SOL Review Booklet
Math 8
2015-2016
Name: _______________
Block: ______
SOL Date: ___________
SOL 8.1
The student will
a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and
properties of operations with real numbers; and
b) compare and order decimals, fractions, percents, and numbers written in scientific notation.
HINTS & NOTES




HINTS & NOTES
To write a number in scientific notation, you write the
number
as two factors.
How
to simplify
numeric expressions:
o Move the decimal to the left or right to make a factor between 1 and 10.
o The exponent will be the number of places that you moved the decimal.
G
 Example: 25,000,000 = 2.5 x 107
E
 Example: .000345 = 3.4 x 10-4
MD
To write a number in standard form, you move the decimal point to the left or right as many places as the
AS
exponent indicates. Put 0 in any space.
o Example: 3.4 x 105 = 340,000
Step 1: Perform operations with
o Example: 5.8 x 10-3 = .0058
grouping symbols (parenthesis and
Steps for ordering numbers:
brackets).
o Change all of the numbers to decimals.
o Remember to look for the order that the questions asks. (L →G or G→L)
Step (top
2: Simplify
exponents.
To change a fraction to a decimal → divide the numerator
number) by
the denominator (bottom
number).

Example:
Step 3: Perform all multiplication and
division (in order from left to right)
= 0.375
 To change a percent to a decimal →move the decimal two places to the left
Step 4: Perform all addition and
o Example: 78% = 0.78
subtraction (in order from left to right).
 Ascending means…
 Descending means…
PRACTICE
1. Identify each number between 𝟏. 𝟕 × 𝟏𝟎𝟎 and
195%.
1.8 × 101
1
7
8
18.5
2. What is 102,000,000 expressed in scientific
notation?
A. 1.02 x 109
B. 1.02 x 108
C. 1.02 x 107
D. 1.02 x 106
7
4
4. Which list is ordered from least to greatest?
1 3
A. , , 30%, 3 × 10−2
3 5
B.
3 1
, , 30%, 3 ×
5 3
10−2
C. 3 × 10−2 , 30%,
1 3
,
3 5
1
, 30%, 3 ×
3
3
5
D.
10−2 ,
5. Arrange the numbers from greatest to least.
9.1 × 102
918%
1830
2
920.0
3. Which statement is true?
A. 0.09 >
B. 6% < 0.09
C.
< 8.0 x 10-3
D. 8.0 x 10-3 > 6%
6. Arrange the numbers from least to greatest.
2
65%
6.40
6.04 × 10−1
3
SOL 8.1 (CONTINUED)
The student will
a) simplify numerical expressions involving positive exponents, using rational numbers, order of operations, and
properties of operations with real numbers; and
b) compare and order decimals, fractions, percents, and numbers written in scientific notation.
HINTS & NOTES
 How to simplify numeric expressions:
G  Perform operations with Grouping symbols (parentheses, brackets, absolute value)
E  Simplify Exponents
MD  Perform all Multiplication and Division (in order from left to right)
AS  Perform all Addition and Subtraction (in order from left to right)
PRACTICE
7. According to the order of operations, which
operation should be performed first to simplify the
expression?
12 + 2 • 52 – 1
A.
B.
C.
D.
12 + 2
5–1
2 • 52
52
8. Which value is equivalent to
A.
B.
C.
D.
11. What is the value of the expression shown?
−𝟒 − 𝟐𝟎
+ 𝟏𝟐𝟏
𝟖
?
2
14
16
30
12. What is the value of 4(6 + 2)2?
A. 64
B. 160
C. 256
D. 1,024
13. Identify each expression that is equivalent to 24.
9. What is the value of (4 – 2)2 + 4 -1?
A.
B.
C.
D.
𝟏𝟖 + 𝟑𝟐
𝟐𝟑 ∙ 𝟑
7
9
15
17
10. What is the value of the expression shown?
𝟐𝟐𝟓
+ −𝟏𝟎 + 𝟔
𝟓
𝟐+𝟑 ∙𝟒
𝟒+𝟒∙𝟓
𝟑𝟔 ÷ 𝟐 + 𝟔
14. According to the order of operations, what should
be performed first to simplify the expression.
𝟏𝟎 + 𝟏𝟖 ÷ 𝟔 + 𝟑 ∙ 𝟐
A.
B.
C.
D.
10 + 18
6+3
3∙2
18 ÷ 6
SOL 8.2
The student will describe orally and in writing the relationship between the subsets of the real number system.
