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Algebra Final Exam Study Guide
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Algebra Final Exam Review
Ms. Walker
This study guide is a review of everything that will be on the final exam. Sample problems
are provided for you to practice.

Rules of divisibility
- Tell whether 3,420 is divisible by 2, 3, 5, or 10
- Tell whether 728 is divisible by 4, 6, or 9

Powers and Exponents
- Write 34 as a product
- Write 2  2  2  2  2 using an exponent. Then find the value of the power.
- b to the eighth power
- nine to the yth power
- x6 when x = 10

Order of Operations [PEMDAS]
- Find the value of the expression 7 + 3  5.
- Find the value of the expression 36  9 + 12  (7 – 5).

Algebra: Variables and Expressions
- Evaluate 19 – a if a = 11
- Evaluate 3k – 4 if k = 7
- Evaluate 8x – 2v if x=5 and v=3 (34)
- Evaluate mn/6 if m=8 and n=12 (16)

Statistics and Graphs [Remember KAATZ: Key, Axis Y, Axis X, 3 Titles, Zero]
- How to read and construct a line plot
- How to read and construct a box-and-whiskers plot
- How to read and construct a circle graph
- How to read and construct a scatter plot
- How to read and construct a bar graph
- Exam Scores - Make a stem-and-leaf plot of the exam scores shown below.

Ordering decimals, fractions and percents from least to greatest.
- Order 34.03, 34, 33.98, and 34.1 from least to greatest.
- Order –0.01, 0.01, .42 from least to greatest
5 3 5
1
- Order the fractions , , , and
from least to greatest.
8 4 6
2
- Order 3 7/10%, 3 4/5%, 3.75 and 7/2 from least to greatest.
Algebra Final Exam Study Guide
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
Dividing Decimals
- Find 6.93  1.8.
- Find 83.2  0.52.

Multiplying and Dividing Fractions
2 3
- Find 
5 4
1 2
- Find 
6 3
1
5
2
3
6
2
1
- Find 3  1
3
6
- Find

Simplifying Fractions

Integers
- Find −3 + (−5).
- Find 4 + (−6).
- Find −7 + 3.
- Find −8 − (−5).
- Find –4 – 6.
- Multiply 5  (−3).
- Multiply −9  (−5).
- Divide −6  3.
- Divide −35  (−7).

Algebra: Solving Equations
- Solve m + 2 = 7
- Solve c – 2 = – 3.
- Solve 4x – 9 = 15
- Solve −4x = 24
- Solve 3x + 7 = 16.

Solve Equations Using Addition and Subtraction
- -9 = 2 + y
- R+3¼=2½

Solve Equations Using Multiplication and Division
x/5 = -30
* -3x = 5

Evaluate Expressions
- When x = 3 x + 29
- 32 – 5 x (2+ 1) + 4
When r=30 and s=5, r/s x 7

Is the given number a solution of the equation or inequality 13 – 3x = 7; 2

Similar Triangles

Variable Expressions? Addition, Subtraction, Multiplication or Division
4 + s (ADD) 16/b (DIVIDE) 9-x (SUBTRACT) 8y (MULTIPLY)

Ratio, Proportion, and Percents
- CEREAL A 16-ounce box of cereal is priced at $3.68. Find the cost per ounce.
1.4 w
 .
- Solve
1.8 9
- Convert: Fraction to Decimal, Decimal to Fraction, Fraction to Percent, Percent to
Fraction
Algebra Final Exam Study Guide


