Scope and Sequence Overview…………...…………………. 1
Scope and Sequence …………………………………….…... 2
Utah Core Standards Map………….………………………... 5
Appendices A – C
A – Pre-assessments
B – Benchmarks
C – Summative Assessments
Math 8 Scope and Sequence Overview 1st Trimester Rational Numbers Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 8.NS.1 Solve one and two‐step equations with integer and rational coefficients. 8.EE.7 Graphs and Functions Apply and extend previous understandings of graphing ordered pairs and interpreting graphs. 8.F.5 Define, evaluate, and compare functions. Explore, graph, and write functions in y=mx+b form. 8.F.1, 8.F.2, 8.F.3 Exponents and Roots Apply and extend previous understandings of operations exponents and roots. 8.EE.1, 8.EE.2, 8.EE.3, 8.EE.4, 8.NS.2 Solve real‐life and mathematical problems using the Pythagorean Theorem and its converse. 8.G.6, 8.G.7, 8.G.8 2nd Trimester 3rd Trimester Multi‐Step Equations Ratios, Proportions, and Similarity Analyze and solve linear equations and pairs of simultaneous linear equations. Apply and extend previous understanding of ratios, rates, and unit rates. Understand similarity of figures obtained by transformations. 8.EE.7, 8.EE.8 Graphing Lines Define, evaluate, and compare functions. Graph functions. Use functions to model relationships between quantities. 8.F.3, 8.F.4, 8.F.5 Data, Prediction, and Linear Functions Investigate patterns of association in bivariate data. 8.SP.1, 8.SP.2, 8.SP.3, 8.SP.4 8.G.3, 8.G.4 Geometric Relationships Understand congruence and similarity using physical models and geometry software. 8.G.5, 8.G.1, 8.G.2, 8.G.3 Explore transformations. 8.G.3 Measurement and Geometry Solve real‐world and mathematical problems involving volume of prisms, cylinders, cones, and spheres. 8.G.9 MATH 8 SCOPE AND SEQUENCE
Topic
Review
Rational
Numbers
Rational Numbers
Content
Students will be able to (SWBAT) know rational numbers and use rational approximations.
Solving Equations with SWBAT solve one and two‐step equations in one variable.
Rational Numbers
Solving Equations using Addition, Subtraction, Multiplication, and Division
Graphing Ordered Pairs and Interpreting Graphs
Skills
Identify rational vs. irrational numbers, Classify number
sets
8.NS.1
Identify Number Sets and find decimal equivalents.
8.NS.1
# Days
5
3
3
4
Find solutions for the variable in equations.
8.EE.7
4
SWBAT solve one and two‐step equations in one variable using Solve equations by regrouping and following correct inverse multiple operations.
operation steps.
SWBAT graph on a coordinate plane and interpret these graphs.
Graph ordered pairs and know each variable’s sign in all quadrants.
SWBAT understand a function is a rule the each input has Construct a one‐to‐one pairing of x and y values.
exactly one output.
Equations, Tables, and SWBAT compare properties of functions in different forms and Represent functions algebraically, graphically, numerically in Graphs
represent functions in multiple ways.
tables, or by verbal description.
Graphing Slope‐
SWBAT interpret and the equation y=mx+b as a linear Graph y=mx+b functions and describe the slope and Intercept and function.
intercepts and their meaning.
Understanding as a Linear Equation
Integer Exponents, SWBAT know and apply the properties of exponents.
Multiply, divide, and raise exponential expressions to a power.
Properties of Exponents
SWBAT write numbers and perform calculations in scientific Write small and large numbers in scientific notation and Scientific Notation
notation.
multiply and divide them.
Squares and Square SWBAT use square and cube root symbols and evaluate square Memorize perfect squares and cubes and their perspective Roots and cube roots.
roots.
SWBAT solve linear equations whose solutions require Solving Equations with Solve equations with variables on both sides using
expanding expressions using the distributive property and Variable on Both Sides
inverse operation.
collecting like terms
Solve systems of equations with substitution for zero,
SWBAT analyze and solve pairs of simultaneous linear Systems of Equations
one, or infinitely many solutions.
equations.
Functions
Graphing Linear Standards
SWBAT describe the functional relationship between two 8.EE.7.a
and
8.EE.7.b
3
8.F.5
8.F.1
8.F.2
2
4
3
8.F.3
8.EE.1
8.EE.3 and
8.EE.4
8.EE.2
8.EE.7.b
8.EE.8
8F5
4
3
3
4
4
3
MATH 8 SCOPE AND SEQUENCE
8.F.5
Equations
quantities using a graph.
Graph equations in y=mx+b form.
Explore Slope
SWBAT determine slope for the line connecting any two points.
Calculate slope given two points.
8.EE.6
Slope of a Line
SWBAT graph proportional relationships, interpret the unit rate as the slope.
Understand slope as a unit rate. Slope as the rate of
change in y compared to change in x.
8.EE.5
Using Slopes and Intercepts
Point‐Slope Form
Graph Equations in Slope‐Intercept Form
Direct Variation
Solving Systems of Linear Equations by Graphing
SWBAT construct a function to model a linear relationship between two quantities.
SWBAT interpret the equation y=mx+b as defining a linear function, whose graph is a straight line.
SWBAT describe qualitatively the functional relationship between two quantities.
SWBAT construct and interpret scatter plots for bivariate measurement data.
Linear Best Fit Models
SWBAT use the equation of a linear model to solve problems and interpret the slope and the intercept.
Linear Functions and SWBAT understand that a function is a rule that assigns to Rate of Change
each input exactly one output.
8.F.4
Identify and graph y-intercept. Identify and graph slope.
8.F.3
Identify positive, negative, and no correlation. Identify
clusting and outliers. Identify strong and weak correlation.
Informally construct a line of best fit. Use graphing
calculator to perform a linear regression for the formal
line of best fit.
Write functions given the domain and range. Model realworld situations with functions as a verbal description,
graph, and equation.
SWBAT compare properties of two functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.
Describe relationship between slopes and y-intercepts of
different functions.
Geometry
Pythagorean Theorem
SWBAT explain a proof of the Pythagorean Theorem and determine unknown side lengths in right triangles.
Applying the Pythagorean Theorem and its Converse
SWBAT apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Similar Figures
SWBAT find unknown sides on pairs of similar figures.
8.F.5
2
3
4
8.EE.8
8.SP.1 and
8.SP.2
3
3
8.SP.3
4
8.F.1
3
Comparing Multiple Representations
Geometry
2
4
Write equations in slope-intercept and point-slope form.
Convert between forms of linear equations.
Solve for a direct variation equation y=kx.
Graph systems of linear equations. Find solution as the
SWBAT understand the solutions to a system of two linear intersection of the graphs which is zero, one, or infinitely
equations in two variables correspond to points of intersection many solutions. Find ordered pair of the solution of a
of their graphs.
system of linear equations.
Scatter Plots
2
Solve proportions to find missing sides in similar figures and justify whether or not two figures are similar using 8.F.2
8.G.6 and
8.G.7
8.G.8
4
3
4
8.G.4
MATH 8 SCOPE AND SEQUENCE
proportions.
Transformations
Parallel and Perpendicular Lines, Triangles
SWBAT describe the effect of dilations, translations, rotations, Dilate, translate, rotate, and reflect figures on graph paper.
and reflections on two‐dimensional figures using coordinates.
SWBAT establish facts about angles from parallel lines cut by a Solve for vertical and adjacent angles in figures containing transversal and properties of similar triangles.
parallel lines cut by transversal lines.
Solve for missing angles using calculations and multiple‐step SWBAT find missing angles.
equations.
4
8.G.3
8.G.5
8.G.5
Congruence
SWBAT obtain congruent figures through a sequence of rotations, reflections, and translations.
Create congruent figures through transformations.
8.G.2
Transformations
SWBAT verify experimentally the properties of rotations, reflections, and translations.
Experiment with transformations on graph paper to further understand transformations.
8.G.1
Volume of Prisms, Cylinders, Pyramids, Cones, and Spheres
SWBAT know the formulas for the volumes of cones, cylinders, Solve for the volume of various rectangular prisms and and spheres and use them to solve real‐world and cylinders.
