Download SOL Golden Ticket Review (doc)

Name ________________________________ Period ______________
SOL Test Date_______________
Math 8
SOL TEST
GOLDEN TICKET
8.1- Simplifying Expressions and Fractions, Decimals, Percents, and Scientific Notation

ORDER OF OPERATIONS --
GROUPING SYMBOLS Parentheses ( ), brackets [ ], braces { }, the
absolute value
, division/fraction bar
, and the square root symbol
should be treated as grouping symbols
EXPONENTS 𝒙𝟐
MULTIPLY/DIVIDE -LEFT TO RIGHT
ADD/SUBTRACT - LEFT TO RIGHT

∙ or ÷
+ or −
Fraction to decimal - numerator divided by denominator. The top number goes into the calculator first.
If you can't use a calculator, then the NUMERATOR goes INside the house. (another way is to say “Top
dog goes in the house”)
 Decimal to percent - move the decimal right 2 times. If you do not see a decimal it is at the end of the
number. .16 = 16% OR multiply your decimal by 100 (.16 x 100 = 16%)
 Percent to decimal – move the decimal left 2 times. IF THE PERCENT HAS A DECIMAL IN IT,
YOU STILL MUST MOVE IT 2 TIMES...EXAMPLE .16% = .0016 OR divide percent by 100!
 Scientific Notation to Standard Form – Move the decimal the number of places the exponent says and
the direction of the value of the exponent (positive exponent move decimal right/ negative exponent
move decimal left). EXAMPLE: 2.357 x 10-5 means the decimal will move 5 places to the left since the
exponent is a negative 5. So the answer is 0.00002357.
*When comparing/ordering decimals, fractions, percents and scientific notation - change ALL of
them to decimals. Line up your decimals (money) and compare!!
8.2 – Real Number System
 The set of real numbers includes natural numbers, counting numbers, whole numbers, integers, rational
and irrational numbers.
 The set of natural numbers is the set of counting numbers {1, 2, 3, 4, ...}.
 The set of whole numbers includes the set of all the natural numbers or counting numbers and zero {0, 1,
2, 3…}.
 The set of integers includes the set of whole numbers and their opposites {…-2, -1, 0, 1, 2…}.
 The set of rational numbers includes the set of all numbers that can be expressed as fractions in the form
a
1
where
a
and
b
are
integers
and
b
does
not
equal
zero
(e.g.,
25 , , -2.3, 75%, 4.59 ) .
b
4
 The set of irrational numbers is the set of all nonrepeating, nonterminating decimals. An irrational
number cannot be written in fraction form
{e.g.,  , 2 , 1.232332333…}.
8.3- Taxes, Tips, Discounts, Proportions, Simple Interest, and Percent Increase/Decrease
 Taxes, Tips and Discounts
o Step 1: Change your percent to a decimal
o Step 2: Multiply your decimal by the amount of the product
 This will represent the TAX, TIP, or the AMOUNT TO TAKE OFF of the product.
 Check to see if you need Step 3 – step 3 is asking for the FINAL TOTAL
o Step 3
 For TAX and TIP ADD your answer from step 2 to the cost of the original product.
 For DISCOUNT SUBTRACT your answer from step 2 from the original product.
 Proportions
o Step 1: Set up your KEY in order to have information matching in the ratio.
o Step 2: Set up your problem using your key.
o Step 3: Cross multiply.
o Step 4: Solve your one step equations.
 Example: A plant grows 2 millimeters every 6 hours. If it continues to grow at the same
rate, how many millimeters will it have grown in 15 hours?


Step 1:

Step 2:

Step 3:

Step 4:
Simple Interest
o Formula: I  prt I- interest, p- principal (amount of $ you start with), r- rate (given in %
change to decimal), t- time in years (if given in months use that as the numerator and 12 as the
denominator)
 Read carefully to determine whether the question is asking for interest only or the total
amount of money. Total value of the investment--- add the Interest you calculated to
the Principal

Percent Increase/Decrease
o Percent Increase: determines the rate of growth: results in a positive number
o Percent Decrease: determines the rate of decline: results in a negative number
 Formula
Change (new – original)
original
8.4 – Algebraic Expression
 Plug the numbers in for the letters
 Solve the problem following the order of operations (look back at 8.1). – TAKE YOUR TIME AND
SHOW ALL WORK!
o Remember – the SOL test is going to try to trick you, so if you show your work – they cannot
trick you up!
8.5 – Perfect Squares and Estimating Square Roots
 Perfect Squares: A whole number whose square root is an integer
o Example: 25 is 5 and -5 so 25 is a perfect square
 Square Root of a number: any number which when multiplies by itself equals the number
o Example: 25 is 5 and -5 so 5 and -5 are the square roots of 25
o Example: 15 - 15 is not a perfect square but it lies between the perfect squares 9 and 16 so the
two consecutive whole numbers between which 15 lies are 3 and 4 because 9  3 and
16  4
8.6 – Vertical Angles, Adjacent Angles, Supplementary Angles, and Complementary Angles
 Vertical angles are (all nonadjacent angles) formed by two intersecting lines. Vertical angles are
congruent and share a common vertex.

o
Complementary angles are any two angles such that the sum of their measures is 90°.

o
Supplementary angles are any two angles such that the sum of their measures is 180°.