HINTS & NOTES
Natural: “counting numbers”; 1, 2, 3, …
Rational
Whole: the Natural numbers plus 0; 0, 1, 2, 3, …
Integers
Integers: Whole numbers and their opposites; …, -2, -1, 0, 1, 2, …
Whole
Rational: Numbers that can be written as a ratio; decimals end or
repeat; ½, ¼, 5, -2, 0
Natural
 Irrational: Decimals that never end and never repeat; 13, π
 Subset – smaller or more specific group within a set
o Example: The Integers are a subset of the Rational Numbers
 “Contained in” – EVERYTHING is a subset of the bigger group
o Example: The Natural numbers are completely contained in the Whole numbers




Real
Irrational
PRACTICE
1. Which of the following does not contain the
number 24?
A.
B.
C.
D.
Integers
Whole Numbers
Natural Numbers
Irrational Numbers
2. Which of the following is not a rational number?
A. -0.75
B. 0
C.
D.
3. What subset of the real number system is
completely contained in the Whole Numbers?
A.
B.
C.
D.
Natural
Integer
Rational
Irrational
4. The set of whole numbers is not a subset of A.
B.
C.
D.
irrational numbers
integers
rational numbers
real numbers
5. Which number in this list is NOT an integer?
𝟏𝟐
, −𝟒𝟐 , 𝟐𝟓, −𝟒. 𝟖
𝟒
12
A. 4
B. −42
C. 25
D. −4.8
6. Which number is an irrational number?
A. − 9
B. −10
C. 5.499
D. 17
7. Which of the following sets of numbers contain the
𝟏
number − 𝟑?
Integers
Real Numbers
Rational Numbers
Whole Numbers
Irrational Numbers
Natural Numbers
8. Identify each classification of the real number
system that can describe the set of numbers shown.
− 𝟑𝟔, 𝟑𝟓%, 𝟐
Real
Natural
Whole
Integer
Irrational
Rational
SOL 8.3
The student will
a) Solve practical problems involving rational numbers, percents, ratios, and proportions; and
b) Determine the percent increase or decrease for a given situation.
HINTS & NOTES
 Set up a proportion with two equal fractions with similar information, cross multiply and divide to solve
the equation.
 Percent Proportion 
 Change a percent to a decimal and multiply: Move the decimal place two places to the left.
o Ex: 5.5% is 0.055 or 1% is 0.01
 Tax: Find the % tax in $ by MULTIPLYING the $ times the % as a decimal. ADD to original amount.
 Tip: Find the % tip in $ by MULTIPLYING the $ times the % as a decimal. ADD to original amount.
 Mark-Up: Find the % mark-up in $ by MULTIPLYING the $ times the % as a decimal. ADD to original
amount.
 Sales/Discount: Find the % in $ by MULTIPLYING the $ times the % as a decimal. SUBTRACT from the
original amount
 Interest: I = prt, where p is the _______ amount ($), r is the ______ (%), and t is the _______ (years).
 Checkbook Vocabulary:
o Credit/Deposit = ________
o Debit/Withdraw = ________
 Percent Increase/Decrease (change):
o new value - old value x 100
old value
PRACTICE
1. Manuel can paint 5 pictures in 12.5 hours. At this
rate, which proportion can be used to find p, the
number of pictures Manuel can paint in 8 hours?
3.
A.
B.
C.
D.
2. Xavier saved money to purchase a bike that
originally cost $250, not including tax. The store
discounted the bike by 20%. What is the discounted
price he will pay for the bike, not including tax?
A. $200
B. $230
C. $270
D. $280
4. A librarian knows that 45% of the books currently
checked out will NOT be returned on the due date.
The library has a total of 5,040 books. How many of
the library’s books will be returned on the due date?
SOL 8.3 (CONTINUED)
The student will
c) Solve practical problems involving rational numbers, percents, ratios, and proportions; and
d) Determine the percent increase or decrease for a given situation.
PRACTICE
5. At a water park, $8 buys 15 tickets. Sue is going to
spend $96 on tickets. How many tickets will her $96
buy?
A. 12
B. 18
C. 120
D. 180
6. Dora bought a total of 48 cupcakes. Each cupcake
cost $0.55, including tax. Of the cupcakes she
𝟑
bought, were vanilla cupcakes. What was the total
𝟖
cost of only the vanilla cupcakes?
A. $6.60
B. $9.90
C. $16.50
D. $26.40
7. Emil bought a camera for $268.26, including tax.
He made a down payment of $12.00 and paid the
balance in 6 equal monthly payments. What was
Emil’s monthly payment for this camera?
A. $42.71
B. $44.71
C. $46.71
D. $56.71
8. A food company reduced the amount of salt in one
of their food products from 700 milligrams to 630
milligrams. What is the percent decrease in the
amount of salt in this food product?
A. 10%
B. 12%
C. 70%
D. 90%
9. Kyle caught 9 insects for his science project in the
first week. He caught 13 insects in the second week.
What is the percent increase in the number of insects
Kyle caught from the first week to the second week?
Round your answer to the nearest whole number.