mathematical problems.
3
4
3
3
4
8.G.9
Utah CORE Math 8 Curriculum Standards Map Critical Areas 8.NS The Number System Clusters Know that there are numbers that are not rational, and approximate them by rational numbers. 8. EE Work with Expressions radicals and and Equations integer exponents Standard 1. Know that there are numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually and convert a decimal expansion which repeats eventually into a rational number. 2. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g. π2) 1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. 2. Use square roots and cube root symbols to represent solutions to equations in the form of x2=p and x3=p, where p is a positive rational number. 3. Scientific Notation. 4. Scientific Notation Operations. Areas of Concern Math 8 Activities Assessment 1 & 2. Vocabulary, calculation skills, estimation skills (continuing throughout the core) Terms, like terms, variables, constants, etc. Identify Number Sets and find decimal equivalents for real numbers. Memorize fraction, decimal, percent equivalents to 12ths. SWBAT compare sizes of irrational numbers using approximations and graphing on a number line.
Identify Number Sets and find decimal equivalents for real numbers. Memorize fraction, decimal, percent equivalents to 12ths. 1. Application of the Properties of Exponent rules. (estimation) 2.Inverse operation of roots and exponents 3 & 4. Introducing the concept in 8th grade. Exponents and Roots Benchmark Assessment Find relative values of square and cube roots and plot them on a number line. Standard 5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. 6. Use similar triangles to explain why the m is the same between any two distinct points on a non‐vertical line in the coordinate plane; derive the equation y = mx+ b for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. 7. Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). 7. Solve linear equations in one variable. a. Solve linear equations with rational number coefficients, including equations whose solutions require expanding 8. EE Expressions and Equations 8. EE Expressions and Equations Understand the connections between proportional relationships, lines, and linear equations. Analyze and solve linear equations and pairs of simultaneous linear equations. Analyze and solve linear equations and pairs of simultaneous Areas of Concern Clusters Critical Areas Understand the 8. EE connections Expressions and Equations between proportional relationships, lines, and linear equations. Assessment Activities 5. Slope!! Slope in the Real World activity Setting up proportions with corresponding sides both when in same and rotated orientations. Draw similar triangles along the graph and find ratio of corresponding sides Comparing cell phone plans, etc. Basic use of algebra and understanding the properties that justify solving equations. Applying the Distributive Property to expand or factor expressions. Don’t forget to distribute Tennis and ping pong balls in bags activity. Standard expressions using the distributive property and collecting like terms. Clusters linear equations. Areas of Concern Critical Areas Assessment Activities the coefficient over EVERY term inside the parentheses. 8. EE Expressions and Equations Analyze and solve linear equations and pairs of simultaneous linear equations. 8. EE Expressions and Equations Analyze and solve linear equations and pairs of simultaneous linear equations. 8. EE Expressions and Equations Analyze and solve linear equations and pairs of simultaneous linear equations. 8. Analyze and solve pairs of simultaneous equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. 8. Analyze and solve pairs of simultaneous equations. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 27 cannot simultaneously be 5 and 6. 8. Analyze and solve pairs of simultaneous equations. c. Solve real‐world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the a. Recognizing when to use graphing, substitution, and elimination. b. Same concerns, but what do parallel or overlapping (the same) lines mean. Writing equation from two ordered pairs. Comparing cell phone plans, etc. Comparing cell phone plans, etc. Clusters 8.F Functions Define, evaluate, and compare functions. 1.
8.F Functions Define, evaluate, and compare functions. 2.
8.F Functions Define, evaluate, and compare functions. 3.
8.F Functions Use functions to model relationships between quantities. 4.
Standard line through the first pair of points intersects the line through the second pair. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting to an input and the corresponding output. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions.) For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For 2 example, the function A = s giving the area of a square as a function of its side length is not linear because its graph contains points (1,), (2,4), and (3,9), which are not on a straight line. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Areas of Concern Critical Areas Assessment Activities Functional notation confuses students Functions Pre‐
Assessment Slope = rate of change Linear function has constant rate of change. Understanding the difference between linear and quadratic equations. Slope‐Intercept Benchmark Assessment Slope = a rate of change. Can students apply the ratios and slope interchangeably? Clusters 8.F Functions Use functions to model relationships between quantities. 8.G Geometry Understand congruence and similarity using physical models, transparencies, or geometric software. Understand congruence and similarity using physical models, transparencies, or geometric software. Understand congruence and similarity using physical models, 8.G Geometry 8.G Geometry Standard Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 5. Describe quantitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. 1. Verify experimentally the properties of rotations, reflection, and translations. a. Lines are taken to lines, and line segments to line segments of the same length. 1. Verify experimentally the properties of rotations, reflection, and translations. b. Angles are taken to angles of the same measure. 1. Verify experimentally the properties of rotations, reflection, and translations. c. Parallel lines are taken to parallel lines. Areas of Concern Critical Areas Assessment Activities Use of previous knowledge to apply to a new situation. Graph multiple real‐world relationships Graphing Lines Benchmark and Summative Assesments Geometer’s Sketchpad Patty Paper Geometer’s Sketchpad Patty Paper Geometer’s Sketchpad Patty Paper 8.G Geometry 8.G Geometry 8.G Geometry 8.G Geometry Clusters transparencies, or geometric software. Understand congruence and similarity using physical models, transparencies, or geometric software. Understand congruence and similarity using physical models, transparencies, or geometric software. Understand congruence and similarity using physical models, transparencies, or geometric software. Understand congruence and similarity using physical models, transparencies, Standard Areas of Concern Critical Areas Assessment Activities 2. Understand that a two‐dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
3. Describe the effect of dilations, translations, rotations, and reflections on two‐dimensional figures using coordinates. Lots of graphing and comparing ordered pairs. 4. Understand that a two‐dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two‐dimensional figures, describe a sequence that exhibits the similarity between them. 5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle‐angle criterion for similarity of triangles. For Ratios, Proportions, and Similarity Benchmark Assessment Geometer’s Sketchpad Standard example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. 6. Explain a proof of the Pythagorean Theorem and its converse. Students’ understanding of a proof Clusters or geometric software. 8.G Geometry Understand and apply the Pythagorean Theorem. 8.G Geometry Understand and apply the Pythagorean Theorem. 7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real‐world and mathematical problems in two and three dimension. 8.G Geometry Understand and apply the Pythagorean Theorem. 8. Apply the Pythagorean Theorem to find Trouble calculating the the distance between two points in a distance using the coordinate system. distance formula 8.G Geometry Solve real‐world and mathematical problems involving volume of cylinders, cones, and spheres. 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real‐world and mathematical problems. Areas of Concern Critical Areas Assessment Activities Solve for unknown legs or the hypotenuse given the other two sides. Solve for the distance between any two points on the coordinate plane. Justify the use of the Pythagorean Theorem’s Converse. Concrete calculations using worksheets and quizzes. Apply concepts to objects in classroom and outside. Pythagorean Theorem Benchmark Assessment Measurement and Geometry Benchmark Assesment Clusters Investigate patterns of association in bivariate data. 8.SP Statistics and Probability Investigate patterns of association in bivariate data. 2.