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Geometry: Perimeter, Area, Volume, Circumference, Surface Area
- Find the area of a rectangle with length 14 feet and width 9 feet.
- Find the circumference of a circle whose diameter is 7.2 centimeters. Round to
the nearest tenth.
- GARDENING Tom is trying to determine the area of his garden so that he will
know how much fertilizer to buy. His garden is a circle with a radius of 10 feet.
About how much land does Tom’s garden cover?
- Find the volume of the rectangular prism.
-
Find the area of the triangle.
Find the perimeter of a trapezoid with sides of 6 feet, 9 feet, 3 feet and 3 feet.
-
Find the surface area of the rectangular prism.
-
Know how to find the volume and surface area of a
cylinder.
Prime Factorization
54 = 2 x 27 = 2 x 3 x 9 = 2 x 3 x 3 x 3 = 2 x 33
 Mr. Wilson’s students have completed more than 50% of the class work planned for the
entire school year. Which fraction could be used to represent a value GREATER than
50%?
1/5, 4/10, ½ 2/3
 Which inequality is TRUE?
25% > 7/8 , 7/8 < 0.83
Algebra Final Exam Study Guide
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 Associative Property of Addition (The way numbers are groups does not change sum or
product)
- (3 + 4) + 5 = 3 + (4 + 5)
 Commutative Property of Addition (order does not change sum or product)
- 4+3=3+4
 Identity Property (The sum of any number and 0 is the number)
- 5+0=5
 Multiplicative Identity (The product of any number and 1 is the number)
- 7x1-7
 Distributive Property
- 2(7 +4) = 2 x 7 + 2 x 4 ** What is equivalent to 5(n-9) = 5n-45
 The distance from Josie’s house to school is 4.25 blocks. What is the total number of
blocks she walks directly to and from school during a 5-day school week?
 Miguel, Sara and Joey ride to school together. Miguel rides a distance of 2.25 miles to
Sara’s house. Then they go to Joey’s house, which is 1.625 miles past Sara’s house and
5.25 miles from school. What is the total distance in miles, from Miguel’s house to
school?
 Profit or loss for a product
 Discount and Sales Tax
- A store is having a 30%-off sale on all games. Lance wants a board game that
cost $26.95 after the discount is applied. What is the discounted price of the
game to the nearest cent?
- A girl purchased treats for the class party. The sales tax was 6 1/2 %. The total
cost of the items was $33.21, what the cost of the treats after the sales tax was
applied?

Circle J is shown below.
Which line segment is a radius of Circle J? What line segment is the chord of Circle J?
Algebra Final Exam Study Guide
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
Lines, Angles, Triangles
Identify the following: Right Angle, Acute Angle, Obtuse Angle, Straight Line, Parallel
Lines, Perpendicular Lines, Supplementary Angles, Complementary Angles, Vertical
Angles, Congruent Angles, Equilateral Triangle, Isosceles Triangle, Scalene Triangle,
Acute Triangle. YOU SHOULD KNOW THE DEGREES AND MEASURES OF THE
OUTSIDE AND INSIDE OF THE SHAPES.

Scale Drawings
A house and a storage shed are built with the geometrically similar roof parts shown
below.
What is the length of the side labeled with a measure of x feet?

Write each phrase as an algebraic expression
- Twice as old as Sammy = 2s * Maria’s allowance divided by 4 = a/4
- Three more than the quantity fives times a number n = 5n + 3
- A number x decreased by the sum of 10 and the square of a number y = x-(10+y2)

Write a sentence as an algebraic equation
- The sum of 5 and a number equal 14 = n + 5 = 14
- The product of k and -9 equals 17 = -9k = 17

Quadrants and Coordinate Grids
You should know the coordinate grids with the corresponding [negative and positive]
ordered pairs. You should also be able to identify and plot points on a grid.

Measure of angles, shapes, missing measure

Average Speed: 120 miles in 3 hours [distance/time]

Simple Interest: Principal x Rate x Time

Translation, Rotation, Reflection
Translate: Move 3 units left and 5 units up
Rotation: ¼ (90 degrees), ½ (180 degrees), ¾ (270 degrees), 4/4 (360 degrees)
Reflection: Reflect over x axis (up and down) Reflect over y axis (left and right)

Square, Square Root, Missing Numbers in Pattern, Patterns in a Table
2.7, 5.6, 8.5, 11.4 … (add 2.9) Next 3 numbers are 14.3, 17.2, 20.1
Algebra Final Exam Study Guide
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
Absolute Value

Ratios: There were 5 tables and 12 balls, what is the ration of tables to balls?
5:12 * 5/12 * 5 out of 12 [REMEMBER: ALL RATIOS ARE TO BE REDUCED]

Finding the Domain of a Function
Find the domain of the function y = -x/1-x [Answer: All real numbers except x = 1] You
must exclude any values which make the denominator equal to zero. Solve the equation
for 1-x = 0

Measures of Central Tendency: Mean, Median, Mode, Range

Circumference and Area of a Circle
Figure the circumference when given the radius and the diameter
 C= pi x diameter * pi x 2 x radius
 Area = pi x radius2

Scientific Notation and Standard Form
5 x 104 = 50,0000
9.3 x 105 = 930,000
4,250 = 4.25 x 10?