10. Susan’s checkbook had a balance of $22.05 on
April 1. On April 5, she wrote a check for $106.30 to
the auto repair shop. On April 7, she wrote a check in
the amount of $310.00 for rent. On April 9, her dad
sent her $95.00 to deposit into her account. What is
the balance of Susan’s account after this deposit?
11. Jane bought a new sweater. It was priced at
$32.00 and there was a 25% discount. Jane gave the
cashier $40. What was her change?
12. If a pole 9 feet tall casts a shadow of 3 feet, how
long of a shadow would a 6 foot man cast?
A. 1 ft
B. 1.5 ft
C. 2 ft
D. 2.5 ft
13. Don buys a car for $22,500. Don gets a loan for 5
years with an interest rate of 3% per year. How much
total interest will Don pay over the five years?
A. $675
B. $3,375
C. $19,125
D. $25,875
14. While shopping at a store, Billy found a $900
television that was on sale at a discount rate of 30%.
What is the amount of discount?
A. $270
B. $630
C. $870
D. $1170
SOL 8.4
The student will apply the order of operations to evaluate algebraic expressions for given replacement values of
the variables.
HINTS & NOTES
 Substitution: Replace the variable with the appropriate given value. Follow the order of operations.
G  Perform operations with Grouping symbols (parentheses, brackets, absolute value)
E  Simplify Exponents
MD  Perform all Multiplication and Division (in order from left to right)
AS  Perform all Addition and Subtraction (in order from left to right)
PRACTICE
1. What is the value of 3(x2 - 4x) when x =5?
A. 5
B. 15
C. 30
D. 55
2. What is the value of the expression
5(a + b) - 3(b + c)
if a=4,b=3,and c=-2?
A. 20
B. 18
C. 14
D. 9
5. What is the value of 𝒙𝟑 + 𝒙𝟐 + 𝒙 when 𝒙 = 𝟑?
A. 9
B. 18
C. 21
D. 39
6. If 𝒙 = 𝟐 and 𝒕 = 𝟒, what is the value of
𝟏
𝒙𝟑 − 𝟒 𝒕𝟐 + 𝟖 ?
𝟖
A. 12
B. 4
C. -72
D. -144
𝟖
3. What is the value of the following when b = 2?
𝟑
7. What is the value of 𝟑 𝒏𝟑 when 𝒏 = 𝟐?
A. 4
B. 6
C. 9
D. 12
3b + 3(b - 4)
b2 - b
8. Identify each expression that has a value of 53
when given the corresponding replacement set.
𝑎3 + 13𝑏 when 𝑎 = 3 and 𝑏 = 2
1
2
10𝑏 2 ∙ + 𝑎3 when 𝑎 = 2 and 𝑏 = 3
4. What is the value of 𝟐 𝟓 − 𝒂
A. 16
B. 20
C. 32
D. 50
𝟐
+ 𝟕𝒂 when 𝒂 = 𝟐?
𝑎2 + 1 ∙ 𝑏 2 when 𝑎 = 4 and 𝑏 = 6
3𝑎+4𝑏2
2
when 𝑎 = 2 and 𝑏 = 5
5 + 𝑎2 ∙ 𝑏 + 8 when 𝑎 = 2 and 𝑏 = 5
SOL 8.5
The student will
a) Determine whether a given number is a perfect square; and
b) Find the two consecutive whole numbers between which a square root lies.
HINTS & NOTES
 Perfect Square: is the product of an integer and itself.
Ex.:
52 =
102 =
152 =
122 =
 Square Root: is the base which when multiplied by itself is equal to the original number.
Ex:
=
=
=
=
 Estimating Square Roots: Identify the two consecutive whole numbers between which square root of a
given whole number lies.
Ex.
o
o
o
o
Determine the two perfect squares that 21 falls between.
Take the square root of the two perfect squares
Answer.
Example
16 & 25
&
4
&
5
PRACTICE
1. Which of the following numbers is a perfect
square?
A. 36
B. 28
C. 22
D. 14
2. Between which two whole numbers is
A. 32 and 34
B. 16 and 17
C. 6 and 7
D. 5 and 6
3. Which number is a perfect square?
A. 2
B. 5
C. 25
D. 52
4. Which has a value between -2 and -3?
A. B. C. -
D. -
5. Place the
?
where it belongs on a number line.
6. What is − 𝟑𝟐𝟒?
7. Which pair of numbers are both between 6 and 7?
A. 30 and 42
B. 36 and 49
C. 37 and 50
D. 42 and 48
8. Which statement best describes 𝟓𝟎?
A. Exactly 7
B. Exactly 25
C. Between 7 and 8
D. Between 24 and 26
SOL 8.6
The student will
c) Verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary
angles, and complementary angles; and
d) Measure angles of less than 360⁰.
