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Mastering the California Mathematics Standards
Grade 7
ReviewerEvelyn R. Brown, Ed.D.
Rockway Middle SchoolLos Angeles, California
California Standards Review Series
CA©08_Gr7_Flipbook_TP_A_879533-81 1CA©08_Gr7_Flipbook_TP_A_879533-81 1 2/19/07 4:26:58 PM2/19/07 4:26:58 PM
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher.
Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 978-0-07-879533-6MHID: 0-07-879533-8 Mastering the California Mathematics Standards, Grade 7
Printed in the United States of America.
1 2 3 4 5 6 7 8 9 10 024 15 14 13 12 11 10 09 08 07
Image Credits: COVER (l c r)CORBIS; i (l c r)CORBIS
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Mastering the California Mathematics Standards, Grade 7 Aiii
Contents
California Mathematics Standards, Grade 7 . . . . . . . . . . . . . . . . . . . Aiv
Diagnostic Test—Student Recording Sheet . . . . . . . . . . . . . . . . . . . . Aix
Diagnostic Test—Student Answer Sheet . . . . . . . . . . . . . . . . . . . . . A1
Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A3
Practice by Standards
Number Sense (Rational Numbers) . . . . . . . . . . . . . . . . . . . . . . A15
Number Sense (Exponents, Powers, and Roots) . . . . . . . . . . . . . . . A24
Algebra and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . A31
Measurement and Geometry . . . . . . . . . . . . . . . . . . . . . . . . . A47
Statistics, Data Analysis, and Probability . . . . . . . . . . . . . . . . . . . A61
Standards Assessment—Student Answer Sheet . . . . . . . . . . . . . . . . . A65
Standards Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A67
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Aiv Mastering the California Mathematics Standards, Grade 7
California Mathematics Standards, Grade 7
= Key Standard * = standard assessed on the CAHSEE
Number Sense
1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:
1.1* Read, write, and compare rational numbers in scientific notation (positive and
negative powers of 10) with approximate numbers using scientific notation.
1.2* Add, subtract, multiply, and divide rational numbers (integers, fractions,
and terminating decimals) and take positive rational
numbers to whole-number powers.
1.3* Convert fractions to decimals and percents and use these
representations in estimations, computations, and applications.
1.4 Differentiate between rational and irrational numbers.
1.5 Know that every rational number is either a terminating or repeating decimal
and be able to convert terminating decimals into reduced fractions.
1.6* Calculate the percentage of increases and decreases of a quantity.
1.7* Solve problems that involve discounts, markups, commissions, and profit
and compute simple and compound interest.
2.0 Students use exponents, powers, and roots and use exponents in working with fractions:
2.1* Understand negative whole-number exponents. Multiply and divide
expressions involving exponents with a common base.
2.2* Add and subtract fractions by using factoring to find common
denominators.
2.3* Multiply, divide, and simplify rational numbers by using exponent rules.
2.4* Use the inverse relationship between raising to a power and
extracting the root of a perfect square integer; for an integer that is not
square, determine without a calculator the two integers between which its
square root lies and explain why.
2.5* Understand the meaning of the absolute value of a number; interpret the
absolute value as the distance of the number from zero on a number line;
and determine the absolute value of real numbers.
Algebra and Functions
1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:
1.1* Use variables and appropriate operations to write an expression, an equation,
an inequality, or a system of equations or inequalities that represents a verbal
description (e.g., three less than a number, half as large as area A).
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Mastering the California Mathematics Standards, Grade 7 Av
1.2* Use the correct order of operations to evaluate algebraic expressions such
as 3(2x + 5)2.
1.3 Simplify numerical expressions by applying properties of rational numbers
(e.g., identity, inverse, distributive, associative, commutative) and justify the
process used.
1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient,
inequality, expression, constant) correctly.
1.5* Represent quantitative relationships graphically and interpret the meaning
of a specific part of a graph in the situation represented by the graph.
2.0 Students interpret and evaluate expressions involving integer powers and simple roots:
2.1* Interpret positive whole-number powers as repeated multiplication and
negative whole-number powers as repeated division or multiplication by
the multiplicative inverse. Simplify and evaluate expressions that include
exponents.
2.2* Multiply and divide monomials; extend the process of taking powers and
extracting roots to monomials when the latter results in a monomial with
an integer exponent.
3.0 Students graph and interpret linear and some nonlinear functions:
3.1* Graph functions of the form y = nx2 and y = nx3 and use in solving
problems.
3.2 Plot the values from the volumes of three-dimensional shapes for various
values of the edge lengths (e.g., cubes with varying edge lengths or a triangle
prism with a fixed height and an equilateral triangle base of varying lengths).
3.3* Graph linear functions, noting that the vertical change (change in y-value)
per unit of horizontal change (change in x-value) is always the same and
know that the ratio (“rise over run”) is called the slope of a graph.
3.4* Plot the values of quantities whose ratios are always the same (e.g., cost
to the number of an item, feet to inches, circumference to diameter of a
circle). Fit a line to the plot and understand that the slope of the line
equals the quantities.
4.0 Students solve simple linear equations and inequalities over the rational numbers:
4.1* Solve two-step linear equations and inequalities in one variable over the
rational numbers, interpret the solution or solutions in the context from
which they arose, and verify the reasonableness of the results.
4.2* Solve multistep problems involving rate, average speed, distance, and time
or a direct variation.
California Mathematics Standards, Grade 7 (continued)
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Avi Mastering the California Mathematics Standards, Grade 7
Measurement and Geometry
1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:
1.1* Compare weights, capacities, geometric measures, times, and temperatures
within and between measurement systems (e.g., miles per hour and feet
per second, cubic inches to cubic centimeters)
1.2* Construct and read drawings and models made to scale.
1.3* Use measures expressed as rates (e.g., speed, density) and measures
expressed as products (e.g., person-days) to solve problems; check the
units of the solutions; and use dimensional analysis to check the
reasonableness of the answer.
2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale:
2.1* Use formulas routinely for finding the perimeter and area of basic
two-dimensional figures and the surface area and volume of basic three-
dimensional figures, including rectangles, parallelograms, trapezoids,
squares, triangles, circles, prisms, and cylinders.
2.2* Estimate and compute the area of more complex or irregular two-and
three-dimensional figures by breaking the figures down into more basic
geometric objects.
2.3* Compute the length of the perimeter, the surface area of the faces, and the
volume of a three-dimensional object built from rectangular solids.
Understand that when the lengths of all dimensions are multiplied by a scale
factor, the surface area is multiplied by the square of the scale factor and the
volume is multiplied by the cube of the scale factor.
2.4* Relate the changes in measurement with a change of scale to the units
used (e.g., square inches, cubic feet) and to conversions between units
(1 square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is
approximately 16.38 cubic centimeters or [1 in3] = [16.38 cm3]).
3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:
3.1 Identify and construct basic elements of geometric figures (e.g., altitudes,
mid-points, diagonals, angle bisectors, and perpendicular bisectors; central
angles, radii, diameters, and chords of circles) by using a compass and
straightedge.
California Mathematics Standards, Grade 7 (continued)
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Mastering the California Mathematics Standards, Grade 7 Avii
3.2* Understand and use coordinate graphs to plot simple figures, determine
lengths and areas related to them, and determine their image under
translations and reflections.
3.3* Know and understand the Pythagorean theorem and its converse and use it
to find the length of the missing side of a right triangle and the lengths of
other line segments and, in some situations, empirically verify the
Pythagorean theorem by direct measurement.
3.4* Demonstrate an understanding of conditions that indicate two
geometrical figures are congruent and what congruence means about the
relationships between the sides and angles of the two figures.
3.5 Construct two-dimensional patterns for three-dimensional models, such as
cylinders, prisms, and cones. Not assessable in multiple-choice format on the Grade 7 CST.
3.6 Identify elements of three-dimensional geometric objects (e.g., diagonals
of rectangular solids) and describe how two or more objects are related in
space (e.g., skew lines, the possible ways three planes might intersect).
Statistics, Data Analysis, and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:
1.1* Know various forms of display for data sets, including a stem-and-leaf plot
or box-and-whisker plot; use the forms to display a single set of data or to
compare two sets of data.
1.2* Represent two numerical variables on a scatterplot and informally describe
how the data points are distributed and any apparent relationship that
exists between the two variables (e.g., between time spent on homework
and grade level).
1.3 Understand the meaning of, and be able to compute, the minimum, the lower
quartile, the median, the upper quartile, and the maximum of a data set.
Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1* Analyze problems by identifying relationships, distinguishing relevant
from irrelevant information, identifying missing information, sequencing
and prioritizing information, and observing patterns.
1.2* Formulate and justify mathematical conjectures based on a general
description of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.
California Mathematics Standards, Grade 7 (continued)
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Aviii Mastering the California Mathematics Standards, Grade 7
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1* Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex
problems.
2.3* Estimate unknown quantities graphically and solve for them by using
logical reasoning and arithmetic and algebraic techniques.
2.4* Make and test conjectures by using both inductive and deductive
reasoning.
2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs,
tables, diagrams, and models, to explain mathematical reasoning.
2.6 Express the solution clearly and logically by using the appropriate
mathematical notation and terms and clear language; support solutions with
evidence in both verbal and symbolic work.
2.7 Indicate the relative advantages of exact and approximate solutions to
problems and give answers to a specified degree of accuracy.
2.8 Make precise calculations and check the validity of the results from the
context of the problem.
3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original
situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual
understanding of the derivation by solving similar problems.
3.3* Develop generalizations of the results obtained and the strategies used and
apply them to new problem situations.
All Mathematical Reasoning Standards are embedded in the questions on the Grade 7 CST.
California Mathematics Standards, Grade 7 (continued)
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Mastering the California Mathematics Standards, Grade 7 Aix
Diagnostic TestStudent Recording Sheet
QuestionStandard Assessed
Practice Page
1 7NS1.1 A15
2 7AF1.3 A33
3 7AF4.1 A43
4 7AF2.2 A38
5 7AF3.3 A41
6 7NS1.3 A18
7 7MG1.2 A49
8 7MG1.3 A49
9 7NS1.4 A19
10 7AF4.2 A45
11 7AF1.1 A31
12 7NS1.7 A22
13 7NS1.7 A22
14 7NS1.5 A20
15 7MG3.3 A57
16 7SDAP1.3 A63
17 7MG3.1 A55
18 7NS2.5 A29
19 7AF1.3 A18
20 7AF4.2 A45
21 7NS1.2 A16
22 7SDAP1.3 A63
23 7MG1.1 A47
24 7NS2.2 A25
25 7MG3.4 A59
QuestionStandard Assessed
Practice Page
26 7AF4.1 A43
27 7SDAP1.1 A61
28 7AF3.4 A42
29 7NS1.2 A16
30 7MG3.3 A57
31 7AF1.3 A33
32 7NS2.4 A28
33 7NS1.7 A22
34 7AF4.1 A43
35 7NS2.3 A26
36 7MG1.3 A49
37 7NS1.6 A21
38 7MG3.6 A60
39 7NS2.1 A24
40 7SDAP1.2 A62
41 7AF4.2 A45
42 7AF4.2 A45
43 7MG3.2 A56
44 7MG3.3 A57
45 7NS1.2 A16
46 7AF1.5 A36
47 7AF3.3 A41
48 7NS1.7 A22
49 7NS1.2 A16
50 7MG2.4 A54
Color in the bubble for each question that you answered correctly on the Diagnostic Test. For each
question you did not answer correctly, your teacher may ask you to do the exercises on the practice sheet
prescribed.
(continued on the next page)
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Ax Mastering the California Mathematics Standards, Grade 7
QuestionStandard Assessed
Practice Page
51 7AF1.2 A32
52 7MG2.2 A52
53 7AF1.3 A33
54 7NS2.3 A26
55 7NS2.3 A26
56 7AF3.4 A42
57 7SDAP1.3 A63
58 7AF1.4 A35
QuestionStandard Assessed
Practice Page
59 7AF2.1 A37
60 7MG2.3 A53
61 7NS2.5 A29
62 7MG2.1 A51
63 7AF4.1 A43
64 7AF3.1 A39
65 7AF3.2 A40
Total Number of Questions CorrectCount how many questions you got correct.
Find your score in the table below and circle your level.
Far Below Below Basic Basic Proficient Advanced
0–16 17–36 37–45 46–55 56–65
Diagnostic TestStudent Recording Sheet (continued)
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Diagnostic TestStudent Answer Sheet
Mastering the California Mathematics Standards, Grade 7 A1
Record your answers by coloring in the appropriate bubble for the best answer to each question.
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O
-2-3-4
21 43-2-3-4
1234
y
x
(1,4)
(-1, -2)
Mastering the California Mathematics Standards, Grade 7 A3
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Name Date
Diagnostic Test
1 Which of the following is equivalent to 2.6 × 104?
A 0.000026
B 26,000
C 260,000
D 2,600,000
2 Which property is used in the equation below?
15 - 5x = 5 (3 - x)
F Associative Property of Addition
G Commutative Property of Addition
H Commutative Property of Multiplication
J Distributive Property
3 What value of x makes the equation below true?
2x + 5 = 37
A 16
B 21
C 30
D 40
4 Which expression is equivalent to 9a5 _
3a7 ?