o
Reflex angles measure more than 180°.
o

Adjacent angles are any two non-overlapping angles that share a common side and a common vertex.
o
8.7- Surface Area and Volume
 Surface Area: wrapping a present, aluminum the makes a soda can, cardboard that makes a box (there
is no pattern if you change an attribute)
 Volume: sand inside a box, soda inside a can, water inside a pool, cereal inside a box (whatever change
you make to the attribute is made to the new volume (example: double length the volume doubles)
o Step 1: Determine if the question is asking for Surface Area or Volume
o Step 2: Write the formula
o Step 3: Make your key for your variables
 Be careful – sometimes they give you a diameter instead of a radius for cylinders!
o Step 4: Plug in your numbers to the formula
o Step 5: Solve using the Order of Operations
o REMEMBER: surface area is units2 and for volume is units3
8.8 – Transformations
 Translations: when an object SLIDES to another location

Rotation: when an object TURNS
o Remember – each quadrant is equivalent to 90 degrees.

Dilation: when an object gets bigger OR smaller
o Remember to multiply each number in the ordered pair by the scale factor.

Reflection: when an object FLIPS over a line of reflection
8.9 - Three Dimensional Views
 Construct a 3-D model, given the top or bottom, side, and front views.
 Identify a 3-D model given a 2-D perspective
o Example: Given the 2-D perspectives below, construct the 3-D model
8.10 – Pythagorean Theorem
 In a right triangle, the square of the length of the hypotenuse (c) equals the sum of the squares of the legs
(a and b). This relationship is known as the Pythagorean Theorem: a2 + b2 = c2.
o
8.11 - Composite Plane Figures
 Subdivide a figure into triangles, rectangles, squares, trapezoids and semicircles. Estimate the area of
subdivisions and combine to determine the area of the composite figure.
 Use the attributes of the subdivisions to determine the perimeter and circumference of a figure.
 Apply perimeter (distance around a polygon), circumference (distance around a circle) and area (inside
portion of a polygon or circle) formulas to solve practical problems.
8.12 –Probability
 Probability is the chance that a particular outcome will occur, measured as the ratio of the total of
possible outcomes.




Independent event: the outcome of one event DOES NOT affect the outcome of the other event.
Dependent event: the second event depends on the outcome of the first event.
When you have two events: multiply your fractions together.
When finding the number of possible combinations you can
o Make a tree diagram (LONG WAY)
o Multiply the options together
8.13 – Scatterplots
 A scatterplot illustrates the relationship between two sets of data. A scatterplot consists of points. The
coordinates of the point represent the measures of the two attributes of the point.
 Scatterplots can be used to predict trends and estimate a line of best fit.
 In a scatterplot, each point is represented by an independent and dependent variable. The independent
variable is graphed on the horizontal axis (x-axis) and the dependent is graphed on the vertical axis (yaxis).

8.14 – Tables, Graphs, Rules, and Words
 Tables, graphs and equations represent the SAME information.
o Find matching graphs and tables by plotting points from the tables onto the graph to see which
table contains points for the graphed line.
o Find the matching graphs and equations by CREATING a table to make ordered pairs.
 Most of the time, you can create your x/y table by using the x values of -2, -1, 0, 1, 2
o Find the matching equations and tables by plugging in ALL of the values from the tables to see
which table contains ordered pairs that make the equation true.
8.15 – Solving Equations & Inequalities, and Properties
 Equations
o Your goal = GET THE VARIABLE ALONE!
o Follow these steps:
o Step 1: Draw a line through your equal sign, this reminds you – what you do to one side
of the equations needs to be done to the other.
o Step 2: Identify your variable: this is what you are trying to get alone
o Step 3: Use the inverse operations the get the numbers away from the variable. You can
use a DO/UNDO chart to help you identify what the order of operations are being done to
the variable then
 Example 1:
Steps 1 & 2:

Step 3:
Example 2:
Step 3 cont:
Answer:

Inequalities
o Always start by asking yourself these two questions to determine if the inequality sign flips!
 Question 1: Is the problem multiplying or dividing?
 If the answer is no – then the inequality sign stays the same
 If the answer is yes – ask question number 2
 Question 2: Is the number ATTACHED to the variable negative?
 If the answer is no – then the inequality sign stays the same
 If the answer is yes – THEN FLIP THE INEQUALITY SIGN IN THE
ANSWER!
o Solve the problem by isolating the variable.
o When graphing inequalities, there are two steps:
 Step 1: Put the correct circle over the number
 Step 2: Draw an arrow towards all the numbers that are true for the inequality

Properties
o Commutative: Changes Order
 Ex: 3 + 4 = 4 + 3
o Associative: Always Stays Same Order (parenthesis move)
 Ex: 7+ (9 + 1) = (7+ 9) + 1
o Distributive: Teacher Property – the number outside gives itself away to the numbers inside
parenthesis
 Ex: 5(6+8) = 5(6) + 5(8)
o Identity: Stays the same
 Ex: a + 0 = a OR a x 1 = a
o Inverse: The opposite
1
 Ex: a ∙ 𝑎 = 1
o Multiplicative Property of Zero: Multiply by zero ... to get zero
8.16 – Graph Linear Equations
 Make a table of values with at least 3 points
 Graph the points from the table of values you created
o Example:
8.17 – Domain, Range, Independent Variable, and Dependent Variable
 Domain – all x values
 Range – all y values
 Independent Variable (x) – graphed on the horizontal/x-axis INPUT
 Dependent Variable (y) – graphed on the vertical/y-axis OUTPUT