HINTS & NOTES
 Vertical angles: Angles directly opposite that are congruent.
 Complementary angles: Two Angles are Complementary if they add up to ______ degrees (a Right
Angle). Complementary think Corner.
 Supplementary angles: Two angles are Supplementary if they add up to ________ degrees (straight line).
Supplementary think Straight Line.
 Reflex angles: Angles that measure between 180 and 360 degrees.
 Adjacent angles: any two non-overlapping angles that share a common side and a common vertex.
PRACTICE
1. In which diagram do <1 and <2 appear to be
vertical angles?
2. Which pair of angles is supplementary?
SOL 8.6 (CONTINUED)
The student will
e) Verify by measuring and describe the relationships among vertical angles, adjacent angles, supplementary
angles, and complementary angles; and
f) Measure angles of less than 360⁰.
PRACTICE
3. Which of the following could be the
measurements of two supplementary angles?
A. 7⁰ and 83⁰
B. 83⁰ and 83⁰
C. 97⁰ and 83⁰
D. 117⁰ and 83⁰
7. Which statement is true?
4. Look at the angles.
A.
B.
C.
D.
Identify each angle that is adjacent to Angle 2.
Angle 1
Angle 3
Angle 4
Angle 2 and angle 4 are vertical angles.
Angle 3 and angle 6 are complementary angles.
Angle 1 and angle 2 are supplementary angles.
Angle 1 and angle 5 are complementary angles.
8. Which is the closest to the measure of <WXY?
Angle 5
5. In this figure, 𝒎 < 1 = 15𝒙 − 𝟓 ⁰ and
𝒎 < 2 = 10𝒙 + 𝟑𝟓 ⁰.
A.
B.
C.
D.
What is 𝒎 < 1?
A. 31⁰
B. 65⁰
C. 85⁰
D. 115⁰
45⁰
55⁰
135⁰
145⁰
9. In the figure shown,
𝒎 < 1 = 4𝒙 + 𝟏𝟐 ⁰ and 𝒎 < 2 = 6𝒙 + 𝟖 ⁰.
6. Label each angle with its measure.
127⁰
What is m < 1?
A. 20⁰
B. 40⁰
C. 50⁰
D. 76⁰
SOL 8.7
The student will
a) Investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones,
and pyramids; and
b) Describe how changing one measured attribute of a figure affects the volume and surface area.
HINTS & NOTES
 Volume is the number of unit cubes, or cubic units, needed to fill a solid figure. (filling a box)
o Formulas:
Rectangular Prism: V = lwh
Where:
Triangular Prism: V = Bh
V = volume
Cylinder: V = πr 2h
SA = surface area
1
Cone: V = 3πr 2h
B = area of the base
1
Pyramid: V = 3Bh
 Surface Area is the sum of the areas of its surfaces. (wrapping a box)
o Formulas:
Rectangular Prism: SA = 2lw + 2lh + 2wh
Triangular Prism: SA = hp + 2B
Cylinder: SA = 2πrh + 2πr 2
Cone: SA = πrl + πr 2
Pyramid: SA = ½l p + B
l = length or slant height
w = width
h = height
r = radius
p = perimeter of the base
PRACTICE
1. What is the volume of a square-based pyramid
with base side lengths of 16 meters, a slant height of
17 meters, and a height of 15 meters?
A.
B.
C.
D.
3. The volume of a square-based pyramid is 588 cubic
inches. The height of this pyramid is 9 inches. What is
the area of the base of this pyramid?
1280 m3
1360 m3
1450 m3
2040 m3
2. Which is the closest to the surface area of the cone
with dimensions as shown?
4. What is the total surface area and volume of this
prism?
Surface Area =
Volume =
A.
B.
C.
D.
66 sq in.
75 sq in.
113 sq in.
207 sq in.
5. Which is closest to the volume of this cylinder?
A.
B.
C.
D.
15.7 in3
19.7 in3
31.4 in3
78.5 in3
SOL 8.7 (CONTINUED)
The student will
c) Investigate and solve practical problems involving volume and surface area of prisms, cylinders, cones,
and pyramids; and
d) Describe how changing one measured attribute of a figure affects the volume and surface area.
PRACTICE
6. What is the surface area of a rectangular prism
with the dimensions shown?
A.
B.
C.
D.
7 sq in.
14 sq in.
18 sq in.
25 sq in.
9. Josh has two rectangular prisms. The length of the
second prism is 10 times the length of the first prism.
The heights and widths of the two prisms are the
same. Which best describes the volume of the second
prism?
A. The volume is 10 times the volume of the first
prism.
B. The volume is 30 times the volume of the first
prism.
C. The volume is 100 times the volume of the first
prism.
D. The volume is 1,000 times the volume of the
first prism.