F 3a2 H a2
_ 3
G 3 _
a2 J
1 _
3 a2
5 What is the slope of the following line?
A -3 C 5 _
3
B 1 _
3 D 3
6 A store is having a sale, and all items
are 1 _ 5 off their original prices. Which of
the following represents the discount on
a shirt that originally cost $35?
F 0.02 × $35
G 0.05 × $35
H 0.2 × $35
J 0.5 × $35
7 The scale on a map states that 1 inch represents 5 miles. If two towns on the map are 8.5 inches apart, how far apart are the towns in real life?
A 13.5 miles
B 42.5 miles
C 135 miles
D 425 miles
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A4 Mastering the California Mathematics Standards, Grade 7
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8 Amanda is running a 10-mile race. For the first 6 miles, she runs at a rate of 7 minutes per mile. For the last 4 miles, she runs at a rate of 8 minutes per mile. What is the total time that it takes Amanda to finish the race?
F 70 minutes
G 74 minutes
H 75 minutes
J 76 minutes
9 Which of the following numbers is irrational?
A √ � 25
B √ � 15
C 7 _
8
D -4
10 A fish swims 4 miles per hour for 2 hours, and then swims 6 miles per hour for 3 hours. How far has the fish swum in all?
F 4 miles
G 10 miles
H 15 miles
J 26 miles
11 The product of 15 and some number (x) is 45. Which equation shows this relationship?
A x + 15 = 45
B 45x = 15
C 15x = 45
D x - 15 = 45
12 Nick deposits $20.00 into a savings account that earns 4% interest compounded annually. Assuming Nick makes no withdrawals, how much should Nick have in his account after three years (to the nearest penny) ?
F $21.63
G $22.40
H $22.50
J $54.88
13 A shirt that originally costs $60.00 is on sale for 15% off. As a special promotion, the store is offering the shirt at 20% off the discounted price. What is the final cost of the shirt?
A $51.00
B $48.00
C $40.80
D $39.00
Diagnostic Test (continued)
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25 feet
7 feet
?
Mastering the California Mathematics Standards, Grade 7 A5
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14 Which of the following fractions is equal to 2.36?
F 118
_ 5
G 59
_ 25
H 59
_ 50
J 59
_ 250
15 A 25-foot ladder is placed 7 feet from the base of a wall. How high up the wall can the ladder reach?
A √ � 24 feet
B 18 feet
C 24 feet
D √ �� 674 feet
16 A group of ten students are asked how many brothers and sisters they have: three students have no brothers or sisters; two have one; four students have two; and one student has four. What is the upper quartile of these data?
F 0.0
G 1.5
H 2.0
J 4.0
17 Which of the following describes the relationship of
−− AD to �ABC?
A −−
AD is the median from A.
B −−
AD is the angle bisector of ∠BAC.
C −−
AD is the altitude from A.
D −−
AD is the perpendicular bisector of −−
BC .
18 ⎪3 + 1⎥ - ⎪2 - 7⎥ =
F -9
G -5
H -1
J 5
19 Which of the following expressions is equivalent to 5x2 - 2x?
A x (5x - 2)
B 5x2 (x - 2)
C 5 (x - 2)
D 2x (x - 5)
20 Ahmed works for 4 hours and earns $32. At that rate, how long would he have to work to earn $400?
F 8 hours
G 12 hours
H 50 hours
J 100 hours
Diagnostic Test (continued)
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0 inches 10 inches 20 inches
Weekly Rainfall in Columbus
∠
55
A6 Mastering the California Mathematics Standards, Grade 7
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21 ( 3 _ 4 )
3 =
A 3 _
64 C
27 _
64
B 9 _
64 D
27 _
4
22 A certain group of fifteen students took a test: three students got 6 questions correct. Four got 7 questions correct, five got 8 questions correct, two got 9 questions right, and one got 10 questions right. What is the median of the scores?
F 10 H 8
G 9 J 7
23 Which of the following speeds is slowest?
A 50 meters per minute
B 2 meters per second
C 1500 centimeters per minute
D 20 centimeters per second
24 Which of the following is equal to 1 _ 3 + 1 _
4 ?
F 7 _
12
G 2 _
7
H 1 _
6
J 1 _
12
25 In the figure below, find the measure of ∠A.
A 35° C 125°
B 55° D 145°
26 What is the solution set to the inequality 7y - 6 > 15?
F {y | y > 28}
G {y | y > -3}
H {y | y < 3}
J {y | y > 3}
27 The box-and-whisker plot below represents the amount of weekly rainfall in Columbus during the spring.
What is the median weekly rainfall?
A 10 inches
B 14 inches
C 16 inches
D 20 inches
Diagnostic Test (continued)
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Tota
l Cos
t ($)
0 5 10 15 20
Number of Apples
10
8
6
4
2
Tota
l Cos
t ($)
0 5 10 15 20
Number of Apples
10
8
6
4
2
Tota
l Cos
t ($)
0 5 10 15 20
Number of Apples
10
8
6
4
2
Tota
l Cos
t ($)
0 5 10 15 20
Number of Apples
10
8
6
4
2
12
15
Mastering the California Mathematics Standards, Grade 7 A7
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28 Apples are being sold at a price of $2 for 5 apples. Which of the following graphs shows the relationship between the number of apples and the total cost?
F
G
H
J
29 5 _ 6 ÷ 2 _
3 =
A 9 _
5
B 5 _
4
C 4 _
5
D 5 _
9
30 Point D is the midpoint of −−
AC . Find the length of
−− AC .
F 2 √ �� 369
G 18
H 9
J 6
31 What property is shown in the equation below?
(2x + 3) + 4 = 2x + 7
A Associative Property of Addition
B Distributive Property
C Commutative Property of Addition
D Associative Property of Multiplication
Diagnostic Test (continued)
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A8 Mastering the California Mathematics Standards, Grade 7
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32 √ � 88 lies between which two integers?
F 7 and 8
G 8 and 9
H 9 and 10
J 10 and 11
33 Juan is a car salesman who earns a 7.5% commission on his monthly sales. Juan’s sales total for this month is $12,000. How much commission does he earn?
A $90
B $900
C $11,100
D $12,900
34 What is the value of x if -5x + 11 = -4?
F -10
G -3
H 3
J 12
35 (26) 4
_ 22
=
A 222
B 212
C 28
D 25
36 A certain construction project will take 120 hours of work to complete. The construction team is composed of 4 members, each of whom works 6 hours per day. How many days will it take for the team to complete the project?
F 5
G 12
H 20
J 30
37 Concert tickets that normally cost $45 each are 15% off if they are purchased in advance. How much do the tickets cost if they are purchased in advance?
A $6.75
B $38.25
C $44.33
D $51.75
38 Which of the following is a diagonal of the cube pictured below?
F −−
AF
G −−
CD
H −−
DF
J −−
AB
Diagnostic Test (continued)
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y
xO
Ave
rag
e G
rad
e
Amount of TimeSpent Studying
O
-2-3-4
21 43-2-3-4
1234
y
x
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39 Which of the following is equal to 5-3 × 52?
A -5 C 1 _
25
B 5-6 D 1 _
5
40 The scatter plot below shows the amount of time the students in a certain class spend studying, as well as each student’s average grade.
Which statement best describes the relationship between time spent studying and average grade shown on the scatter plot?
F As a student’s time spent studying
increases, his or her average
grade decreases.
G As a student’s time spent studying
increases, his or her average
grade increases.
H As a student’s time spent studying
increases, his or her average grade
increases at first and then decreases.
J As a student’s time spent studying
increases, his or her average grade
decreases at first, and then increases.
41 If a train from Chicago to Cleveland travels for 120 miles at an average speed of 30 miles per hour, and travels the remaining 180 miles at an average speed of 60 miles per hour, how long should the entire trip take?
A 3.3 hours
B 4.0 hours
C 7.0 hours
D 10.0 hours
42 The distance a spring stretches varies directly with the force applied to it. If a spring stretches 21.6 inches when a 6-pound weight is hung on it, how far will the spring stretch with a 2-pound weight?
F 3.6 inches
G 7.2 inches
H 10.8 inches
J 64.8 inches
43 What is the area of triangle ABC?
A 9 square units
B 10 square units
C 15 square units
D 20 square units
Diagnostic Test (continued)
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O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
xMon
thly
Cos
t ($)
0 1 2 3 4 5 6 7 8 9 10
Songs Purchased
20
18
16
14
12
10
8
6
4
2
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44 The dimensions of the screen on a portable DVD player are 10 inches by 6 inches. Find the length of the diagonal of the screen.
F √ � 60 in. H
√ �� 136 in.
G 8 in. J 16 in.
45 Anita bought 6 CDs at a total cost of $67.68. Each CD was the same price. How much did each CD cost?
A $10.28 C $14.68
B $11.28 D $61.68
46 The graph below represents the monthly cost for a digital music download store. There is a monthly subscription fee and a charge for each song purchased. Based on the information in the graph, which statement is true?
F The cost of a song is $10.
G The monthly subscription fee is $1.
H The monthly subscription fee is $15.
J The cost of a song is $1.
47 Which best represents the graph of y = 0.5x - 3?
A
B
C
D
Diagnostic Test (continued)
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45
8
6
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48 A shoe store purchases shoes from a supplier at a cost of $50 per pair. The store then marks up the price by 12% before selling the shoes. If the shoe store sells 20 pairs of shoes, how much profit has the store earned?
F $6
G $12
H $60
J $120
49 Jamar bought 2 books for $9.95 each and 5 magazines for $3.25 each. What was the total cost for his purchases?
A $13.20
B $19.90
C $26.20
D $36.15
50 A room is 11 meters in length and 6 meters in width. How many square centimeters is the room?
F 66
G 6,600
H 66,000
J 660,000
51 If x = 3, then 3(2x - 3)2 =
A 0
B 27
C 81
D 225
52 Find the area of the shape below.
F 32 units2
G 54 units2
H 60 units2
J 63 units2
53 Which of the following expressions is equivalent to 6(3 + 2 × 4)?
A 26
B 48
C 66
D 120
54 (23 × 32)
_ (3 × 26)
=
F 3 _
8 H
9 _
8
G 3 _
4 J
9 _
4
Diagnostic Test (continued)
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Tota
l Cos
t
0 1 2 3 4 5
Number of Hours
$20
$16
$12
$8
$4
6 inches
4 inches
12 inches
A12 Mastering the California Mathematics Standards, Grade 7
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55 Which of the following is equal to 35 × 93?
A 330
B 313
C 311
D 310
56 The graph below shows the relationship between the total cost of renting a boat at Sparrow Lake and the number of hours the boat is used. How much does it cost per hour to rent the boat?
F $0.25
G $1.00
H $4.00
J $20.00
57 The following data represent the ages of different students in a school.
11, 12, 13, 14, 15, 16, 17
These data are shown on the box-and-whisker plot below.
What is the median of the data?
A 12
B 14
C 16
D 17
58 In the expression 3x2 + 6y, which number is the coefficient of x2?
F 2 H 6
G 3 J 9
59 Which expression below has the same value as x-3?
A -3x C 1 _ x ×
1 _ x ×
1 _ x
B 3 _ x D -x3
60 What is the surface area of the rectangular solid shown below?
F 88 in2
G 144 in2
H 178 in2
J 288 in2
61 Which of the following values is largest?
A ⎪11⎥
B ⎪-28⎥
C ⎪24⎥
D ⎪-12⎥
Diagnostic Test (continued)
A03-A14_Gr7_DT-879533.indd 12A03-A14_Gr7_DT-879533.indd 12 2/15/07 4:51:16 PM2/15/07 4:51:16 PM
20 in.
15 in.
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
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62 Point D is the midpoint of −−
AC . Find the perimeter of �ABC.
F 60 inches
G 65 inches
H 80 inches
J 120 inches
63 Miguel wants to save $56 to buy a new skateboard. He already has $21, and he can earn $5 per hour shoveling snow for his neighbor. If the equation below shows this relationship, how many hours must Miguel work to have the money he needs?
5h + 21 = 56
A 7
B 16
C 30
D 72
64 Which of the following graphs shows y = -x3?
F
G
H
J
Diagnostic Test (continued)
A03-A14_Gr7_DT-879533.indd 13A03-A14_Gr7_DT-879533.indd 13 2/15/07 4:51:17 PM2/15/07 4:51:17 PM
Volu
me
0 1 2 3 4 5
Side Length
25
20
15
10
5
Volu
me
0 1 2 3 4 5
Side Length
150
125
100
75
50
25
Volu
me
0 1 2 3 4 5
Side Length
25
20
15
10
5
Volu
me
0 1 2 3 4 5
Side Length
25
20
15
10
5
A14 Mastering the California Mathematics Standards, Grade 7
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65 Which of the following shows the graph of the relationship between the side length of a cube and the volume of that same cube?
A
B
C
D
Diagnostic Test (continued)
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7NS1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.