8.SP Statistics and Probability Investigate patterns of association in bivariate data. 3.
8.SP Statistics and Probability Investigate patterns of association in bivariate data. 4.
1.
Standard Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1/5 cm/hr as a meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two‐way table. Construct and interpret a two‐way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies Areas of Concern Critical Areas 8.SP Statistics and Probability Activities Drawing scatter plots Draw lines of best fit Linear regression on graphing calculator Applying understanding of slope Assessment Data, Prediction, and Linear Functions Benchmark Assessment Collect students’ data and organize in a two‐way table Clusters Standard calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Areas of Concern Critical Areas Activities Assessment Name
Date
Period
Data, Prediction, and Linear Functions
1. What kind of correlation is shown by
the data displayed in the scatter plot?
Use the scatter plot below for 3-4.
Gasoline Cost per Gallon
50
45
40
Cost ($)
35
30
25
20
15
10
5
0
0 2 4 6 8 10 12 14 16
Gallons
3. What is the line of best fit?
________________________________________
________________________________________
2. Does the data set on this scatter plot
appear to have a positive correlation,
a negative correlation, or no
correlation?
4. What does the slope and y-intercept
mean?
________________________________________
5. Determine whether the function is
linear or non-linear f(x)  x(x  1):
________________________________________
6. Mark needs to bring enough snacks
to a club meeting to have 2 snacks
for each member and 4 extra snacks
in case some guests arrive. Write a
function rule to determine how many
snacks he should bring if he expects
x club members.
________________________________________
________________________________________
7. Write a rule for the linear function.
________________________________________
Name
Date
Period
Data, Prediction, and Linear Functions
8.Write a rule for the linear function in
the table.
0
0
x
y
1
5
2
10
3
15
________________________________________
Use the graph of f(x) below,
9. Compare the slopes and yintercepts of the linear functions f
and g.
g(x) = 2x + 3, and the table of
h(x) for problems 9-10.
________________________________________
y
f (x)
24
4
3
2
1
22 21 O
________________________________________
________________________________________
1 2
10. Compare the slopes and yintercepts of the linear functions f
and h.
3 4 x
22
23
24
________________________________________
________________________________________
x
h(x)
0
2
1
4
2
6
3
8
________________________________________
Name ________________________________________ Date __________________ Class __________________
Exponents and Roots Test
1. Simplify 104.
10. Write the quotient of (6.72 x 109) ÷
(3.2 x 102) in scientific notation.
________________________________________
2. Simplify (4)2.
________________________________________
________________________________________
3. Simplify (2  6)2  (1  2)0.
________________________________________
For 4–6, simplify. Write your answer in
exponential form.
4. (3)2  (3)3
________________________________________
5.
23
25
________________________________________
11. Write the product of (1.7 x 109) x
(1.4 x 102) in scientific notation.
________________________________________
12. In 2010, the population of Sweden was
about 9.413 x 106. The population of
Switzerland was about 7.783 x 106.
About how much more was the
population of Sweden than Switzerland?
Write your answer in scientific notation.
6. (43)5
________________________________________
7. Write 1.75 103 in standard notation.
________________________________________
For 8–9, write each answer in scientific
notation.
8. 445,000,000,000
________________________________________
13. Write the two square roots of 196.
________________________________________
14. A square parking lot has an area of
225 yards. There is a sidewalk along
one side of the parking lot. How long
is the sidewalk?
________________________________________
9. The diameter of the nucleus of a
hydrogen atom is about 1 10–14
meters. The diameter of the entire
atom is 10,000 times that size. What
is the approximate diameter of a
hydrogen atom expressed in scientific
notation?
________________________________________
15. Simplify 2 81  64 .
________________________________________
________________________________________
Name ________________________________________ Date __________________ Class __________________
16. A square kitchen floor has an area of
500 square feet. Estimate the length of
one wall to the nearest tenth of a foot.
the book is 5 inches from the wall, how far
up the wall is the top of the book?
________________________________________
________________________________________
For 17–18, each square root is between
two integers. Find the two integers.
17.
23. What is the value of the hypotenuse?
185
________________________________________
18.
29
________________________________________
19. Find a number between
36 and (3)2.
24. Find the distance between points
(3, –4) and (–2, 1) to the nearest
tenth.
________________________________________
20. Could the following set of numbers be
the measures of the sides of a right
triangle: 5, 12, 13?
________________________________________
21. Find the length of the unknown side to
the nearest tenth.
________________________________________
22. A book that is 13 inches tall is leaning
against the edge of a wall. If the bottom of
________________________________________
24. Find the distance between points
(–6, -2) and (4, 7) to the nearest tenth.
Name ________________________________________ Date __________________ Class __________________
Exponents and Roots Test
1. Simplify 10.
10. What is the quotient of (5.04 x 106) ÷
(3.6 x 102) in scientific notation?
________________________________________
2. Simplify ().
________________________________________
________________________________________
3. Simplify (1  3)2  ( -6 + 5 )0.
________________________________________
For 4–6, simplify. Write your answer in
exponential form.
4. Simplify (2)3  (2)4.
88
5.
84
11. What is the product of (9.45 x 102) x
(6.2 x 108) in scientific notation?
________________________________________
12. In 2010, the population of Brazil was
about 1.907 x 108. The population of
Mexico was about 1.123 x 108. About
how much more was the population of
Brazil than Mexico? Write your
answer in scientific notation.
________________________________________
6. (155)10
________________________________________
7. Write 2.54 10 in standard notation.
________________________________________
For 8–9, write each answer in scientific
notation.
8. 576,000,000
________________________________________
13. Write the two square roots of 324.
________________________________________
14. A square sheet of art paper has an
area of 625 square inches. What is
the minimum side length of an easel
that supports the whole sheet of
paper?
________________________________________
9. The length of your classroom is about
3.5  102 inches. If the soccer field is
one hundred times as long as the
classroom, what is the length of the
soccer field expressed in scientific
notation?
________________________________________
15. Simplify 4 25  200.
________________________________________
________________________________________
Name ________________________________________ Date __________________ Class __________________
