draw the graph of the function. (graph paper)
g) State the domain and range of the function.
#64 Suppose a person is riding in a hot-air balloon, 154 feet above the ground. He drops an apple. The height h, in
feet, of the apple above the ground is given by the formula ℎ = −16𝑡 2 + 154, where t is the time in seconds. Round
values to the nearest hundredth when necessary.
a) When does the apple reach it’s maximum height? (show work)
b) What is the apple’s maximum height? (show work)
c) When is the apple 10 feet above the ground? (show work)
d) How long does it take for the apple to reach the ground? (show work)
e) What is the apple’s height at 2.5 seconds?
f) Use the answers from parts a through e to draw the graph of the function. (graph paper)
g) State the domain and range of the function. (use the correct variables)
Algebra B
Second Semester Final Review
8
LT 5.10 I can write and solve a quadratic equation for real world situations.
#65 You are making a rectangular table. The area of the table should be 10 ft2. You want the length of the table to be
1 foot shorter than twice the width. What should the dimensions of the table be? Write and solve an equation to find
the length and width. (show work and define your variables.)
#66 You are building a rectangular deck. The area of the deck should be 250 ft2. You want the length of the deck to be
5 feet longer than twice its width. What should the dimensions of the deck be? Write and solve an equation to find the
length and width. (show work and define your variables.)
#67 You are planning a rectangular patio with length that is 7 feet less than three times its width. The area of the patio
is 98 ft2. What are the dimensions of the patio? Write and solve an equation to find the length and width. (show work
and define your variables.)