1 What is 7.85 × 105 in standard notation?
A 7,850
B 78,500
C 785,000
D 7,850,000
2 Which of the following shows 1,230,000 in scientific notation?
F 1.23 × 104
G 1.23 × 105
H 1.23 × 106
J 1.23 × 107
3 Last year, 8.35 × 103 people visited the local historical museum. What is 8.35 × 103 in standard notation?
A 8,350
B 83,500
C 835,000
D 8,350,000
4 Which of the following shows 0.0536 in scientific notation?
F 5.36 × 10-2
G 5.36 × 10-1
H 5.36 × 101
J 5.36 × 102
5 A total of 830,000 people went to rock concerts last year. Which of the following shows this number in scientific notation?
A 8.3 × 103
B 8.3 × 104
C 8.3 × 105
D 8.3 × 106
6 What is 1.002 × 10-3 in standard notation?
F 0.0001002
G 0.001002
H 100.2
J 1002
7 Which of the following shows 9,999 in scientific notation?
A 9.99 × 103
B 99.99 × 102
C 9.999 × 103
D 0.999 × 104
8 Which of the following shows 0.0000166 in scientific notation?
F 166 × 10-7
G 1.66 × 10-5
H 1.66 × 105
J 1.66 × 10-6
Practice by StandardNumber Sense 1.1
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A16 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardNumber Sense 1.2
7NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
1 Cathy bought 4 pairs of shorts for $38.60. If the 4 pairs of shorts cost the same amount, what was the cost of each pair of shorts?
A $7.95
B $8.55
C $9.55
D $9.65
2 ( 4 _ 5 )
3 =
F 12
_ 5
G 16
_ 125
H 64
_ 125
J 48
_ 5
3 Six tennis racquets cost $437.04. All the racquets cost the same amount. What is the cost of each racquet?
A $71.18
B $72.04
C $72.84
D $77.04
4 ( 3 _ 4 )
4 =
F 17
_ 22
G 81
_ 256
H 3 _
11
J 27
_ 256
5 Greg bought 7 pairs of jeans for $178.36. Each pair cost the same amount. How much did each pair of jeans cost?
A $25.05
B $25.48
C $27.05
D $27.48
6 Maria, Jose, and Michael had lunch together. The cost of each of their lunches was $9.42, $7.23, and $8.59. What was the total cost of their lunches?
F $24.24
G $25.24
H $26.14
J $26.24
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Practice by StandardNumber Sense 1.2 (continued)
7 Ms. Juarez bought a book for each of her 23 students. Each book cost $3.25. How much did Ms. Juarez spend on the books?
A $69.00
B $74.75
C $75.00
D $81.25
8 Humberto purchased four shirts at a total cost of $64.16. Each shirt cost the same amount. How much was each shirt?
F $11.04
G $13.12
H $14.12
J $16.04
9 ( 1 _ 4 )
3 =
A 1 _
7
B 4 _
7
C 1 _
64
D 3 _
64
10 (5.2)2 =
F 10.4
G 25.4
H 27.04
J 29.0
11 Darren paid $78.20 for 5 basketballs. If each basketball cost the same, what was the price of each basketball?
A $13.15
B $15.15
C $15.64
D $16.64
12 ( 2 _ 7 )
3 =
F 6 _
7
G 6 _
21
H 8 _
343
J 6 _
343
13 Mr. Smith bought 8 tools that cost $49.36. Each of the tools cost the same amount. How much did each tool cost?
A $6.17
B $6.92
C $7.05
D $7.17
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A18 Mastering the California Mathematics Standards, Grade 7
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7NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.
1 Which of the following decimals is
equivalent to 13 _ 5 ?
A 2.2
B 2.4
C 2.6
D 2.8
2 A book costs $11.79, and David receives a 15% student discount. Which of the following expressions can be used to estimate the amount of David’s discount?
F 0.0015 × $12.00
G 0.015 × $12.00
H 0.15 × $12.00
J 1.5 × $12.00
3 A new radio costs $58.99. Michelle receives a 10% discount for being a mall employee. Which of the following expressions can be used to estimate the amount of the discount on the radio?
A 0.01 × $59.00
B 0.10 × $59.00
C 1.0 × $59.00
D 1.1 × $59.00
4 Bianca has a coupon that is valid for a 30% discount on a sweater. She wants to buy a sweater that costs $64.50. Which of the following expressions can be used to estimate the amount of the discount?
F 0.03 × $65
G 0.30 × $65
H 0.07 × $65
J 0.70 × $65
5 Which of the following decimals is
equivalent to 15 _ 4 ?
A 3.25
B 3.75
C 4.50
D 4.75
6 Which of the following percents is
equivalent to 1 _ 8 ?
F 12.5%
G 18.0%
H 70.0%
J 87.5%
7 Which of the following expressions has the greatest value?
A 3 _
8 · $1000
B 45% of $1000
C 0.3 · $1000
D $1000 ÷ 3
Practice by StandardNumber Sense 1.3
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Practice by StandardNumber Sense 1.4
7NS1.4 Differentiate between rational and irrational numbers.
1 Which of the following is a rational number?
A √ � 5
B √ � 2
C 0.555
D π
2 Which of the following is an irrational number?
F 5 _
1
G 1 _
2
H √ �� 1.69
J √ � 2
3 Which of the following is an example of an irrational number?
A 5.6
B √ � 5
C √ � 4
D 1.8
4 Which of the following is an example of a rational number?
F √ � 2
G √ � 5
H √ � 7
J √ � 9
5 Which of the following is an irrational number?
A √ � 7
B √ � 9
C 1.25
D 1 _
4
6 Which of the following is a rational number?
F √ � 1 _
4
G √ � 6
H √ � 19
J √ � 35
7 Which of the following is a rational number?
A π × π
B π3
C π + π
D π ÷ π
8 Which of the following is an irrational number?
F 3.14159
G 1.41421
H 22
_ 7
J √ � 10
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A20 Mastering the California Mathematics Standards, Grade 7
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7NS1.5 Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.
1 Which of the following fractions is equivalent to 3.2?
A 8 _
3 C
13 _
4
B 11
_ 3 D
16 _
5
2 Which of the following fractions is equivalent to 4.125?
F 13
_ 4 H
27 _
6
G 33
_ 8 J
34 _
8
3 Which of the following fractions is equivalent to 0.22?
A 1 _
5 C
11 _
50
B 1 _
10 D
22 _
10
4 Which of the following fractions is equivalent to 2.25?
F 7 _
3 H
9 _
4
G 8 _
3 J
10 _
4
5 Shana earned a score of 80% on her last math test. Which of the following fractions is equivalent to Shana’s score?
A 1 _
9
B 1 _
8
C 4 _
5
D 5 _
6
6 Which of the following is not a rational number?
F 0.111
G 0.111…
H 0.101101110…
J 0.10101010…
7 Andrew’s baseball team won 9 _ 12
of their
games. Which of the following decimals
is another way to write 9 _ 12
?
A 0.25
B 0.75
C 0.666…
D 1.333…
8 Which of the following fractions is equivalent to 0.02?
F 1 _
200 H
1 _
40
G 2 _
200 J
1 _
50
Practice by StandardNumber Sense 1.5
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Practice by StandardNumber Sense 1.6
7NS1.6 Calculate the percentage of increases and decreases of a quantity.
1 A bike originally cost $75.00. It was discounted 30% this week. Which of the following is equal to the amount of the discount?
A $22.50
B $30.00
C $45.00
D $52.50
2 All softball gloves are on sale for 20% off the original price. If the glove originally cost $32.50, how much isthe discount?
F $6.50
G $12.50
H $16.25
J $26.00
3 A flashlight originally cost $8.50. The hardware store is giving 20% discounts this week. What is the amount of the discount on a flashlight?
A $6.80
B $6.50
C $4.25
D $1.70
4 Marco received a score of 80 on his first math quiz. He received a score of 100 on his second quiz. What is the percentage of increase in his scores from the first to the second?
F 20%
G 25%
H 33%
J 60%
5 Last year, the fee for entering a soccer tournament was $75 per team. This year, the fee is $100. What is the percentage of increase in the tournament fee from last year to this year?
A 25%
B 30%
C 33%
D 50%
6 A video game originally cost $45.00. A 15% discount is being given this week. What is the amount of the discount on the video game?
F $3.00
G $6.75
H $30.00
J $38.25
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A22 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardNumber Sense 1.7
7NS1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.
1 Chris bought a television set that was on sale for 10% off the original price and an additional 20% off the discounted price. If the television originally cost $200, what is the price Chris paid?
A $136
B $144
C $170
D $180
2 A book was on sale for 25% off the original price. As a special promotion, an additional 20% was taken off the discounted price. If the original price was $40, what is the price paid after all the discounts?
F $5
G $20
H $24
J $30
3 Marisol borrows $800 at 7% simple interest for one year. If she makes no payment for one year, how much interest will she owe?
A $15
B $56
C $66
D $100
4 Jim earns a 6% commission on his sales at a computer store. Last month, he sold $12,480.00 worth of computers. How much commission did Jim earn?
F $20.60
G $206.00
H $728.80
J $748.80
5 Sara deposits $4000 into her bank account. The bank pays 4% interest annually. If she makes no deposits or withdrawals for one year, how much interest will she earn?
A $80
B $100
C $160
D $400
6 Mike receives an 8% commission on clothes he sells at his job. If he sold $1280.00 worth of clothing, how much should he expect to earn in commission?
F $48.80
G $102.40
H $480.00
J $880.00
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Practice by StandardNumber Sense 1.7 (continued)
7 A skateboard is on sale for 15% offthe original price, and as a special promotion, there is an additional 20% discount on the sale price. What price should a customer pay if the original price was $40.00?
A $27.20
B $29.80
C $34.00
D $35.00
8 Basketballs are on sale for 25% off the original price. As a special promotion, the sale price has been discounted by an additional 20%. If basketballs cost $25.00 originally, what is the price a customer should expect to pay?
F $5.00
G $6.25
H $15.00
J $18.75
9 Ivan opens a savings account with $100.00. The account pays 5% interest, compounded monthly. If Ivan makesno other deposits or withdrawals, what will the account balance be at the end of two months?
A $100.10
B $110.00
C $110.25
D $125.00
10 A sporting goods store buys softball bats at a cost of $40. The store then marks the price up by 40%. What is the store’s profit on the sale of a bat?
F $16
G $20
H $40
J $56
11 Sierra uses a coupon in order to receive a 20% discount on her purchase at the home improvement store. After the discount is given, there is a tax of 5% added to the cost. How much does Sierra pay if her total before the discount was $90.00?
A $77.00
B $75.60
C $75.00
D $72.00
12 The cost of an item after a 7% sales tax is applied to it is $53.50. What is the cost of the item before the sales tax is added?
F $46.50
G $50.00
H $52.80
J $57.24
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A24 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardNumber Sense 2.1
7NS2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.
1 Which of the following has the same value as 4 6 × 4 -3 ?
A 4-3
B 4-2
C 42
D 43
2 ( 1 _ 5 )
-4 × ( 1 _
5 )
2 =
F ( 1 _
5 )
-8
G ( 1 _
5 )
-5
H ( 1 _
5 )
-2
J ( 1 _
5 )
6
3 53 _
5-2 =
A 5-6
B 5-5
C 55
D 56
4 Which of the following has the same value as 3-2 × 32?
F 3-4
G 3-1
H 30
J 34
5 33 _
3-4 =
A 3-7
B 3-1
C 37
D 312
6 8-2 _
83 =
F 8-6
G 8-5
H 81
J 86
7 ( 2 _ 3 )
5 · ( 2 _
3 )
-3 =
A - 4 _
9
B 4 _
6
C 4 _
9
D 9 _
4
8 2-2 ÷ 2-3 =
F 2
G 1 _
2
H 2º
J 1 _
4
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Practice by StandardNumber Sense 2.2
7NS2.2 Add and subtract fractions by using factoring to find common denominators.
1 Which of the following shows the next
step for using the least common
denominator to simplify 4 _ 5 - 1 _
3 ?
A ( 4 _
5 ×
5 _
5 ) - (
1 _
3 ×
3 _
3 )
B ( 4 _
5 ×
3 _
3 ) - (
1 _
3 ×
5 _
5 )
C ( 4 _
5 ×
1 _
1 ) - (
1 _
3 ×
4 _
4 )
D ( 4 _
5 ×
2 _
2 ) - (
1 _
3 ×
5 _
5 )
2 What is the least common denominator
of 1 _ 5 and 1 _
7 ?
F 35 H 10
G 28 J 2
3 Sara completed 3 _ 8 of her project on
Monday and 1 _ 4 of her project on
Thursday. How much of her project
has Sara completed so far?
A 4 _
12 C
3 _
32
B 5 _
8 D
2 _
3
4 4 _ 8 - 1 _
5 =
F 1 H 2 _
5
G 4 _
5 J
3 _
10
5 Which of the following shows the next
step for using the least common
denominator to simplify 2 _ 3 + 1 _
4 ?
A ( 2 _
3 +
4 _
4 ) + (
1 _
4 +
3 _
3 )
B ( 2 _
3 +
2 _
2 ) + (
1 _
4 +
3 _
3 )
C ( 2 _
3 ×
2 _
2 ) + (
1 _
4 ×
2 _
2 )
D ( 2 _
3 ×
4 _
4 ) + (
1 _
4 ×
3 _
3 )
6 1 _ 12
+ 1 _ 15
=
F 9 _
60
G 2 _
60
H 2 _
27
J 1 _
27
7 Mr. Yakuro had 1 _ 2 tank of gas before
work on Monday. He used 3 _ 8 of the tank
to drive to work. How much of the tank
did he have left after driving to
work?