7. What is the volume of the cube?
10. If a rectangular prism has a length of 3 feet, a
width of 4 feet, and a height of 5 feet and you double
the width, what will happen to the volume and
surface area?
A.
B.
C.
D.
144 m3
432 m3
864 m3
1,728 m3
8. Raymond needs to cover the entire surface are of
this square-based pyramid with paper.
What is the minimum amount of paper he will need?
A. 276 sq ft
B. 408 sq ft
C. 528 sq ft
D. 672 sq ft
11. Two triangular prisms show have bases with the
same area.
The Volume of prism N can be found by multiplying
the volume of prism M by what scale factor?
1
A. 5
B. 3
C. 5
D. 8
SOL 8.8
The student will
a) Apply transformations to plane figures; and
b) Identify applications of transformations
HINTS & NOTES
 A transformation is a change in the position, shape, or size of a figure.
o The original figure you start with is called a pre-image.
o The figure you end with is called the image.
 There are 4 types of transformations:
o Rotations are transformations that turn a figure about a fixed point called the center of rotation.
The angle of rotation is the number of degrees the figure rotates.
o Reflections are transformations that flip a figure over a line. This line is called the line of
reflection.
o Translations are transformations that move each point of a figure the same distance in the same
direction.
o Dilations are transformations that create similar figures of larger or smaller sizes. The ratio of the
pre-image and the image is called the scale factor.
 A dilation with a scale factor greater than 1 is called an enlargement.
 A dilation with a scale factor less than 1 is called a reduction.
PRACTICE
1. Which grid shows only a translation of the shaded
polygon to create the unshaded polygon?
3. Dwight drew a line segment on a coordinate grid.
He plans to reflect the line segment over the y-axis.
Graph the new line segment.
2. One piece of stained glass is transformed three
times.
4. A figure was rotated 180⁰ clockwise about the
origin.
What transformation was used to create this section
of stained glass window?
A. Translation
B. Reflection
C. Rotation
D. Dilation
Which is most likely the new figure?
A.
B.
C.
SOL 8.8 (CONTINUED)
The student will
c) Apply transformations to plane figures; and
d) Identify applications of transformations
PRACTICE
5. What are the new coordinates of point B after
∆𝑨𝑩𝑪 is translated 2 units down and 3 units to the
left?
7. What type of transformation has occurred?
A.
B.
C.
D.
Dilation
Rotation
Reflection
Translation
8. What type of transformation has occurred?
6. Dilate the pre-image using a scale factor of 3.
Draw the new image.
A.
B.
C.
D.
Translation
Reflection across the y-axis
Reflection across the x-axis
Rotation 90⁰ clockwise around the origin
9. Look at the transformation of polygon A to polygon
A’. Polygon A was rotated counterclockwise how
many degrees?
SOL 8.9
The student will construct a three-dimensional model, given the top or bottom, side, and front views.
HINTS & NOTES
 Dimensional Figures
o 1-D: Length
o 2-D: Length and width
o 3-D: Length, width and depth
 Parts of a Cube
o Vertex – Corner where three sides meet.
o Face – Flat part of a cube.
o Edge – Part where two faces meet.
 3-D Views:
o Front – Part that faces you.
o Top – Looking down on the object (bird’s eye view)
o Side – Tilted part (profile view)
o Bottom – Opposite of top. Looking up at the object.
PRACTICE
1. The front view of a three-dimensional figure using
identical cubes is shown.
3. A three-dimensional figure is constructed using
identical cubes. Three views of this figure are shown.
Identify each three-dimensional figure that has this
front view.
Which could be this three-dimensional figure?
2. A figure has the bottom and left-side views shown,
and its front view is shaded. Which represents the
figure?
4. Identify each three-dimensional figure that could
be represented by these three views.
A.
C.
B.
D.
SOL 8.10
The student will
a) Verify the Pythagorean Theorem; and
b) Apply the Pythagorean Theorem
HINTS & NOTES
Pythagorean Theorem: leg2 + leg2 = hypotenuse2
Can only be applied to right triangles.
The hypotenuse of a right triangle is always opposite the right angle.
The longest side of a right triangle is always the hypotenuse. The legs
of a right triangle are always adjacent (next to) the right angle; they
form the right angle.
 Three numbers will form a right triangle if 𝑎2 + 𝑏 2 = 𝑐 2 and c is the
biggest number.




PRACTICE
1. Which group of three side lengths could form a
right triangle?
A. 5 ft, 12 ft, 13 ft
B. 7 ft, 11 ft, 14 ft
C. 15 ft, 20 ft, 22 ft
D. 18 ft, 34 ft, 39 ft
2. Which of the following equations is represented
by the figure?
A.
B.
C.
D.
4. For the rectangle shown, which equation can be
used to find the value of x?