Rounding Off Numbers (To the nearest tenth, and to the nearest hundredth)

Reciprocal of a Number 8 = 1/8

Two-Dimensional Figures
Identify a shape by its sides: Triangle (3) Quadrilateral (4) Pentagon (5) Hexagon (6)
Heptagon (7) Octagon (8) Nonagon (10)
 Rectangle, Square, Parallelogram, Rhombus, Trapezoid
 Regular Polygon, Irregular Polygon (Not regular)
 Similar, Congruent, Symmetry
3/5 = 5/3
Three-Dimensional Figures
 Identify: Prism (shape of the base tells the name of the prism: Rectangular prism,
triangular prism, square prism/cube), Pyramid(shape of the base tells the name of the
pyramid: triangular pyramid, square pyramid), Cone, Cylinder, Sphere
Benchmark Fractions
 ¼ = .25
1/5 = .20 1/3 = .666
 Remember Bar Notation and Repeating Fractions
Number Line
 Identify positive and negative integers on a number line
 Identify given measurements (1/2, ¾, 2/5) on a number line
 Graphing Real Numbers
Algebra Final Exam Study Guide
Rates: compares two quantities with different kinds of units
- 100 words/2 minutes lets you see the different units are words and minutes
Unit Rates: when a rate is simplified so that the denominator is 1 unit
- Unit Rate 50 words/1 minute can be read as 50 words per minute.
{The 100/2 was divided by 2 which left 50/1 – denominator made into 1 unit}
Solving Proportions – Cross Multiplying
Tree Diagrams
Matrices (Add and Subtract)
Functions –
 Input/Output Table  Domain (x) and Range (y)
 Determine if the data demonstrates a function
 If domain given, determine the range
Solve Multiple Step Equations
 5x + 3(x+4) = 28
5x + 3x + 12 = 28
8x + 12 = 28
8x = 16
X=2
Solve 66 = -6/5(x + 3)
(-5/6) (66) = (-5/6) (-6/5) (x + 3)
-55 = x + 3
-58 = x
Solve Equations with Variables on Both Sides
 7x + 19 = -2x + 55
7x + 19 + 2x = -2x + 55 + 2x
9x + 19 = 55
9x + 19 – 19 = 55 – 19
9x = 36
X=4
Solving Decimal Equations
 -38x – 39 = 118
Formulas and Functions
 Solve for r
I/Pt = Prt/Pt
I/Pt = r
I = Prt
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Algebra Final Exam Study Guide
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Rewrite the equation so that y is a function of x
 3x + y = 4
Solve for y
y = 4 – 3x
Rewrite the equation so that x is a function of y
 3x + y = 4
Solve for x
x=4–y/3
Graph Linear Equations
 Verify Solutions of an Equations
 Use Table of Values
 Rewrite equation in Function Form y = mx + b
 Equations and Graphing of Horizontal and Vertical Lines
Quick Graphs Using Intercepts
 Find x and y intercepts (x,0) (0,y)
 Graph with given intercepts
Slope of a Line
 M = rise/run change in y/change in x yx – y1/ x2 – x1
 Slopes Classified: Positive (rise) Negative (falls) Zero (horizontal) Undefined(Vertical)
Direct Variation
 Y = kx
Slope is k
Quick Graphs Using Slope-Intercept Form
 2x – 4y = 16
 Slope-Intercept Form: y = 0.5x – 4
 Slope: m= 0.5
 Y-intercept = -4
Polynomials
Solve Linear Equations Using Graphs
 Solve 2x – 5 = 1 algebraically
 2x = 6
 X=3
 Write equation in form ax + b = 0
 2x – 6 = 0
 Write function in two variables
 Y = 2x - 6
 Graph function: Plot 3 (x-intercept) from algebraic solving and y-intercept = -6