A 1 _
2
B 1 _
8
C 2 _
6
D 4 _
8
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A26 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardNumber Sense 2.3
7NS2.3 Multiply, divide, and simplify rational numbers by using exponent rules.
1 22 · 53 · 64
_ 24 · 52 · 62
=
A 45
B 90
C 180
D 360
2 23 · 43 · 84
_ 22 · 44 · 82
=
F 16
G 32
H 64
J 128
3 84 _
82 =
A 10
B 16
C 24
D 64
4 Which expression is equivalent to
35 × 33?
F 32
G 38
H 92
J 98
5 Which expression is equivalent to 99 × 96?
A 8115
B 813
C 915
D 93
6 Which of the following has the greatest value?
F 34
_ 34
G 34
_ 33
H 34 × 3-2
J 32 × 3-3
7 ( 2 _ 3 )
2 · ( 1 _
6 )
2 =
A 1 _
81
B 2 _
18
C 8 _
18
D 4 _
9
8 Which expression is equivalent to 56 · 53?
F 52
G 53
H 59
J 518
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Practice by StandardNumber Sense 2.3 (continued)
9 126 _
122 =
A 1212
B 128
C 124
D 123
10 (53 · 46 · 81)
_ (52 · 44 · 82)
=
F 5 _
8
G 9 _
8
H 10
J 20
11 Which expression is equivalent to 84?
A 87 · 83
B 87
_ 83
C 82
_ 82
D 82 + 82
12 710 _
75 =
F 72
G 75
H 715
J 750
13 There are 210 · 22 bacteria in Kevin’s science sample. How many bacteria is this?
A 25
B 28
C 212
D 220
14 Which expression has the greatest value?
F 61 × 64
G 62 + 62
H 65
_ 62
J 6-2 × 64
15 104 · 102 _
103 · 103 =
A 10
B 1.0
C 0.1
D 0.01
16 23 · 32 =
F 55
G 66
H 36
J 72
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11 12 13 14 15
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Practice by StandardNumber Sense 2.4
7NS2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.
1 √ �� 441 =
A 17
B 19
C 21
D 23
2 The square root of 20 is between which two numbers?
F 3 and 4
G 4 and 5
H 5 and 6
J 6 and 7
3 The square root of 80 is between which two numbers?
A 7 and 8
B 8 and 9
C 9 and 10
D 10 and 11
4 Find the length of one side of a square that has an area of 289 square units.
F 13
G 17
H 23
J 27
5 √ �� 625 =
A 15
B 25
C 35
D 45
6 Which of the following points shows the location of √ �� 150 on the number line?
F point AG point BH point CJ point D
7 √ �� 225 =
A 15
B 25
C 35
D 45
8 The square root of 1000 is between which two numbers?
F 29 and 30
G 30 and 31
H 31 and 32
J 100 and 110
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Practice by StandardNumber Sense 2.5
7NS2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.
1 |8 - 13| × |6 - 4| =
A -12
B -10
C 10
D 12
2 |38 - 45| - |12 - 14| =
F -9
G -5
H 5
J 9
3 Which of the following expressions has the smallest value?
A |-58|
B |-38|
C |21|
D |47|
4 Which of the following expressions has the greatest value?
F |-81|
G |-100|
H |58|
J |73|
5 |10 - 40| - |30 - 80| =
A -80
B -20
C 20
D 80
6 Which of the following statements is true?
F |-15| > |15|
G |-33| < |15|
H |-15| > |-33|
J |-33| > |-15|
7 ⎪ 1 _ 5 × -10⎥ + ⎪- 3 _
4 × 12⎥ =
A -11
B -7
C 7
D 11
8 |7 - 6| - |19 - 6| =
F -14
G -12
H 12
J 14
9 Which of the following expressions has the greatest value?
A |-92|
B |-56|
C |47|
D |91|
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A30 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardNumber Sense 2.5 (continued)
10 Which of the following is in order from least to greatest?
F -|12|, |-5|, |-13|
G |-5|, -|12|, |-13|
H |-13|, -|12|, |-5|
J -|12|, |-13|, |-5|
11 -|2.5 - 3.5| + |22| =
A -5
B -3
C 3
D 5
12 |5 - 18| + |7 - 13|
F -19
G -7
H 7
J 19
13 Which of the following statements is not true?
A |-62| > |-26|
B |-26| > |-62|
C |-26| < |62|
D |62| = |-62|
14 Which of the following expressions has a value of 8?
F |-7| - |-1|
G |-7| + |-1|
H |-7| - |1|
J -|-7| + |-1|
15 |8| × |-23|
_ |-2| × 2
=
A -16
B -2
C 12
D 16
16 Which has the greatest value?
F |-7.5|G |-10|H |9.1|J |-8.9|
17 -||-3 - 2| - |6 - 9|| =
A 20
B 2
C -2
D -20
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Practice by StandardAlgebra and Functions 1.1
7AF1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represent a verbal description.
1 The product of a number (n) and 8 is 56. Which of the following equations shows that relationship?
A 8 + n = 56
B 8 - n = 56
C 8n = 56
D 56n = 8
2 Twelve less than a number (x) is 27. Which of the following equations shows this relationship?
F 27 - x = 12
G 12 - 27 = xH 12 - x = 27
J x - 12 = 27
3 The sum of 3 times a number (n) and 14 is 29. Which of the following equations shows this relationship?
A 3n + 14 = 29
B 3n + 29 = 14
C 3n - 14 = 29
D 3n - 29 = 14
4 Which of the following statements describes the equation x + 19 = 47?
F The difference of a number (x) and
19 is 47.
G The sum of a number (x) and 19 is 47.
H The product of a number (x) and
19 is 47.
J The quotient of a number (x) and
19 is 47.
5 Four less than a number (n) is less than 23. Which of the following inequalities shows that relationship?
A 4 - n > 23
B 4 - n < 23
C n - 4 > 23
D n - 4 < 23
6 The product of 6 and a number (x) is greater than or equal to 84. Which of the following inequalities describes that relationship?
F 6 + x ≥ 84
G 6 + x ≤ 84
H 6x ≥ 84
J 6x ≤ 84
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Practice by StandardAlgebra and Functions 1.2
7AF1.2 Use the correct order of operations to evaluate algebraic equations.
1 If x = -4, then x2 - 3 =
A -19.
B -11.
C 5.
D 13.
2 If x = -2 and y = 3, then x(x - y) =
F -10.
G -2.
H 2.
J 10.
3 Evaluate the expression for x = 4, y = 3, and z = 2.
xy - 3z
A 1
B 2
C 6
D 18
4 Evaluate 2(x + 4)2 for x = 3.
F 28 H 100
G 98 J 196
5 If x = -2 and y = -3, then xy - x =
A -8. C 4.
B -4. D 8.
6 If x = -2 and y = -3, then xy2
_ x =
F -9.
G -6.
H 6.
J 9.
7 (22)3 =
A 512
B 256
C 64
D 32
8 - (-3)2 - (-1)3 =
F -8
G -10
H 8
J 10
9 Evaluate (x - x2)2 for x = -1
A 4
B 1
C 0
D -1
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7AF1.3 Simplify numerical expressions by applying properties of rational numbers and justify the process used.
1 Which property is used in the equation below?
13(z + 5) = 13z + 65
A Associative Property of Addition
B Commutative Property of Addition
C Distributive Property
D Inverse Property of Addition
2 Which property is demonstrated in the following equation?
x + (y + z) = x + (z + y)
F Associative Property of Addition
G Commutative Property of Addition
H Distributive Property
J Inverse Property of Addition
3 Which of the following expressions is equivalent to 5x + 75?
A x + 75
B 5(x + 75)
C x + 15
D 5(x + 15)
4 Which property is used in the equation below?
x · (y · z) = (x · y) · z
F Associative Property of Multiplication
G Commutative Property of Multiplication
H Distributive Property
J Inverse Property of Multiplication
5 Which property is used in the equation below?
x ( 1 _ x ) = 1
A Associative Property of Multiplication
B Commutative Property of Multiplication
C Distributive Property
D Inverse Property of Multiplication
6 Which property is used in the equation below?
x · (y · z) = x · (z · y)
F Associative Property of Multiplication
G Commutative Property of Multiplication
H Distributive Property
J Inverse Property of Multiplication
7 Which operation will change the value of any integer except 0?
A add 0
B multiply by 2 _
2
C divide by 1
D multiply by 0
Practice by StandardAlgebra and Functions 1.3
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A34 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardAlgebra and Functions 1.3 (continued)
8 Which property is used in the equation below?
2(6 + x) = 12 + 2x?
F Commutative Property of Addition
G Commutative Property of Multiplication
H Associative Property of Multiplication
J Distributive Property
9 Which property is used in the equation below?
3x + (2x + y( = (3x + 2x) + y
A Associative Property of Addition
B Commutative Property of Addition
C Distributive Property
D Inverse Property of Addition
10 Simplify the expression below.
-(-7 + 3)
F 10
G 4
H -4
J -10
11 Which of the following operations will not change the value of any non zero number?
A multiplying by zero
B adding zero
C adding one
D subtracting one
12 Which is equivalent to the following expression?
3x2(6x + 2x)
F 24x3
G 24x4
H 18x3 + 2xJ 20x3
13 Which of the following expressions is equivalent to (3x + 7) + 5y?
A 15xyB 8xy + 7C 10x + 5yD 3x + (7 + 5y)
14 Which property is used in the equation below?
2b + 5 = 5 + 2b
F Associative Property of Addition
G Cummutative Property of Addition
H Distributive Property of Addition
J Identity property of Addition
15 Evaluate the expression below whenx = 75.
(x + 36) + 25
A x + 100
B x + 61
C 136
D 126
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Practice by StandardAlgebra and Functions 1.4
7AF1.4 Use algebraic terminology correctly.
1 How many variables are there in the following equation?
5x + 2y + z = 37
A 1
B 2
C 3
D 4
2 Complete the following sentence.5x + 2 ≤ 17 is an example of a(n)
.
F parabola
G inequality
H constant
J coefficient
3 What is the coefficient in the following expression?
3x2y
A 3
B 2
C xD y
4 What is the constant in the following equation?
y = 4x2 + 7
F xG 2
H 4
J 7
5 The following expression has how many terms?
3y + 4x2
A 1
B 2
C 3
D 4
6 In the following expression, what is the coefficient of the x2 term?
6x2 + 5y
F 2
G 5
H 6
J 12
7 Which of the following is an algebraic expression?
A 0
B 2 + 2
C 2 + 2xD 2 + 2x = 4
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Tota
l Cos
t ($)
0 1 3 5 7 9
Number of Nights
907560453015
Tota
l Cos
t ($)
0 1 3 5 7 9
Number of Nights
907560453015
Tota
l Cos
t ($)
0 1 3 5 7 9
Number of Nights
907560453015
Tota
l Cos
t ($)
0 2 4 6 8 10
Number of Bananas
2.50
2.00
1.50
1.00
0.50
Tota
l Cos
t ($)
0 20 40 60 80 100 120 140 160 180 200
Number of Minutes
25
20
15
10
5
Tota
l Cos
t ($)
0 1 3 5 7 9
Number of Nights
907560453015
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Practice by StandardAlgebra and Functions 1.5
7AF1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.
1 Carlos bought a new cell phone. The graph below represents the relationship between the number of minutes that he uses and the total cost.
How much will Carlos have to pay even if he doesn’t make any calls?
A $1 C $10
B $5 D $20
2 The graph below shows the relationship between the number of bananas Allison buys and the total cost.
How much does each banana cost?
F $4.00 H $1.00
G $2.50 J $0.25
3 The table below shows the cost for one person to stay at a campground for n nights.
Nights (n) 1 3 5 9
Cost ($) 15 45 75 135
Which of the following graphs represents the information from the chart above?
A
B
C
D
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Mastering the California Mathematics Standards, Grade 7 A37
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Practice by StandardAlgebra and Functions 2.1
7AF2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.
1 Which expression below has the same value as x4y3?
A 7xyB 12xyC 4x · 3yD x · x · x · x · y · y · y
2 If x = 4, then x-3 =
F -64.
G -12.
H 1 _
64 .
J 1 _
12 .
3 If x = -2, then 3x3 =
A -24.
B -18.
C 18.
D 24.
4 If x = 2 and y = -3, then x2 - y2 =
F -22.
G -5.
H 13.
J 31.
5 If x = -3, then x3 =
A -27.
B -9.
C 9.
D 27.
6 Which expression below has the same value as x-3?
F -3x
G (-x) · (-x) · (-x)
H (-3x) · (-3x) · (-3x)
J 1 _
x · x · x
7 34 · 3-4 =
A 0
B 1
C 3-8
D 3-16
8 (3-2)3 =
F 3
G 1 _
3
H ( 1 _
3 )5
J ( 1 _
3 )6
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A38 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardAlgebra and Functions 2.2
7AF2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent.
1 Which of the following expressions is
equivalent to 12a8 _
3a4 ?