A. 𝑥 + 5 2 = 122
B. 52 + 𝑥 2 = 122
C. 52 + 122 = 𝑥 2
D. 5 + 12 = 𝑥 2
5. A wire connects to the top of a flagpole to the
ground as shown.
Which is the closest to the height, h, of the flagpole?
A. 3.2 m
B. 5.0 m
C. 8.7 m
D. 11.2 m
32 + 42 = 7 2
32 + 42 = 5 2
32 + 52 = 8 2
42 + 52 = 9 2
3. These triangles are not drawn to scale. Which
triangle is a right triangle?
A.
C.
B.
D.
6. Mr. Malone plans to construct a walkway through
his rectangular garden, as shown in the drawing.
What is the closest value of w?
A. 22 ft
B. 21 ft
C. 15 ft
D. 11 ft
SOL 8.11
The student will solve practical area and perimeter problems involving composite plane figures.
HINTS & NOTES
 Perimeter of a polygon is the distance around the figure.
 The area of any composite figure is based upon knowing how to find the area of the composite parts such
as triangles and rectangles.
 An estimate of the area of a composite figure can be made by subdividing the polygon into triangles,
rectangles, squares, trapezoids and semicircles, estimating their areas, and adding the areas together.
 Remember to use your formula sheet if you don’t remember the area and perimeter formulas!
PRACTICE
1. What is the area of this polygon?
A.
B.
C.
D.
77 sq cm
86 sq cm
96 sq cm
108 sq cm
4. Calculate the area and perimeter of the following
shape.
5. Find the area of the shaded region.
2. This figure is formed by a square and an isosceles
trapezoid.
What is the perimeter of
this figure?
A. 19 in.
B. 34 in.
C. 39 in.
D. 44 in.
3. The net of square-based pyramid is shown.
What is the area of this net?
What is the perimeter of this net?
6. Spotsylvania County has to pay for maintenance on
the football field. They need to replant sod, which
costs $3.50 per meter squared. How much will it cost
to sod the field?
SOL 8.12
The student will determine the probability of independent and dependent events with and without replacement.
HINTS & NOTES
 Two events are either dependent or independent.
 If the outcome of one event does not influence the occurrence of the other event, they are called
independent.
 If the outcome of one event does influence the occurrence of the other event, they are called dependent.
o With dependent events, your denominator will decrease with each occurrence.
 You will multiply the individual probabilities whether it is independent or dependent :
P(A and B) = P(A)∙P(B)
PRACTICE
1. Two fair coins are flipped at the same time. What
is the probability that both display tails?
1
A. 8
B.
1
4
C.
1
3
D.
1
2
2. A box contains 9 new light bulbs and 6 used light
bulbs. Each light bulb is the same size and shape.
Meredith will randomly select 2 light bulbs from the
box without replacement. What is the probability
Meredith will select a new light bulb and then a used
light bulb?
1
A. 54
B.
2
15
C.
6
25
D.
9
35
3. Cynthia has 14 roses in a vase.
 2 yellow roses
 5 pink roses
 3 white roses
 4 red roses
4. Eric and Sue will randomly select from a treat bag
containing 6 lollipops and 4 gumballs.
 Eric will select a treat, replace it, and then
select a second treat.
 Sue will select a treat, not replace it, and then
select a second treat.
Calculate each probability. Who has the greater
probability of selecting 1 lollipop and then 1 gumball?
5. A bag contains 6 red marbles, 8 blue marbles, and 6
white marbles. If one marble is selected at random
from the bag and NOT replaced, what is the
probability that it will be blue and then blue?
4
A. 25
B.
7
50
C.
3
4
D.
14
95
6. There are 8 brownies and 4 cookies. Each student
may have one dessert. You choose one, then the next
person picks one. What type of event is this?
Cynthia will randomly select 2 roses from the vase
with no replacement. What is the probability that
Cynthia will select a red rose and then a pink rose?
7. In an experiment, you are asked to roll a die and
flip a coin. What type of even is this?
SOL 8.13
The student will
a) Make comparisons, predictions, and inferences, using information displayed in graphs; and
b) Construct and analyze scatterplots.
HINTS & NOTES
 Scatterplots: two related sets of data are graphed as points to display correlations (trends).
Positive Trend
Negative Trend
No Trend
PRACTICE
1. The hourly wages of the 25 employees at a
restaurant are shown.
Based on the graph, what is the mean hourly wage of
the 25 employees at this restaurant?
A. $11.75
B. $9.36
C. $9.00
D. $8.56
2. The graph shows Anna’s height on each of her last
five birthdays.
3. The graph shows the number of text messages two
students sent each day for 4 days.
Based on the graph, which statement is true?
A. On Day 2 and Day 3, the total number of text
messages sent by Paul was 4 more than the
total number of text messages sent by Kala.