16. A square box lid has an area of
40 square inches. What is the best
estimate of the length of one side?
________________________________________
For 17–18, each square root is
between two integers. Find the two
integers.
17.
70
________________________________________
18.
22. A support wire runs from the top of a
tower to the ground. If the tower is 1200
feet tall and the wire is
attached to the ground 500 feet from the
base of the tower, how long is the
support wire?
10
________________________________________
23. What is the value of the leg?
________________________________________
19. Find a number between (2)2
and
25 .
________________________________________
20. Could the following set of numbers
be the measures of the sides of a
right triangle: 8, 15, 17?
________________________________________
24. Find the distance between points
(4, –3) and (–1, 2) to the nearest
tenth.
21. Find the length of the unknown side
to the nearest tenth.
________________________________________
25. Find the distance between points
(–8, -1) and (5, 6) to the nearest
tenth.
________________________________________
Name ________________________________________ Date __________________ Class __________________
Name Date Define the following terms.
1. Congruent Figures
2. Image
Period 9. If line r and line s are parallel and 8
measures 145°, what is the measure
of 3?
________________________________________
10. Name all of the angles in the figure
that are supplementary to 5.
3. Complementary Angles
________________________________________
4. Isosceles Triangle
5. Transversal
11. In triangle GHJ, what is the value
of g°?
6. Vertical Angles
Use the illustration for 78.
________________________________________
12. A parallelogram has vertices at the
following coordinates:
(4, –5), (2, –5), (2, 3). What are the
coordinates of the fourth vertex?
________________________________________
7. Which of the angles in the figure is
supplementary to ABD ?
13. Point A has coordinates A(–3, –1) and
point B has coordinates B(5, 5). Find
the coordinates of the midpoint M of
AB .
________________________________________
8. If angle CBF measures 56°, what is
the measure of EBF ?
________________________________________
14. The trapezoids below are congruent
figures. What is the value of w?
________________________________________
Use the illustration for 910.
________________________________________
Name Date Period Use the graph for 1516.
19. Reflect across the x-axis.
15. What transformation changes figure
ABC to figure EDC?
________________________________________
16. If triangle ABC is translated 2 units
up, what are the new coordinates of
point A?
20. Write the ordered pairs for the
image’s vertices.
________________________________________
17. Translate 5 units right and 2 units up.
21. Rotate 90 degrees counterclockwise
around the origin.
18. Write the ordered pairs for the
image’s vertices.
22 Write the ordered pairs for the image’s
vertices.
Name Date Period Name Date Period Quiz Linear Equations
Complete the tables and the graphs. (3 pts. for each table and 4 pts. for each graph) 1. y = 2x + 3 x y = 2x + 3 ‐1 0 1 y ( x, y ) 2. y = ‐x + 2 x y = ‐x + 2 ‐1 0 1 y ( x, y ) Find the slope of the lines. Be sure to reduce to simplest form. (1 pt. for the work and 1 pt. for the correct answer) 3. Find the slope of the line that passes through each pair of points. (1 pt. for the work and 1 pt. for the correct answer) 7. ( 4, 2 ) , ( 7, 8 ) 5. ( ‐3, 3) , ( 2, 1 ) 8. ( 5, ‐2 ) , ( ‐1, ‐2 ) 6. ( 2, 4 ) , ( 6, 1 ) REVIEW: Combine like terms. (1 pt. for the work and 1 pt. for the correct answer) 9. 3n + 7 ‐5n + 3 10. 5 ( ‐2x + 4 ) ‐2 ( 3x – 6 ) REVIEW: Solve each equation. (1 pt. for the work and 1 pt. for the correct answer) 11. ‐5x + 7 = ‐8 12. 5y + 4 = 4y + 5 Name ________________________________________ Date __________________ Class __________________
Determine whether the ordered pair
is a solution of the given equation.
1. y  x  9; (7, 16)
For 7 and 8, write the coordinates of
a point located in the same quadrant
as the point on the coordinate plane.
7. point A
________________________________________
2. y  2x  8; (5, 28)
________________________________________
8. point D
________________________________________
________________________________________
3. Make a table for the equation
y  -3x  4
9. Draw a line graph that corresponds
to this situation: a car is moving at a
constant speed and then gradually
stops. Show speed on the y-axis
and
time on the x-axis.
4. CDs cost $10 each. The cost, c, of n
CDs can be calculated using the
equation C  $10n. Write an ordered
pair to show the cost of 5 CDs.
________________________________________
Use the following graph to answer
questions 5 through 8.
10. If distance is represented on the
y-axis and time on the x-axis, what
does a horizontal line represent?
________________________________________
Define the following terms:
11. Relation
12. Domain
Define the following terms:
For 5 and 6, give the coordinates of
the point on the coordinate plane.
13. Range
5. point A
________________________________________
6. point D
________________________________________
14. Function
Name ________________________________________ Date __________________ Class __________________
15. Vertical Line Test
________________________________________
22. Is the relation in the domain map below
a function? Why or why not?
16.Determine if the relationship
represents a function.
Domain
Range
4
5
-8
7
-1
8
3
7
-6
________________________________________
Use the table to answer questions 23–25.
Use the following relation to answer
questions 17-19.
x
y
{ ( -2, 8 ), ( -4, 11 ), ( -6, 14 ), ( -8, 17 ) }
-8
2
-4
3
0
4
4
5
17. Identify the domain.
18. Identify the range.
23. What is the slope of the function?
19. Is the relation a function? Why or why
not?
24. What is the y-intercept of the function?
25. Write the function in Slope-Intercept
20. Write the equation that represents
the values in the table below.
x
y
2
0
0
2
2
4
4
6
________________________________________
21. List the coordinates of two points
that fall on the graph of y  x.
form.
Name
Date
Period
Chapter 6 Test: Measurement and Geometry
For every problem write the formula, show the work, and write the answer in the correct
form with the correct units.
1. To the nearest tenth, find the area of a circle whose diameter is 12 m.
Use 3.14 for  .
2. A circle has a diameter of 60.8 in. Find the circumference to the nearest tenth. Use
3.14 for  .
3. A circle with center at (−9, 5) passes through (−9, 12). Find the circumference and
area of the circle in terms of  .
4. Find the volume of this figure to the nearest tenth. Use 3.14 for  .
5. The dimensions of an appliance carton are 3 ft  5 ft  3 ft. What is the volume of
the carton?
Name
Date
Period
6. Find the volume of the figure shown to the nearest tenth.
7. A cone-shaped paper cup has a top diameter of 8.5 cm and a height of
12 cm. What is the volume of the cone to the nearest tenth?
Use 3.14 for  .
8. Find the volume of the figure to the nearest hundredth.
9. In terms of  , find the volume of a sphere with a diameter of 10 cm.
10. Find the volume and surface area of a sphere with a radius of 2.4 m to the nearest
tenth. Use 3.14 for  .
Name
Date
Test Multi-Step Equations
Define the following terms.
1. Like terms
2. System of Equations
Combine like terms:
3. 4x 2 + 2x  3x  x 2
4. 4r  6s  2r + s
5. 3b 2(b  6a)  13a + 3c + 5c
Solve
6. 3y + 5 = 16.
7. 2 + 3j = 4.
8.
9.
1
1
3
b+ b= .
2
4
4
x x
+ = 2.
2 6
10. y + 1 = 2y  5.
Period
Name
Date
Period
Solve
11.
a a
+ + 1 = a + 2.
3 3
12. Solve g  4 = 2g + 6.
13. Wanda makes deliveries for a local store on Saturday. She has a choice of being
paid $20.00 per day plus $1.00 per delivery or $30.00 per day plus $0.50 per
delivery. For what number of deliveries does she make the same amount of money
with either pay schedule?
14. Solve the system:
y = 2x + 5
y = 3x + 4
15. Solve the system:
3x + 6y = 24
x = 3y + 10
16. Solve the system:
x+y=2
x = 2y + 4
17. The sum of two numbers is 10. The difference between the numbers is 4. What are
the two numbers?
Name ________________________________________ Date __________________ Class __________________
6
1. Simplify  .
9
2. Write 0.39 as a fraction in simplest
form.
3. Write
7
as a decimal.
10
For 8 and 9 divide. Write the answer
in simplest form.
1
1
16