A 9a2
B 9a4
C 4a2
D 4a4
2 5x3y7
_ 25xy10
=
F 5x2y3
G 5x2
_ y3
H 1 _
5x2y3
J x2
_ 5y3
3 Which of the following expressions is
equivalent to (3y3)(4y)?
A 12y4
B 12y3
C 12y2
D 7y4
4 Which of the following expressions is
equivalent to √ �� 9x6 ?
F 3x3
G 3x4
H 9x3
J 9x4
5 Which of the following expressions is
equivalent to x-2y5
_ x4y2
?
A x2y3
B 1 _
x2y3
C y3
_ x6
D y3
_ x2
6 Which of the following expressions is
equivalent to (6x)(2x-2)?
F 8x
G 8 _ x
H 12
_ x
J 12
_ x3
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O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
Area
of S
quar
e
0 1 2 3 4
Length of Side
108642
Mastering the California Mathematics Standards, Grade 7 A39
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Practice by StandardAlgebra and Functions 3.1
7AF3.1 Graph functions of the form y = nx2 and y = nx3 and use in solving problems.
1 Which of the following graphs shows
y = - 1 _ 3 x2
A
B
C
D
2 Look at the graph shown below. Which equation is represented on the graph?
F y = 2xG y = 2x2
H y = -2x2
J y = 2x3
3 A designer measured the area of a square and compared it to the length of one of its sides. The graph below represents the relationship between the side length and the total area of the square.
Using the graph, determine which equation best expresses the relationship between the length of the side and the area of a square.
A y = x3
B y = x2
C y = -x2
D y = x
A15–A64_Gr7_PS-879533-8.indd 39A15–A64_Gr7_PS-879533-8.indd 39 2/17/07 11:38:42 AM2/17/07 11:38:42 AM
0 0.5 1 1.5 2 2.5 3 3.5 r4
V20π
16π
12π
8π
4π
0 0.5 1 1.5 2 2.5 3 3.5 4
20π
16π
12π
8π
4π
r
V
0 0.5 1 1.5 2 2.5 3 3.5 4
20π
16π
12π
8π
4π
r
V
0 0.5 1 1.5 2 2.5 3 3.5 4
20π
16π
12π
8π
4π
r
V
0 0.5 1 1.5 2 2.5 3
12108642
0 0.5 1 1.5 2 2.5 3 3.5 4
20
15
10
5Volu
me
Height (h)
A40 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardAlgebra and Functions 3.2
7AF3.2 Plot the values from the volumes of the three-dimensional shapes for various values of the edge lengths.
1 A cylinder has a height of 3 inches and a circular base of radius r. Which of the following graphs shows the relationship between the volume of the cylinder and the radius r?
A
B
C
D
2 The following graph shows the relationship between the volumeof a solid and one of its edges x.
The graph could represent which of the following?
F the volume of a triangular prism with
edge length xG the volume of a rectangular prism with
edge length 2 + xH the volume of a cylinder with height xJ the volume of a cube with edge length x
3 The Rugged Box Company makes a number of boxes whose bases are the same size but whose heights are different. The graph below shows the volumes of the boxes for a given height h.
What is the area of the base?
A 1 in2
B 4 in2
C 5 in2
D 25 in2
A15–A64_Gr7_PS-879533-8.indd 40A15–A64_Gr7_PS-879533-8.indd 40 2/17/07 11:38:46 AM2/17/07 11:38:46 AM
y
xO 1 2 3 4 5 6 7
56
4321
-2
-1
y
xO 1
56
4321
-2
-7 -6-5-4 -3-2-1
xO 1 2 3 4
56
4321
-2
-4 -3-2-1
y
y
xO 1 2 3 4
1
-2-3-4-5-6-7
-4 -3-2-1
O
-2-3-4-5
21 4 53-2-3-4-5
y
x
12345
O
-2-3-4
21 43-2-3-4
1234
y
x
Mastering the California Mathematics Standards, Grade 7 A41
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Practice by StandardAlgebra and Functions 3.3
7AF3.3 Graph the linear function, noting that the vertical change per unit of horizontal change is always the same and know that the ratio is called the slope of the graph.
1 Which best represents the graph of
y = - 1 _ 2 x + 5?
A
B
C
D
2 Which of these equations describes the line graphed below?
F y = 4x - 2
G y = -4x - 2
H y = 2x - 4
J y = 2x + 4
3 Which of the following is the slope of the line shown below?
A 2
B -2
C 1 _
2
D - 1 _
2
A15–A64_Gr7_PS-879533-8.indd 41A15–A64_Gr7_PS-879533-8.indd 41 2/17/07 11:38:49 AM2/17/07 11:38:49 AM
Tota
l Cos
t ($)
0 1 2 3 4 5 6 7 8 9 10
Pounds of Strawberries
654321
Tota
l Cos
t ($)
0 1 2 3 4 5 6 7 8 9 10
Number of Tacos
654321
Tota
l Cos
t ($)
0 1 2 3 4 5 6 7 8 9 10
Number of Tacos
654321
Tota
l Cos
t ($)
0 1 2 3 4 5 6 7 8 9 10
Number of Tacos
654321
Tota
l Cos
t ($)
0 1 2 3 4 5 6 7 8 9 10
Number of Tacos
654321
A42 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardAlgebra and Functions 3.4
7AF3.4 Plot the values of quantities whose ratios are always the same. Fit a line to the plot and understand that the slope of the line equals the ratio of quantities.
1 Strawberries are on sale at 3 pounds for $1.00. The following graph shows the relationship between the number of pounds of strawberries purchased and the total cost.
How many pounds of strawberries can be purchased for $6.00?
A 2
B 6
C 12
D 18
2 Tacos are on sale, 2 for $1.00. Which of the following graphs shows the relationship between the number of tacos bought and the total cost?
F
G
H
J
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Practice by StandardAlgebra and Functions 4.1
7AF4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the result.
1 What is the solution to the inequality3n - 7 > 17?
A n > 3
B n > 8
C n > 9
D n < 8
2 What is the value of p if p _
8 + 4 = 260?
F 32
G 64
H 1,048
J 2,048
3 Which inequality has the solutionx < 3?
A 3x + 2 < 35
B 5x - 2 > 15
C -3x - 2 < 9
D -4x + 3 > -9
4 Marty has $10 in his pocket on Monday. What will he have left on Friday if he spends $2.50 every day on a fruit smoothie?
F -$2.50 H $2.50
G $0 J $5.00
5 Sara read 13 books during the first half of the year. In the second half of the year, she read the same number of books each month. She read 31 books in all. How many books per month (b) did she read in the second half of the year?
A 5
B 6
C 7
D 8
6 What value of n makes the equation below true?
7n - 23 = 89
F 14
G 16
H 18
J 21
7 What is the value of x if 5x + 9 = 74?
A 13
B 15
C 115
D 361
8 What is the solution to the following inequality?
15.8 + y ≤ 50
F y ≤ 34.2
G y ≤ 33.8
H y ≥ 33.8
J y ≥ 34. 2
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A44 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardAlgebra and Functions 4.1 (continued)
9 What value of x makes the equation below true?
x _ 7 + 4 = 9
A 5
B 14
C 35
D 49
10 What is the value of x if -2x + 6 = -14?
F -10
G -4
H 4
J 10
11 Jebari needs $120 to fix his car. He has $65. He earns $5 an hour mowing lawns. The equation below shows this relationship. How many hours must Jebari work to have the money he needs?
5h + 65 = 120
A 9
B 10
C 11
D 12
12 Michael needs $75 for a new cell phone. He has $33. He makes $7 an hour babysitting. The equation below shows this relationship. How many hours must Michael work to buy the phone he wants?
7h + 33 = 75
F 3
G 4
H 5
J 6
13 What value of y makes the equation below true?
y _
4 + 3 = 7
A 8
B 12
C 16
D 20
14 Sarah has $300. Each week, she buys a $15 CD and a $5 book. How much money will she have left after 6 weeks?
F $180
G $210
H $270
J $280
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Practice by StandardAlgebra and Functions 4.2
7AF4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.
1 Jay drove his car for 2 hours at 65 miles per hour, and then he drove for another 4 hours at 50 miles per hour. How far did Jay drive in all?
A 130 miles
B 200 miles
C 265 miles
D 330 miles
2 Miguel is saving for a new video game system that costs $199. If he gets an allowance of $15 a week, how many weeks will it take for him to save up enough money for the video game system?
F 13
G 14
H 15
J 20
3 An eagle flew at a speed of 17 miles per hour for 2 hours, and then it flew 15 miles per hour for 3 hours. How far did the eagle fly altogether?
A 32 miles
B 47 miles
C 59 miles
D 79 miles
4 The number of tablespoons of sea salt needed in a saltwater fish tank varies directly with the number of gallons of water in the tank. A pet shop owner recommends adding 100 tablespoons of sea salt to a 20-gallon tank. How many tablespoons of sea salt should be added to a 30-gallon saltwater fish tank?
F 100
G 150
H 200
J 250
5 The distance you travel on a bicycle varies directly with the number of revolutions that the rear tire completes. You travel about 2 meters on a mountain bike for every revolution of the tire. About how many meters do you travel per 1500 tire revolutions?
A 1500
B 2000
C 2500
D 3000
6 The amount of vacation Sabrina earns varies directly with the amount time she works. If Sabrina works 2 weeks, she earns 3 hours of vacation. At that rate, how many hours of vacation time would Sabrina earn in 8 weeks?
F 6
G 8
H 12
J 16
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A46 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardAlgebra and Functions 4.2 (continued)
7 Micah’s scooter can go 1000 miles on 20 gallons of gas. How far could the scooter go on 25 gallons of gas?
A 750 miles
B 1000 miles
C 1250 miles
D 1500 miles
8 Allie rode her bike for 2 hours at 7 miles per hour, and then for 3 hours at 5 miles per hour. How far did Allie ride in all?
F 10 miles
G 19 miles
H 29 miles
J 39 miles
9 Mandy rode her bike for 3 days at 40 miles per day, and then for 5 days at50 miles per day. What is the average number of miles per day for this 8 day trip?
A 92.5 miles per day
B 46.25 miles per day
C 45.0 miles per day
D 42.0 miles per day
10 Ron drove his car for 200 miles at55 miles per hour, and then for 3 more hours at 45 miles per hour. How far did Ron drive in all?
F 135 miles
G 139 miles
H 200 miles
J 335 miles
11 A train travels at 120 miles per hour for 3 hours, and then increases its speed to 140 miles per hour for 9 hours. Find the average speed of the train.
A 125 miles per hour
B 130 miles per hour
C 135 miles per hour
D 138 miles per hour
12 Jack’s car gets an average of 31 miles per gallon of gas. If he plans to drive 155 miles to his grandparent’s house, and then 186 miles to a friend’s house, how many gallons of gas will he use in all?
F 11 gallons
G 31 gallons
H 55 gallons
J 62 gallons
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Mastering the California Mathematics Standards, Grade 7 A47
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Practice by StandardMeasurement and Geometry 1.1
MG1.1 Compare weights, capacities,geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).
1 David ran the 100-yard dash in 20 seconds. How many feet per second was David running?
A 5
B 15
C 50
D 80
2 Daniela rode 6 miles in 1 hour. If there are 5,280 feet in 1 mile, about many feet per second did Daniela travel?
F 9
G 15
H 60
J 75
3 The length of a pencil is 8 centimeters. What is the length of the pencil expressed in millimeters?
A 0.8 millimeters
B 8 millimeters
C 80 millimeters
D 800 millimeters
4 Jeff caught a fish that weighed
2 1 _ 2 pounds. How many ounces did
the fish weigh?
F 5
G 25
H 30
J 40
5 A thermometer reads 25 degrees Celsius. What is the temperature expressed in degrees Fahrenheit?
A 50°F
B 65°F
C 77°F
D 86°F
6 Rich has a piece of rope that measures 200 millimeters. What is the length of the rope expressed in centimeters?
F 0.02 centimeters
G 0.2 centimeters
H 2.0 centimeters
J 20 centimeters
F = 9 _ 5 C + 32
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1 unit = 3 feet
1 unit = 5 feet
1 unit = 3 yards
1 unit = ?
A48 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardMeasurement and Geometry 1.2
7MG1.2 Construct and read drawings and models made to scale.
1 Mrs. Jones drew a shaded figure to represent the teacher’s supply room.
What is the length and width of the supply room?
A 48 feet by 18 feet
B 24 feet by 9 feet
C 12 feet by 4.5 feet
D 6 feet by 2.25 feet
2 A computer room is represented below. What is the width of the room?
F 12 feet
G 15 feet
H 27 feet
J 35 feet
3 Brandon drew the picture below to represent a parking lot. According to the scale of the picture, what are the dimensions of the parking lot?
A 3 yards by 10 yards
B 3 yards by 30 yards
C 6 yards by 10 yards
D 6 yards by 30 yards
4 A scale drawing of a soccer field is shown below. If an actual field is 120 yards by 80 yards, what does each unit represent?
F 3 yards
G 5 yards
H 10 yards
J 20 yards
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Mastering the California Mathematics Standards, Grade 7 A49
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Practice by StandardMeasurement and Geometry 1.3
7MG1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.