B. The total number of text messages sent by Kala
was the same as the total number sent by Paul
for these four days.
C. The mean number of text messages Kala sent
on Day 2 and Day 4 was exactly 4.5.
D. Kala sent fewer text messages than Paul on
Day 3 and Day 4 combined.
4. The circle graph displays the items sold at the
football concession stand. The concession stand sold
a total of 450 items. How many more nachos were
purchased than popcorn?
Based on the graph, between which two consecutive
years was the increase in Anna’s height the greatest?
A. Between 8 and 9 years
B. Between 9 and 10 years
C. Between 10 and 11 years
D. Between 11 and 12 years
SOL 8.13 (CONTINUED)
The student will
c) Make comparisons, predictions, and inferences, using information displayed in graphs; and
d) Construct and analyze scatterplots.
PRACTICE
5. The scatterplot shows the relationship between
Marvin’s age and the time it took him to run a mile.
Which statement best describes the relationship
between Marvin’s age and the time it takes him to
run a mile?
A. As Marvin’s age increased, the time it took him
to run a mile increased.
B. As Marvin’s age increased, the time it took him
to run a mile decreased.
C. As Marvin’s age increased, the time it took him
to run a mile remains constant.
D. There is no relationship between Marvin’s age
and the time it took him to run a mile.
6. Mr. Robert took a survey of his sixth period class
to determine what breeds of dogs the students have
as pets. The results are shown in this graph.
7. The following scatterplot shows the scores several
students received in math and music classes last
semester.
Which statement best describes the relationship in
the scatterplot?
A. As the math score decreases, the music score
increases.
B. As the math score increases, the music score
decreases.
C. As the math score decreases, the music score
does not change.
D. As the math score increases, the music score
increases.
8. Which of these best describes the relationship of
data shown on this scatterplot?
What percentage of the dogs owned by Mr. Robert’s
class are a beagle or a terrier?
A.
B.
C.
D.
Constant relationship
Negative relationship
Positive relationship
No relationship
SOL 8.14
The student will make connections between any two representations (tables, graphs, words, and rules) of a given
relationship.
HINTS & NOTES
 Remember the Rule of 5. You can represent relationships in several ways.
o Manipulatives
o Pictures
o Tables
o Graphs
o Rules
 Remember when you are graphing ordered pairs, you move left or right on the x-axis first,
then up or down on the y-axis.
 Test taking strategies:
 If you have to match a table to an equation, substitute the x and y values until you make a
match.
 If you have to match a table to a graph, be sure to check all ordered pairs you are given.
 If you have to match an equation to a graph, create a table of at least 3 x-values, substitute
them in to get the y-values, then match your ordered pairs to the correct graph.
 If you have to match a graph to an equation, make a list of the ordered pairs from each
graph then substitute them into the equation until you find a match.
PRACTICE
1. Which best represents 𝒚 = 𝒙 − 𝟏?
3. Which of these equations represents the table of
values?
A.
B.
C.
D.
𝑦 = −𝑥
𝑦 =𝑥+7
𝑦 = 3𝑥 + 3
𝑦 = 2𝑥 + 6
4. Margaret has $200 in her savings account. She will
deposit $50 into this account each week and will
make no withdrawals. Which table represents this
situation, excluding interest?
2. Which table contains only points that lie on the
𝟐
line represented by 𝒚 = 𝒙 − 𝟔?
𝟑
SOL 8.15
The student will
a) Solve multistep linear equations in one variable with the variable on one and two sides of the equation;
b) Solve two-step linear inequalities and graph the results on a number line; and
c) Identify properties of operations used to solve an equation.
HINTS & NOTES
 Remember to solve equations or inequalities you MUST maintain balance (what you do to one side of the
equation has to be done to the other side of the equation).
 Don’t forget to FLIP the inequality sign if you multiply or divide by a negative when solving inequalities.
 Inverse Operations:
o Addition and Subtraction
o Multiplication and Division
 Don’t forget your integer operation rules. Use your calculator to check your work!
 Test taking strategy: If all else fails, PLUG And CHUG, substitute each answer choice into the equation
until you find the one that works!
Graphing Inequalities
 The symbols:
The dots:
o <  is less than
o <  open dot / circle
o >  is greater than
o >  open dot / circle
o ≤  is less than or equal to
o ≤  closed dot
o ≥  is greater than or equal to
o ≥  closed dot
 Shade the part of the number line that contains the numbers that make the inequality true. Pick a
number and check it in the inequality…if it’s a true statement, shade it!; if it’s not true, shade the other
side.
Properties
 Distributive Property
 Identity Properties
 Inverse Properties
PRACTICE
1. What is the solution of this equation?
𝒙 = 𝟓𝒙 + 𝟔
3
A. − 2
C. 1
B. −1
D.