8.
4
9. 9 
3
4
For 4 and 5 multiply. Write the
answer in simplest form.
 1
4. 6  1 
 4
5.
10. Anna bought socks that cost $2.40
per pair. If she spent $9.60, how
many pairs of socks did she buy?
3 1
•
5
2
2
3
6. Stephanie has skateboarded
of
the way to the library. The library is
2 miles away. How far has she
skateboarded?
11. Evaluate
7. Evaluate 0.6y for y  23.
12. Subtract 3
0.2
for x  0.4
x
1
7
1
6
12
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class __________________
1
miles,
4
stops for lunch, and then hikes
1
another 1 miles. How far did they
2
hike?
13. A group of friends hikes 2
17. Solve y + 2.13 = −9.74
18.
14. Evaluate x 
k 3
=4
4
3
4
for x  2
10
5
19. 3y  6.8  16.1
Solve the following equations.
15. m  0.31  6.13
16. z 
20.
z
93
5
1
1

4
2
Holt McDougal Mathematics
Name _______________________ Date __________ Period _________
Ratios, Proportions, and Similarity
Show ALL of your work! Each problem is worth either 2 points or 4
(1 or 2 for the work and 1 or 2 points for showing the work.) You may
use pencils, calculators, scratch paper but not composition books,
old assignments, or the practice test.
FOLLOW THE ACADEMIC HONESTY POLICY!!
1. 2 points possible - 1 point for the
correct answer and 1 point for the
work.
The mass of a block of stone is
2,000 kg. If the block has a volume
of 0.5 m3, what is its density?
Remember, density is mass per unit
of volume.
4. 2 points possible - 1 point for the
correct answer and 1 point for the
work.
Solve the following proportion for x.
$20
x