1 According to the table below, which reader could read the most pages in 1 hour?
Name Speed of Reading
Ashley 12 pages in 30 minutes
David 7 pages in 15 minutes
Karen 5 pages in 10 minutes
Kyle 3 pages in 5 minutes
A Ashley
B David
C Karen
D Kyle
2 Which color printer is the fastest in the table below?
Name of Copier
Printing Speed
Colorifi c 1 page every 5 seconds
Rainbow 15 pages per minute
Reliable 80 pages every 5 minutes
Smart Copy 400 copies every 30 minutes
F Colorific
G Rainbow
H Reliable
J Smart Copy
3 You are the manager of a clothing store. Your sales goal for a 6-week period is 2500 shirts. About how many shirts must be sold per week to meet your sales goal?
A 625
B 417
C 357
D 250
4 Listed below are bolt production rates for four different companies.
Name of Company Production Speed
Alpha 5 bolts per second
Gamma 180 bolts per minute
Omega 7,000 bolts every half hour
Zulu 10,000 bolts per hour
Which company produces the bolts fastest?
F Alpha
G Gamma
H Omega
J Zulu
5 A person-day represents one person doing one day’s work. As supervisor, you realize that it will take 750 person-days to complete your latest work project. If you have 15 employees available, how many days will it take to complete the project?
A 5 C 50
B 15 D 60
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A50 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardMeasurement and Geometry 1.3 (continued)
6 The rate of a long-distance call is $0.12 per minute. Your monthly bill was $32.04 for long-distance calls.How many minutes did you spend onlong-distance calls?
F 245
G 267
H 284
J 289
7 Listed in the table below are the speeds of 4 different bicycle assemblers.
Assembler Assembling Speed
Bobby 1 bike in 12 minutes
Christina 4 bikes in 1 hour
Doug 12 bikes in 2 hours
Janet 20 bikes in 4 hours
Who could assemble the most bikes in 8 hours?
A Bobby
B Christina
C Doug
D Janet
8 A certain substance has a density of 6 kilograms per cubic meter. What is the volume of a piece of this substance with a mass of 3 kilograms?
F 0.5 m3
G 2 m3
H 9 m3
J 18 m3
9 Amy can type 20 pages per minute and Jordan can type 10 pages per minute. Working together, how long will it take them to type a 6000-page document?
A 30 minutes
B 200 minutes
C 300 minutes
D 600 minutes
10 A project will take 480 person-hours to complete. Each of the 4 people working on the project works for 6 hours per day. At that rate, how many days will it take to complete the project?
F 20
G 48
H 80
J 120
11 At a rate of 25 miles per day, about how many hiking days would it take two through-hikers to complete 2658 miles on the Pacific Crest Trail?
A 53
B 106
C 212
D 160
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6 cm
6 inches8 inches
4 inches
8 cm
14 cm
18 inches
14 inches
6 inches8 inches
4 inches
Mastering the California Mathematics Standards, Grade 7 A51
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Practice by StandardMeasurement and Geometry 2.1
7MG2.1 Use formulas routinely for finding the perimeter and area of basic two- dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.
1 What is the area of �LMN?
A = 1 _ 2 × b × h
A 22 cm2
B 44 cm2
C 56 cm2
D 112 cm2
2 What is the area of the circle shown below? Use 3.14 for π.(A = π × r2)
F 18.84 cm2
G 37.68 cm2
H 113.04 cm2
J 226.08 cm2
3 What is the volume of the rectangular solid shown below? (V = � × w × h)
A 48 in3
B 96 in3
C 192 in3
D 384 in3
4 What is the perimeter of rectangle WXYZ shown below?
F 32 inches
G 64 inches
H 222 inches
J 252 inches
5 What is the surface area of the rectangular solid shown below?
SA = 2 × � × w + 2 × � × h + 2 × w × h
A 72 B 192
B 104 D 208
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4 in.4 in.
4 in.
4 in.20 in.
10 in.
2 in.
3 in.
4 in.
4 cm
4 cm
8 cm
5.75 cm
8 cm
A52 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardMeasurement and Geometry 2.2
7MG2.2 Estimate and compute the area of more complex or irregular two- and three-dimensional figures by breaking the figures down into more basic geometric objects.
1 Nancy cut 2 corners off her rectangle to make it into a hexagon. What is the area of the shaded region?
A 168 in2
B 184 in2
C 196 in2
D 200 in2
2 Jennifer drew the trapezoid below on the chalkboard.
What is the area of the trapezoid?
F 6 in2
G 9 in2
H 16 in2
J 18 in2
3 What is the area of the pentagon shown below?
A 16 cm2
B 32 cm2
C 48 cm2
D 64 cm2
4 During math class, Ms. Patrick drew the shape below on the chalkboard.
What is the best estimate for the area of the parallelogram that Ms. Patrick drew?
F 12 cm2
G 24 cm2
H 36 cm2
J 48 cm2
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5 cm
12 cm6 cm
2 cm
2 cm2 cm
18 cm
12 cm
6 cm
Mastering the California Mathematics Standards, Grade 7 A53
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Practice by StandardMeasurement and Geometry 2.3
7MG2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor.
1 What is the surface area of the rectangular solid shown below?
A 162 cm2
B 250 cm2
C 324 cm2
D 360 cm2
2 What would happen to the volume of the rectangular solid below if the dimensions were doubled?
F The volume would be cut in half.
G The volume would double.
H The volume would be 4 times larger.
J The volume would be 8 times larger.
3 What is the volume of the package shown below?
A 396 cm3
B 792 cm3
C 1266 cm3
D 1296 cm3
4 Janice has a rectangular solid that has a surface area of 242 square inches. What would happen to the surface area if the length, width, and height were all doubled?
F The surface area would double.
G The surface area would triple.
H The surface area would be
4 times larger.
J The surface area would be
8 times larger.
5 The volume of a rectangular solid is measured to be 160 cubic meters. If all of the dimensions of the solid were cut in half, what would be the volume of the new solid?
A 10 m3
B 20 m3
C 40 m3
D 80 m3
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5 m
2 m
A54 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardMeasurement and Geometry 2.4
7MG2.4 Relate the changes in measure-ment with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in3] = [16.38 cm3]).
1 A hardware store is selling a particular kind of floor tile that has an area of 144 square inches. How many square feet is each floor tile?
A 1 ft2
B 2 ft2
C 12 ft2
D 24 ft2
2 The neighborhood garden shop sells pieces of sod that are 2 square feet each. How many square inches is each piece of sod equivalent to?
F 24 in2
G 96 in2
H 288 in2
J 576 in2
3 A rectangular solid has a volume of 320 cubic centimeters. If 1 inch is equal to about 2.54 centimeters, approximately how many cubic inches does that represent?
A 2 cm3
B 15 cm3
C 20 cm3
D 32 cm3
4 A can of paint holds enough paint to cover 200 square feet. How many square inches will the paint cover?
F 2,400 in2
G 2,800 in2
H 24,000 in2
J 28,800 in2
5 What is the area of the figure below in square centimeters?
A 100 cm2
B 1,000 cm2
C 10,000 cm2
D 100,000 cm2
6 A room is 10 feet wide and 18 feet long. What is the area of the room in square yards?
F 20 yd2
G 60 yd2
H 90 yd2
J 180 yd2
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Practice by StandardMeasurement and Geometry 3.1
7MG3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.
1 Which of the following line segments represents the altitude of �RST?
A −−
RS
B −−
ST
C −−
TR
D −−
SV
2 How many radii are shown in the circle below?
F 1
G 2
H 3
J 4
3 Which of the following segments is a diameter of the circle shown below?
A −−
AB
B −−
BC
C −−
FG
D −−
HA
4 Which of the following segments is a chord of the circle shown below?
F −−
ML
G −−
LN
H −−
QS
J −−
LR
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y
xO
-2-3-4-5
-2-3-4-5
12345
21 43 5
y
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12345
21 43 5
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-2-3-4-5
12345
21 43 5
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-2-3
-2 21 4 53 6 7 8
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A56 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardMeasurement and Geometry 3.2
7MG3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.
1 What is the distance between point F and point G on the coordinate plane shown below?
A 2 C 4
B 3 D 5
2 The endpoints of −−
AB are at A(0, 0) and B(2, 3). Which line segment represents a translation of 3 units to the left and 1 unit down?
F −−
CD H −−−
GH
G −−
EF J −−
JK
3 If �MNP is translated 3 units to the left and 3 units down, what are the coordinates of its vertices?
A (-1, 2), (2, 2), (-1, 6)
B (2, -1), (2, 3), (5, -1)
C (-1, -1), (-1, 3), (2, -1)
D (5, 5), (5, 11), (8, 5)
4 What is the area of the rectangle plotted on the graph below?
F 10 units2
G 15 units2
H 16 units2
J 18 units2
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ℓ8 ft
6 ft
13 ft
5 ft3 cm
4 cm
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Practice by StandardMeasurement and Geometry 3.3
7MG3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.
1 What is the length of the hypotenuse ℓ of the right triangle shown below?
A 2 feet
B 6 feet
C 10 feet
D 14 feet
2 What is the length of the hypotenuse in the right triangle shown below?
F 2 centimeters
G 5 centimeters
H 12 centimeters
J 14 centimeters
3 Listed in the table below are the lengths of the sides for four triangles. Which of the triangles is a right triangle?
Triangle Length of Sides in Inches
one 15, 20, 25
two 10, 23, 25
three 5, 6, 51
four 12, 14, 15
A Triangle one
B Triangle two
C Triangle three
D Triangle four
4 What is the missing side length of the in the right triangle shown below?
F 8 feet
G 12 feet
H 18 feet
J 30 feet
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6 in. 10 in.
15
20
40 ft 50 ft
10 ft
12 ft
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Practice by StandardMeasurement and Geometry 3.3 (continued)
5 In the figure shown below, Z is the midpoint of
−− WY, and
−− XZ is perpendicular
to −−
WY . What is the length of −−
XY ?
A 13 feet
B 17 feet
C 22 feet
D 30 feet
6 What is the length of the missing side in �CDE?
F 4 inches
G 6 inches
H 8 inches
J 10 inches
7 What is the length of the hypotenuse of �DEF?
A 15
B 25
C 35
D 45
8 In the figure shown below, D is the midpoint of
−− AC and
−− BD is perpendicular
to −−
AC . What is the length of −−
DC ?
F 90 feet
G 50 feet
H 30 feet
J 10 feet
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15 ft
11 ft
84
35
35
45
75
75
95
115
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Practice by StandardMeasurement and Geometry 3.4
7MG3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.
1 Quadrilaterals MNOP and TSRQ are congruent in the figure shown below.
What is m∠N?
A 75° C 95°
B 80° D 150°
2 In the diagram below, find the valueof a.
F 35°
G 45°
H 55°
J 100°
3 In the figure below, �CDE �EFC. What is the length of
−− DC ?
A 4 feet
B 11 feet
C 15 feet
D 26 feet
4 In the figure shown below, �RST and �XZY are congruent. If m∠S = 48° and m∠T = 23°, then what is m∠X?
F 15° H 109°
G 25° J 119°
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A60 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardMeasurement and Geometry 3.6
7MG3.6 Identify elements of three- dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).
1 Which pair of line segments are parallel in the rectangular solid shown below?
A −−
FK and −−
HJ
B −−
FJ and −−
KN
C −−
JN and −−
FG
D −−−
HM and −−
KN
2 Which of the following line segments would be a diagonal in the prism shown below?
F −−−
GH
G −−
GJ
H −−
NK
J −−−
FM
3 Name a pair of skew lines in the graphic shown below.
A � � MN and � � PO B � � PT and � � NO C � � QR and � � ST D � � NR and � � SO
4 How many diagonals are there in the prism shown below?
F 4
G 6
H 8
J 12
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Age of Customers
Stem Leaf
123456
0 3 60 1 3 5 50 7 81 71 32
Age of Customers
Stem Leaf
123456
0 3 60 0 1 3 50 7 81 71 32
0 5 10 15 20 25 30
Number of Workers
0 10 20 60504030
Points Scored
Age of Customers
Stem Leaf
123456
0 3 60 1 3 50 7 81 71 32
Age of Customers
Stem Leaf
123456
0 3 60 0 0 1 3 5 50 7 81 7 71 32
Mastering the California Mathematics Standards, Grade 7 A61
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Practice by StandardStatistics, Data Analysis, and Probability 1.1
7SDAP1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data.
1 The box-and-whisker plot below shows the number of points scored by a football team.
What is the median number of points scored by the football team?
A 7
B 21
C 35
D 56
2 The box-and-whisker plot below shows the number of workers at given times throughout the day.
What is the upper quartile of the number of workers?
F 10
G 12
H 20
J 30
3 Listed are the ages of customers entering a store:
13, 25, 23, 38, 20, 20, 25, 47, 51, 62, 16, 53, 41, 37, 20, 21, 47, 10, 30
Which of the following stem-and-leaf plots correctly displays the data?
A
B
C
D
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y
x
Aver
age
Grad
e
40%
20%
0
60%80%
100%
1 2 3 4 5 6Average Hours Studying
y
xO
y
xO
y
xO
y
xO
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Practice by StandardStatistics, Data Analysis, and Probability 1.2
7SDAP1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level).
1 The scatterplot below shows the average grade scored and the average amount of time spent studying.
Which of the following statements best describes the relationship between average grade and average amount of time studying?