3
2
2. What value of x makes this equation true?
𝟓𝒙 + 𝟖 + 𝟑𝒙 = 𝟐𝟔 + 𝟔𝒙
A. 36
B. 17
3. What is the solution to
A. n = 4
B. n = 14
C. 16
D. 9
𝒏+𝟒
𝟐
− 𝟑 = 𝟏𝟑?
C. n = 16
D. n = 28
4. Which graph best represents the solution to
𝟕
𝟏
𝟏
≥ 𝟒 𝒙 + 𝟐?
𝟖
SOL 8.15 (CONTINUED)
The student will
d) Solve multistep linear equations in one variable with the variable on one and two sides of the equation;
e) Solve two-step linear inequalities and graph the results on a number line; and
f) Identify properties of operations used to solve an equation.
PRACTICE
5. What is the solution to this inequality?
𝟏. 𝟔 ≥ 𝟎. 𝟖𝒙 + 𝟒
A. −3 ≥ 𝑥
B. −3 ≤ 𝑥
C. 7 ≥ 𝑥
D. 7 ≤ 𝑥
9. The first six steps used to solve an equation are
shown.
6. Solve this inequality for x.
𝒙
𝟐< +𝟓
𝟒
Between which two steps does the zero property of
multiplication justify the work?
A. Steps 2 and 3
B. Steps 3 and 4
C. Steps 4 and 5
D. Steps 5 and 6
7. Identify each equation that illustrates the
commutative property of multiplication.
10. Eric solved the equation 𝒙 − 𝟑 = 𝟏𝟎 as shown.
What property justifies Eric’s work from Step 2 to Step
3?
8. Martha wrote the first step in solving an equation.
𝟒𝒙 + 𝒙 + 𝟐 = 𝟐𝟕
Step 1: 𝟒𝒙 + 𝒙 + 𝟐 = 𝟐𝟕
Which property justifies this step?
A. Associative property of multiplication
B. Commutative property of addition
C. Associative property of addition
D. Distributive property
11. Which is one value of the set of x that makes the
following true?
−𝟔 > −4𝒙 − 𝟏𝟖
A. -21
B. -5
C. -10
D. -21
SOL 8.16
The student will graph a linear equation in two variables.
HINTS & NOTES
 Testing strategies:
o If given a table with coordinates to match with a graph, draw a graph on scratch paper and plot
the points and then choose the graph that matches!
o If given a graph and asked to choose a table that matches, write down all the points in the graph
and then choose the table that matches!
PRACTICE
1. Which line appears to contain both ordered pairs
shown in this table?
3. Which graph appears to contain all the ordered
pairs in this relation?
2. Which line appears to be a graph of the equation
shown?
𝒚 = −𝟐𝒙 − 𝟏
4. Alana is creating a table of values to graph the
equation 𝟐𝒙 + 𝟑𝒚 = 𝟗.
What is the missing y-value?
A. -5
B. -1
C. 1
D. 5
5. Using the graph of the line, fill in the missing values
in each ordered pair in the table: -6, -2, 0, 2, 4
SOL 8.17
The student will identify the domain, range, independent variable, or dependent variable in a given situation.




HINTS & NOTES
Domain: All the VALUES of x, or the independent variable.
Range: All the VALUES of y, or the dependent variable.
Independent Variable: “I Change”; usually associated with the x-axis.
Dependent Variable: This depends on the independent variable; usually associated with the y-axis.
PRACTICE
1. What is the range of this relation?
A.
B.
C.
D.
5. What is the range of 𝒚 = −𝟑𝒙 + 𝟏 for the domain
of {2, 8}?
{1, 2, 4, 6}
{1, 2, 4, 5}
{1, 2, 4, 5, 6}
{0, 1, 2, 3, 4, 5, 6}
2. What is the greatest value in the range of
𝒚 = −𝟓𝒙 + 𝟑 for the domain {-2, 0, 1, 3}?
A. 3
B. 8
C. 13
D. 18
3. Which relation has a domain of {3, 5, 8}?
A. {(5, 1), (3, 4), (8, 2), (3, 3)}
B. {(3, 2), (5, 1), (8, 3), (1, 4)}
C. {(2, 8), (1, 3), (3, 5)}
D. {(3, 8), (5, 3), (3, 5)}
6. Determine the independent and dependent
variable in each situation.
a) Sarah has hired a contractor to replace the
windows in her house. The more people that
work, the less time it takes to install the
windows.
b) Leon sells ice cream cones in the park. He has
observed that when the outside temperature
exceeds ninety degrees, he sells more ice
cream cones.
4. What are the domain and range of this function?
7. A team from the Department of Public Works is
painting lines on the freeway. The number of hours
needed to finish the project depends on the length of
the road that needs to be lined.
h = the number of hours needed
r = the length of the road
Which is the independent variable?