2 hours
8 hours
A $10
B $80
A 4,000 kg/m3
B 1,000 kg/m3
2. 2 points are possible - 1 point for
the correct answer and 1 point for
the work.
C $160
5. Solve the following proportion
for x. 2 points are possible - 1
point for the correct answer and 1
point for the work.
Which of these prices is lower than
8 for $10.00?
$24
x

3 hours
6 hours
A 3 for $4.00
B 11 for $12.00
A $48
B $72
C 6 for $7.50
6. 2 points are possible - 1 point
3. 2 points are possible - 1 point for
the correct answer and 1 point for
the work.
A packing machine can pack
3,000 boxes in 4 hours. At what rate
does the machine work?
for the correct answer and 1 point
for the work.
An airplane traveled 60 miles in 20
minutes. At this rate, how far will it
travel in 40 minutes?
A 340 boxes/hour
B 480 boxes/hour
A 30 miles
C 750 boxes/hour
B 120 miles
C 200 miles
Holt McDougal Mathematics
Name _______________________ Date __________ Period _________
7. 2 points are possible - 1 point
for the correct answer and 1 point
for the work.
Which value completes the table
below comparing two different
serving sizes?
Serving Size (g)
Protein (g)
3
12
4
A 16
10. 4 points possible - 2 points for the
correct answer and 2 points for the
work.
Which of the following rectangles is
similar to a rectangle that measures
12 units by 16 units?
A 18  24
B 9  14
C 6  10
B 12
8. 4 points are possible -2 points for
the correct answer and 2 points for
the work.
A photograph 6 inches wide by
8 inches long is scaled to 12 inches
long in a book. What is the width of
the published picture?
11. 4 points are possible - 2 points for
the correct answer and 2 point for
the work.
The two triangles are similar. Identify
the scale factor of the dilation from the
larger triangle to the smaller triangle.
A 4 inches
A 2
B 9 inches
B 0.5
C 3 inches
12. 4 points are possible - 2 points for
9. 4 points are possible -2 points for
the correct answer and 2 points for
the work.
Triangle ABC is similar to triangle DEF.
What is the value of x?
the correct answer and 2 points for
the work.
A figure is dilated by a scale factor of
4. The origin is the center of dilation.
If a vertex of the enlarged figure is
located at (8, 8), what was its original
location?
A(2, 2)
A 6
B (4, 4)
B 24
Holt McDougal Mathematics
Name _______________________ Date __________ Period _________
1. 2 points possible - 1 point for the correct
answer and 1 point for the work.
The mass of a block of stone is
2,000 kg. If the block has a volume
of 0.5 m3, what is its density? Remember,
density is mass per unit of volume.
4. 2 points possible - 1 point for the correct
answer and 1 point for the work.
Solve the following proportion for x.
2x
160
$20
x