A As average studying time increases,
average grade decreases.
B As average studying time increases,
average grade increases.
C As average studying time decreases,
average grade increases.
D As average studying time decreases,
average grade stays the same.
2 Which scatterplot below best represents the statement that as x increases, y at first increases and then decreases?
F
G
H
J
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0 10 12 14 222018162 4 86
Worker Absences
0 50 60 807010 20 4030
Age of Customers
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Practice by StandardStatistics, Data Analysis, and Probability 1.3
7SDP1.3 Understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set.
1 Listed below are the ages of students receiving tutoring.
11, 13, 9, 21, 18, 16, 16, 12, 14, 13, 12, 15
What is the lower quartile of the data?
A 9
B 11
C 12
D 13
2 The following are the speeds of cars, in miles per hour, traveling on a local street.
25, 37, 42, 21, 30, 32, 25
What is the median speed of the cars?
F 25
G 30
H 37
J 42
3 What is the median number of worker absences, as shown in the box-and-whisker plot below?
A 6
B 8
C 10
D 12
4 What is the maximum age of customers entering a store, as shown in thebox-and-whisker plot below?
F 20
G 30
H 50
J 80
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Temperatures
Stem Leaf
23456
9 9 0 5 72 5 8 97 7 71 2 3
Key: 2 9 represents 29
A64 Mastering the California Mathematics Standards, Grade 7
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Practice by StandardStatistics, Data Analysis, and Probability 1.3 (continued)
5 Temperatures from around the country are listed in the stem-and-leaf plot below.
What is the minimum temperature?
A 29 degrees
B 42 degrees
C 57 degrees
D 63 degrees
6 Ages of volunteers at a local hospital are listed below:
19, 34, 19, 19, 20, 44, 21, 48,55, 57, 46, 59, 44, 74, 69, 72
What is the maximum age of the volunteers?
F 19
G 34
H 59
J 74
7 A group of students are asked how many brothers and sisters they have. The results are as follows: 3 have none, 6 have 1, 7 have 2, 3 have 3, and 1 has 4. What is the median number of brothers and sisters?
A 1
B 2
C 3
D 4
8 A group of dogs are weighed. The results are as follows: 2 weigh 6 pounds, 4 weigh 8 pounds, 5 weigh 12 pounds, 3 weigh 14 pounds, and 1 weighs 16 pounds. What is the upper quartile of the data?
F 12 pounds
G 13 pounds
H 14 pounds
J 16 pounds
9 All of the students in a certain class are measured to see how tall they are. The results of the measurements are that 1 student is 48 inches tall, 2 are 50 inches tall, 3 are 56 inches tall, 3 are 58 inches tall, 2 are 60 inches tall, and 1 is 64 inches tall. What is the median height of the class?
A 48 inches
B 56 inches
C 57 inches
D 58 inches
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Mastering the California Mathematics Standards, Grade 7 A65
Standards AssessmentStudent Answer Sheet
Record your answers by coloring in the appropriate bubble for the best answer to each question.
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Standards Assessment
1 What is the solution to theinequality 4c - 6 > 26?
A c > 8
B c > 32
C c < 8
D c < 32
2 Three less than two times a number n is 18. Which equation shows that relationship?
F 3n - 2 = 18
G 3n + 2 = 18
H 2n - 3 = 18
J 2n + 3 = 18
3 Lisa has $400 in a savings account that pays 3.5% interest compounded annually. How much will she have in the account after 3 years?
A $414.00
B $428.49
C $442.00
D $443.49
4 How many milligrams are in 45 grams?
F 0.45
G 45
H 4,500
J 45,000
5 ( 3 _ 5 )
3
=
A 9 _
125
B 27
_ 125
C 9 _
25
D 27
_ 25
6 The box-and-whisker plot below represents the values of houses sold during the month of July.
What was the upper quartile of the home values?
F $310,000
G $330,000
H $370,000
J $410,000
7 Identify a diagonal in the cube shown below.
A −−
BC
B −−
DF
C −−
EH
D −−
AE
Mastering the California Mathematics Standards, Grade 7 A67
250 300 350 450400
Home Values ($1000s)
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8 What is the value of x if 2x - 5 = -9?
F x = 4
G x = 2
H x = -2
J x = -4
9 Write 7,544,000 in scientific notation.
A 7.544 × 104
B 7.544 × 105
C 7.544 × 106
D 7.544 × 107
10 Evaluate 2(3x - 2)2 - 3(y - 4)2 forx = 3 and y = 6.
F 2
G 24
H 48
J 86
11 The following table shows the cost of taking a taxi.
Which graph in the next column best represents the cost of taking a taxi?
A
B
C
D
A68 Mastering the California Mathematics Standards, Grade 7
Standards Assessment (continued)
Distance Cost ($)
0 4.00
1 4.50
2 5.00
3 5.50
4 6.00
5 6.50
Cost
(dol
lars
)
0 1 2 3 4 5
Distance (miles)
8
7
6
5
4
3
2
1
Cost
(dol
lars
)
0 1 2 3 4 5
Distance (miles)
8
7
6
5
4
3
2
1
Cost
(dol
lars
)
0 1 2 3 4 5
Distance (miles)
8
7
6
5
4
3
2
1
Cost
(dol
lars
)
0 1 2 3 4 5
Distance (miles)
8
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5
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1
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12 Which expression below has the same value as 16x4?
F 2(x)4
G 4x · 4xH 2x · 2x · 2xJ 2x · 2x · 2x · 2x
13 Collin earns $75 for 6 hours of work. At that rate, how many hours would she have to work to earn $500?
A 25 hours
B 40 hours
C 80 hours
D 100 hours
14 Philip bought 4 video games for $183.80. All 4 video games were the same price. How much did each video game cost?
F $36.76
G $44.55
H $45.95
J $61.27
15 The scale on a map shows that 1 centimeter represents 5 kilometers. If two points on the map are 8.4 centimeters apart, how far apart are the points in real life?
A 8.4 kilometers
B 21 kilometers
C 42 kilometers
D 84 kilometers
16 Brandon works in a clothing store and is paid a 15% commission on each of his sales. In June he earned $975 in commissions. How much did Brandon sell in June?
F $6300
G $6400
H $6500
J $6600
17 Which expression is equivalent to 4x - 8y?
A 4(2x - y)
B 4(x - 2y)
C 2x(2 - 4y)
D 4x(4 - 2y)
18 What is the volume of the cylinder?(V = πr2h)
F 1,356.48 cubic units
G 2,712.96 cubic units
H 6,104.16 cubic units
J 24,416.64 cubic units
Mastering the California Mathematics Standards, Grade 7 A69
Standards Assessment (continued)
24
18
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Name Date
19 Find the missing length of the third side of the triangle below.
A 30 centimeters
B 36 centimeters
C 39 centimeters
D 42 centimeters
20 Fran wants to buy an MP3 player that costs $150. She has $42 saved already. She can earn $6 an hour by babysitting on weekends. The equation below shows this relationship. How many hours must Fran work to save the money she needs?
6h + 42 = 150
F 8 hours H 18 hours
G 12 hours J 25 hours
21 Which equation is an example of the Associative Property of Addition?
A 5 × (4 + b) = (5 × 4) + (5 × b)
B 5 + (4 + b) = (5 + 4) + bC 5 + (4 × b) = (5 × 4) + bD 5 + (4 + b) = 5 + 4 + b
22 Rachel started a business selling T-shirts on the beach. She pays $200.00 a week to rent the space. She bought 100 T-shirts of different sizes for $3.00 each. She sells each T-shirt for $12.99. So far, she has sold 29 T-shirts in her first week. What is the minimum number of shirts she has to sell this week in order to make a profit?
F 8 H 12
G 10 J 14
23 Which expression is equivalent to 27b8 _
3b2 ?
A 24b6
B 24b4
C 9b6
D 9b4
24 Which expression has the greatest value?
F ⎪-27⎥
G ⎪-39⎥
H ⎪44⎥
J ⎪12⎥
25 7 _ 8 + 9 _
24 =
A 2 _
3 C 1
1 _
4
B 23
_ 24
D 1 5 _
8
A70 Mastering the California Mathematics Standards, Grade 7
Standards Assessment (continued)
39 cm15 cm
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26 Which graph shows y = 2x3?
F
G
H
J
27 The scatter plot below shows the relationship between the number of hours per week that a basketball team practices and the number of points the team scores in each game that week.
Which statement best describes this relationship?
A As the team members increased their
practice time, their points scored
increased.
B As the team members increased their
practice time, their points scored
decreased.
C As the team decreased their practice
time, their points scored increased.
D As the team members increased their
practice time, their points scored
increased first, and then decreased.
28 An elevator in a downtown office building travels at a rate of 8 feet per second. The building is 28 stories tall, and each story is 10 feet high. How long will it take for the elevator to travel from the ground floor to the top floor?
F 30 seconds H 40 seconds
G 35 seconds J 45 seconds
Mastering the California Mathematics Standards, Grade 7 A71
Standards Assessment (continued)
O
y
x
O
y
x
O
y
x
O
y
x
y
xO
Poin
ts S
core
d
Practice Time(hours)
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Standards Assessment (continued)
Name Date
29 53 × 55
_ 54 × 52
=
A 0.2
B 5
C 25
D 125
30 The following table describes the typing speeds of four applicants for an administrative assistant position.
Which applicant types the fastest?
F Marcus
G Stephanie
H Craig
J Alissa
31 A cube has a volume of 64 cubic units. Suppose one of the faces of the cube is graphed on a coordinate plane and a vertex is at (3, 3). Which of the following points is a possible location for another vertex of that cube face?
A (0, 0)
B (3, -3)
C (3, 7)
D (7, -3)
32 What is the area of the shaded area inside the square?
F 80 cm2
G 12 cm2
H 244 cm2
J 324 cm2
33 Elena buys a box of computer components for $350. She assembles the computer, and then sells it for $560. How much did Elena mark the price up?
A 50%
B 60%
C 80%
D 120%
34 Determine the coordinates of point C in the figure below after a translation of 3 units up and 4 units left.
F (-1, 3)
G (1, 3)
H (6, -4)
J (1, -3)
A72 Mastering the California Mathematics Standards, Grade 7
Applicant Typing Speed
Marcus 50 words in 1 minute
Stephanie 245 words in 4 minutes
Craig 160 words in 3 minutes
Alissa 110 words in 2 minutes
8 cm
8 cm
10 cm
10 cm 8 cm
10 cm
10 cm
8 cm
O
-2-3-4
21 43-2-3-4
1234
y
x
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Standards Assessment (continued)
Name Date
35 What is the multiplicative inverse of3 + 2x?
A 3 - 2x
B 2x - 3
C 1 _
3 + 2x
D - 1 _
3 + 2x
36 Alfredo has a calling card with
12 3 _ 4 minutes left on it. After calling
his friend Stacy, Alfredo now has
5 2 _ 3 minutes left on his card. How long
did he talk to Stacy?
F 6 minutes, 35 seconds
G 6 minutes, 45 seconds
H 6 minutes, 55 seconds
J 7 minutes, 5 seconds
37 Ms. Anderson recorded the following test scores from her Grade 7 math class.
73, 85, 91, 80, 69, 84, 92, 88, 75, 80, 72, 94, 87, 75, 86, 81, 80, 72, 90, 68, 79, 81
Which is the lower quartile?
A 73.5
B 74
C 74.5
D 75
38 Which best represents the graph of y = 3x + 4?
F
G
H
J
Mastering the California Mathematics Standards, Grade 7 A73
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234y
x
O
-2-3-4
21 43-2-3-4
1234y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
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Standards Assessment (continued)
Name Date
39 Renata drove for 4 hours at 55 miles per hour, and then for 3 hours at 35 miles per hour. How far did Renata drive altogether?
A 220 miles
B 245 miles
C 325 miles
D 385 miles
40 Which expression is equivalent to 64 × 68?
F 612
G 632
H 3612
J 3632
41 What is the surface area of the rectangular solid shown below?
A 234 in2
B 468 in2
C 936 in2
D 1008 in2
42 Which of the following has the same value as 4-4 × 4-3?
F 4-12
G 4-7
H 47
J 412
43 What is the slope of the line in the graph?
A -2
B - 1 _
2
C 1 _
2
D 2
44 Identify a chord in the diagram below.
F −−
AD
G −−
CE
H −−
BC
J −−
ED
A74 Mastering the California Mathematics Standards, Grade 7
15 inches
6 inches
18 inches
O
-2-3-4
21 43-2-3-4
1234
y
x
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Standards Assessment (continued)
Name Date
45 Which of the following is equivalent to 4.375?
A 31
_ 8
B 33
_ 8
C 35
_ 8
D 37
_ 8
46 A tablecloth measures 2160 square inches. What is the area of the tablecloth in square feet?
F 15 ft2
G 36 ft2
H 144 ft2
J 180 ft2
47 Which of the following shows the next
step when using the least common
denominator to simplify 5 _ 6 + 7 _
9 ?