2 hours
8 hours
2 2
x  80
(1 pt )
2000kg
0.5m3
(1 pt )
A $10
 4000kg / m3
A 4,000 kg/m3 (1pt)
B $80 (1 pt)
C $160
B 1,000 kg/m3
2. 2 points are possible - 1 point for the
5. Solve the following proportion for x. 2
points are possible - 1 point for the
correct answer and 1 point for the work.
FIND THE UNIT RATE
$24
x

3hours 6hours
3 x 144

 x  48
3
3
(1 pt )
$10.00 / 8 = $1.25 / unit
A $48 (1 pt)
correct answer and 1 point for the work.
Which of these prices is lower than
8 for $10.00?
B $72
A 3 for $4.00 = $4.00/3 = $1.33 / unit
B 11 for $12.00 $12.00/11=
$1.09 / unit (1 pt)+(1 pt)
6. 2 points are possible - 1 point for the
C 6 for $7.50 = $7.50/6 = $1.25 / unit
An airplane traveled 60 miles in 20 minutes.
At this rate, how far will it travel in 40
minutes?
3. 2 points are possible - 1 point for the
correct answer and 1 point for the work.
A packing machine can pack
3,000 boxes in 4 hours. At what rate does
the machine work?
correct answer and 1 point for the work.
60miles
m

20 min 40 min
20m 2400

20
20
m  120
3000boxes 750boxes

A 340 boxes/hour 4hours
hour
(1 pt )
A 30 miles
B 480 boxes/hour
B 120 miles (1pt)
C 750 boxes/hour (1pt)
C 200 miles
(1 pt )
Holt McDougal Mathematics
34 points possible
_____________________________________________
7. 2 points are possible - 1 point for the
correct answer and 1 point for the work.
Which value completes the table below
comparing two different
serving sizes?
Serving Size (g)
Protein (g)
3
12
4
9. 4 points are possible -2 points for the
correct answer and 2 points for the work.
Triangle ABC is similar to triangle DEF. What is
the value of x?
x
10

12 5
3 12

4 p
3p
48

3 3
5 x 120

5
5
x  24
p  16
(2 pts)
(1 pt )
B 24 (2 pts)
A 6
A 16 (1 pt)
B 12
10. 4 points possible - 2 points for the
8. 4 points are possible -2 points for the
correct answer and 2 points for the work.
correct answer and 2 points for the work.
A photograph 6 inches wide by
8 inches long is scaled to 12 inches long in a
book. What is the width of the published
picture?
6 w

8 12
w  12 * 6 / 8  9
(2 pts)
Which of the following rectangles is similar to
a rectangle that measures 12 units by 16
units?
12 3

16 4
3* 4
12 18
 crossproducts 288  288
16 24
(2 pts )
A 4 inches
A 18  24 = 6 x 8 = 3 x 4 (2pts)
B 9 inches (2 pts)
B 9  14
C 3 inches
C 6  10 = 3 x 5
Holt McDougal Mathematics
34 points possible
_____________________________________________
11. 4 points are possible - 2 points for the
correct answer and 2 point for the work.
The two triangles are similar. Identify the
scale factor of the dilation from the larger
triangle to the smaller triangle.
18
 0.5
36
(2 pts)
A 2
B 0.5 (2 pts)
12. 4 points are possible - 2 points for the
correct answer and 2 points for the work.
A figure is dilated by a scale factor of 4. The
origin is the center of dilation.
If a vertex of the enlarged figure is located at
(8, 8), what was its original location?
(2,2) * f = (8,8)
f = 4 = (2*4, 2*4) = (8,8)
Original = (2,2) 2pts
A (2, 2) 2 pts
B (4, 4)
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class __________________
Graphing Lines TEST
1.Determine whether the equation is
linear: 7x- 4y = -19.
________________________________________
6. What is the y-intercept of the line
represented by x + 3y = 15?
2. Find the equation for the line.
________________________________________
7. What is the equation of the line that
passes through the points (1, 5) and
(2, 2)?
________________________________________
________________________________________
8. What is the slope-intercept form of the
line that passes through the point
1
(2, -5) and has a slope of ?
2
3. Find the slope of the line that passes
through the points (5, 4) and (3, 1).
________________________________________
4. Find the slope of the line that passes
through the points (4, 3) and (2, 7).
________________________________________
9. What is the equation of the line that
passes through the point (-3, 2) and
1
has a slope of ?
3
________________________________________
5. What is the slope of the line that
passes through the points (12, -3) and
(6, 2)?
________________________________________
________________________________________
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class __________________
10. What is the point-slope form equation
for the line that passes through the
point (1, 1) and has a slope of 2?
13. Solve
y  x3
2 y  2 x  10
by graphing.
________________________________________
11. Complete this table to show a direct
variation.
x
5
y
10
6
8
14
9
18
________________________________________
14. The graph of a system of linear
equations is shown below. Write the
solution of the system.
12. Write an equation for a direct
variation which includes
y = 10 when x = 2.
________________________________________
________________________________________
________________________________________
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class __________________
Holt McDougal Mathematics
Name
Date
Per
MATH 8 POST TEST
1. The base of a cone has a radius of 6 centimeters. The cone is 7 centimeters tall. What is
the volume of the cone to the nearest tenth? Use 3.14 for .
2.Identify the type of transformation.
3. What is the area of a figure with vertices (1, 1), (8, 1), and (5, 5)?
4. A tree trunk has a radius of 11 inches. What is the circumference of the tree trunk to the
nearest tenth? Use 3.14 for .
5. What are the two square roots of 144?
6. If A and B are supplementary, and mA  57°, what is mB?
7. What is 0.125 as a fraction in simplest form?
Name
Date
8. What are the coordinates of point K?
9. Solve
4
7
13
3
k

k− .
5
10
15
5
10. What is the equation of a line that passes through the points (6, 5) and (-3, 8)?
Use the figure for 11 and 12.
11.
Which angle is supplementary to ABE?
12.
Line AC is parallel to line DF. If mDEC is 150°, what is m1?
Per
Name
Date
Per
13.
Solve 2x = 5 + 3(4 x  5)
14.
What is a solution to the equation y = 12 – 3x?
15.
What is the equation of direct variation given that y is 16 when x is −2?
16.
In 2011, the population of India was about 1.342 x 109. The population of China was
about 1.194 x 109. In scientific notation about how much more was the population of
India than China?
17.
Combine like terms:
7a  4b − 3a − 2b
18.
Find the distance between points(3, 5) and (4, 6) to the nearest tenth.
19.
Which is a linear equation?
A y = 2  5x
C
y = 2  5x2
B y = 5 x 2
D
y =
5
x
20.
Between what two integers does
79 lie?
21.
What is the slope of the line 3x + 4y = 12?
22.
What is the product of (1.117 x 1010) x (9.949 x 104) in scientific notation?
23. What is the quotient of (2.981 x 1020) ÷ (3.25 x 105) in scientific notation?
24. If a pool table measures 4 ft by 8 ft, what is the diagonal length to the nearest tenth?
25. A train traveled 31.2 miles in 52 minutes. At this rate, how far will it travel in 60 minutes?
Name
Date
Per
26. What are the coordinates of the image of the point (9, 2) after a translation 10 units up
followed by a reflection over the x-axis?
27. Solve
a
3

30
18
28. Your favorite brand of cereal comes in four different sized boxes. Which size is the lowest unit
rate?
Toasted Almond Crunch
15 oz
$2.39
18 oz
$2.87
24 oz
$3.79
32 oz
$5.10
29. The line has what type of slope?
A positive
C zero
B negative
D undefined
30. What is the number 0.0000042 in scientific notation?
31. What is the ordered pair that is a solution of the system of equations?
y  3x  1
y  5x – 3
32. A circle with center at (12, −1) passes through (0, −1). Find the circumference
and area of the circle in terms of .
Name
Date
Per
33. If Hannah purchased a 5-day parking pass for $36.25, how much did she pay per day?
34. Find the volume and surface area of a sphere with a radius of 5 cm to the nearest tenth. Use
3.14 for .
35. What type of relationship is shown by the scatter plot?
36. A plumber charges $75 for each service call and $50 per hour. What linear equation (rule) gives
the cost for x hours of plumbing services?
37. Write a linear equation (rule) for the linear function in the table.
x 0 1 2 3
y 2 –3 –8 –13
Name
Date
Per
38. Which best compares the slopes and y-intercepts of the linear functions f and g, where f =
1
x+3
3
and g is shown in the table below?
x
g
0 1 2 3
3 6 9 12
A The slope of f is less than the slope of g.
The y-intercept of f is greater than the y-intercept of g.
B The slope of f is greater than the slope of g.
The y-intercept of f is the same as the y-intercept of g.
C The slope of f is the same as the slope of g.
The y-intercept of f is less than the y-intercept of g.
D The slope of f is less than the slope of g.
The y-intercept of f is the same as the y-intercept of g.
39. Eighth grade students were asked whether they participate in an after-school activity. Complete
the two-way frequency table below.
Participate
Boys
Total
43
Girls
Total
Don’t Participate
119
115
213
Of those who participate in an after-school activity, what is the probability that they are a boy?
40. Find the volume.
Use 3.14 for .