A ( 5 _
6 ×
3 _
3 ) + (
7 _
9 ×
2 _
2 )
B ( 5 _
6 ×
2 _
2 ) + (
7 _
9 ×
3 _
3 )
C ( 5 _
6 ×
9 _
9 ) + (
7 _
9 ×
6 _
6 )
D ( 5 _
6 ×
6 _
6 ) + (
7 _
9 ×
9 _
9 )
48 Find the value of x in the equation 2 _ 3 x - 6 = 18.
F 8
G 12
H 24
J 36
49 Anita had some change in her change purse. After she gave her friend $0.55, Anita had $1.25 altogether. Which equation can she use to find the original amount of money, m, she had in her change purse?
A 1.25 + m = 0.55
B m × 0.55 = 1.25
C m + 0.55 = 1.25
D m - 0.55 = 1.25
50 √ �� 374 lies between which two integers
on a number line?
F 17 and 18
G 18 and 19
H 19 and 20
J 20 and 21
51 ⎪6 - 10⎥ - ⎪5 - 2⎥ =
A -7
B -1
C 1
D 7
Mastering the California Mathematics Standards, Grade 7 A75
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Standards Assessment (continued)
Name Date
52 Which of the following numbers is not an irrational number?
F √ � 7
G - 3 _
√ � 16
H
√ � 19 _
2
J π
53 �ABC and �DEF are congruent triangles. What is the length of
−− DE ?
A 6 units
B 12 units
C 18 units
D 36 units
54 A pair of hockey skates is selling for $98.00. The store has them on sale at 25% off. Michael receives a 10% discount on the sale price after making a large purchase at the store. What is the final price Michael paid for the hockey skates?
F $88.20
G $73.50
H $66.15
J $63.70
55 The DVD store is selling 3 DVDs for $19.99. Which graph shows the relationship between the number of DVDs purchased and the total cost?
A
B
C
D
A76 Mastering the California Mathematics Standards, Grade 7
Cost
($)
0 1 2 3 4 5 6 7 8
DVDs Purchased
60
50
40
30
20
10
Cost
($)
0 1 2 3 4 5 6 7 8
DVDs Purchased
60
50
40
30
20
10
Cost
($)
0 1 2 3 4 5 6 7 8
DVDs Purchased
60
50
40
30
20
10
Cost
($)
0 1 2 3 4 5 6 7 8
DVDs Purchased
60
50
40
30
20
10
6
66
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Standards Assessment (continued)
Name Date
56 Identify the constant in the expression 3x2 - 4x + 5.
F x2
G xH 2
J 5
57 Which fraction is equivalent to 4.12?
A 97
_ 25
B 103
_ 25
C 21
_ 5
D 62
_ 15
58 Brandon recorded the heights of some students in the 7th grade at his school in the stem-and-leaf plot shown below.
What is the height of the tallest student whose height Brandon recorded?
F 5 feet 4 inches
G 5 feet 5 inches
H 5 feet 8 inches
J 5 feet 9 inches
59 The following graph shows how many inches correspond to each number of feet. Which equation represents the line that contains these points?
A y = 6x
B y = 12x
C y = 1 _
12 x
D y = 1 _
6 x
60 In the figure below, N is the midpoint of
−−− KM , and
−− LN is perpendicular to
−−− KM .
What is the length of −−
LN ?
F 8 centimeters
G 12 centimeters
H 16 centimeters
J 20 centimeters
Mastering the California Mathematics Standards, Grade 7 A77
Heights of Students in Grade 7
5 6 = 56 inches
Stem
456
7 8 8 90 1 3 3 5 6 8 9 90 0 1 1 3 4 5 8
Leaves
Inch
es
0 1 2 3 4 5 6 7 8
Feet
90
80
70
60
50
40
30
20
10
24 cm
20 cm
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Standards Assessment (continued)
Name Date
61 Ian’s car gets an average of 24 miles per gallon of gas. Ian plans to drive 180 miles on Friday, 210 miles on Saturday, and 250 miles on Sunday. How many gallons of gas should he expect to use altogether?
A 22
B 25
C 27
D 30
62 34 · 53 · 26
_ 33 · 54 · 24
=
F 4 _
25
G 6 _
25
H 6 _
5
J 12
_ 5
63 What value of x makes the equation below true?
x _ 4 + 5 = 8
A 6
B 12
C 24
D 48
64 Kia has a resting heart rate of 60 beats per minute. After she exercises for 30 minutes, her heart rate is 84 beats per minute. What is the percent increase or percent decrease of Kia’s heart rate?
F 24% decrease
G 40% decrease
H 24% increase
J 40% increase
65 The following data represent the number of LCD televisions sold by an electronics store over the period of one week. 38, 25, 20, 12, 45, 17, 42, 21These data are shown on the box-and-whisker plot below.
What is the upper quartile of the data?
A 27.50
B 31.50
C 35.00
D 38.00
A78 Mastering the California Mathematics Standards, Grade 7
10 20 30 5040
LCD Televisions Sold
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Standards Practice and Periodic Assessments
ReviewerEvelyn R. Brown, Ed.D.
Rockway Middle SchoolLos Angeles, California
CA©08_Gr7_Flipbook_TP_B_879533-81 1CA©08_Gr7_Flipbook_TP_B_879533-81 1 2/19/07 4:28:00 PM2/19/07 4:28:00 PM
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher.
Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 978-0-07-879533-6MHID: 0-07-879533-8 Mastering the California Mathematics Standards, Grade 7 (Standards Practice and Periodic Assessments)Printed in the United States of America.
1 2 3 4 5 6 7 8 9 10 024 15 14 13 12 11 10 09 08 07
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California Mathematics, Grade 7, Standards Practice Biii
Contents
California Mathematics Standards, Grade 7 . . . . . . . . . . . . . . . . . . . Biv
Practice by Chapter
Chapter 1 Algebra: Integers . . . . . . . . . . . . . . . . . . . . . . . . . . B1
Chapter 2 Algebra: Rational Numbers . . . . . . . . . . . . . . . . . . . . . B3
Chapter 3 Real Numbers and the Pythagorean Theorem . . . . . . . . . . . B5
Chapter 4 Proportions and Similarity . . . . . . . . . . . . . . . . . . . . . B7
Chapter 5 Percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B9
Chapter 6 Geometry and Spatial Reasoning . . . . . . . . . . . . . . . . . B11
Chapter 7 Measurement: Area and Volume . . . . . . . . . . . . . . . . . B13
Chapter 8 Algebra: More Equations and Inequalities . . . . . . . . . . . . B15
Chapter 9 Algebra: Linear Functions . . . . . . . . . . . . . . . . . . . . B17
Chapter 10 Algebra: Nonlinear Functions and Monomials . . . . . . . . . . B19
Chapter 11 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B21
Periodic Assessment 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B23
Periodic Assessment 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B27
Periodic Assessment 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B31
Periodic Assessment 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B36
Periodic Assessments—Student Answer Sheets . . . . . . . . . . . . . . . . . . B41
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Biv California Mathematics, Grade 7, Standards Practice
California Mathematics Standards, Grade 7
= Key Standard * = standard assessed on the CAHSEE
Number Sense
1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:
1.1* Read, write, and compare rational numbers in scientific notation (positive and
negative powers of 10) with approximate numbers using scientific notation.
1.2* Add, subtract, multiply, and divide rational numbers (integers, fractions,
and terminating decimals) and take positive rational numbers to
whole-number powers.
1.3* Convert fractions to decimals and percents and use these representations
in estimations, computations, and applications.
1.4 Differentiate between rational and irrational numbers.
1.5 Know that every rational number is either a terminating or repeating decimal
and be able to convert terminating decimals into reduced fractions.
1.6* Calculate the percentage of increases and decreases of a quantity.
1.7* Solve problems that involve discounts, markups, commissions, and profit
and compute simple and compound interest.
2.0 Students use exponents, powers, and roots and use exponents in working with fractions:
2.1* Understand negative whole-number exponents. Multiply and divide
expressions involving exponents with a common base.
2.2* Add and subtract fractions by using factoring to find common
denominators.
2.3* Multiply, divide, and simplify rational numbers by using exponent rules.
2.4* Use the inverse relationship between raising to a power and extracting the
root of a perfect square integer; for an integer that is not square, determine
without a calculator the two integers between which its square root lies
and explain why.
2.5* Understand the meaning of the absolute value of a number; interpret the
absolute value as the distance of the number from zero on a number line;
and determine the absolute value of real numbers.
Algebra and Functions
1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:
1.1* Use variables and appropriate operations to write an expression, an equation,
an inequality, or a system of equations or inequalities that represents a verbal
description (e.g., three less than a number, half as large as area A).
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California Mathematics, Grade 7, Standards Practice Bv
1.2* Use the correct order of operations to evaluate algebraic expressions such as
3(2x + 5)2.
1.3 Simplify numerical expressions by applying properties of rational numbers
(e.g., identity, inverse, distributive, associative, commutative) and justify the
process used.
1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient,
inequality, expression, constant) correctly.
1.5* Represent quantitative relationships graphically and interpret the meaning
of a specific part of a graph in the situation represented by the graph.
2.0 Students interpret and evaluate expressions involving integer powers and simple roots:
2.1* Interpret positive whole-number powers as repeated multiplication and
negative whole-number powers as repeated division or multiplication by
the multiplicative inverse. Simplify and evaluate expressions that include
exponents.
2.2* Multiply and divide monomials; extend the process of taking powers and
extracting roots to monomials when the latter results in a monomial with
an integer exponent.
3.0 Students graph and interpret linear and some nonlinear functions:
3.1* Graph functions of the form y = nx2 and y = nx3 and use in solving
problems.
3.2 Plot the values from the volumes of three-dimensional shapes for various
values of the edge lengths (e.g., cubes with varying edge lengths or a triangle
prism with a fixed height and an equilateral triangle base of varying lengths).
3.3* Graph linear functions, noting that the vertical change (change in y-value)
per unit of horizontal change (change in x-value) is always the same and
know that the ratio (“rise over run”) is called the slope of a graph.
3.4* Plot the values of quantities whose ratios are always the same (e.g., cost
to the number of an item, feet to inches, circumference to diameter of a
circle). Fit a line to the plot and understand that the slope of the line
equals the quantities.
4.0 Students solve simple linear equations and inequalities over the rational numbers:
4.1* Solve two-step linear equations and inequalities in one variable over the
rational numbers, interpret the solution or solutions in the context from
which they arose, and verify the reasonableness of the results.
4.2* Solve multistep problems involving rate, average speed, distance, and time
or a direct variation.
California Mathematics Standards, Grade 7 (continued)
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Bvi California Mathematics, Grade 7, Standards Practice
Measurement and Geometry
1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:
1.1* Compare weights, capacities, geometric measures, times, and temperatures
within and between measurement systems (e.g., miles per hour and feet
per second, cubic inches to cubic centimeters)
1.2* Construct and read drawings and models made to scale.
1.3* Use measures expressed as rates (e.g., speed, density) and measures
expressed as products (e.g., person-days) to solve problems; check the
units of the solutions; and use dimensional analysis to check the
reasonableness of the answer.
2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale:
2.1* Use formulas routinely for finding the perimeter and area of basic
two-dimensional figures and the surface area and volume of basic three-
dimensional figures, including rectangles, parallelograms, trapezoids,
squares, triangles, circles, prisms, and cylinders.
2.2* Estimate and compute the area of more complex or irregular two-and
three-dimensional figures by breaking the figures down into more basic
geometric objects.
2.3* Compute the length of the perimeter, the surface area of the faces, and the
volume of a three-dimensional object built from rectangular solids.
Understand that when the lengths of all dimensions are multiplied by a scale
factor, the surface area is multiplied by the square of the scale factor and the
volume is multiplied by the cube of the scale factor.
2.4* Relate the changes in measurement with a change of scale to the units
used (e.g., square inches, cubic feet) and to conversions between units
(1 square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is
approximately 16.38 cubic centimeters or [1 in3] = [16.38 cm3]).
3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:
3.1 Identify and construct basic elements of geometric figures (e.g., altitudes,
mid-points, diagonals, angle bisectors, and perpendicular bisectors; central
angles, radii, diameters, and chords of circles) by using a compass and
straightedge.
California Mathematics Standards, Grade 7 (continued)
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California Mathematics, Grade 7, Standards Practice Bvii
3.2* Understand and use coordinate graphs to plot simple figures,
determine lengths and areas related to them, and determine their image
under translations and reflections.
3.3* Know and understand the Pythagorean theorem and its converse and use it
to find the length of the missing side of a right triangle and the lengths of
other line segments and, in some situations, empirically verify the
Pythagorean theorem by direct measurement.
3.4* Demonstrate an understanding of conditions that indicate two
geometrical figures are congruent and what congruence means about the
relationships between the sides and angles of the two figures.
3.5 Construct two-dimensional patterns for three-dimensional models, such as
cylinders, prisms, and cones.
3.6 Identify elements of three-dimensional geometric objects (e.g., diagonals
of rectangular solids) and describe how two or more objects are related in
space (e.g., skew lines, the possible ways three planes might intersect).
Statistics, Data Analysis, and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:
1.1* Know various forms of display for data sets, including a stem-and-leaf plot
or box-and-whisker plot; use the forms to display a single set of data or to
compare two sets of data.
1.2* Represent two numerical variables on a scatterplot and informally describe
how the data points are distributed and any apparent relationship that
exists between the two variables (e.g., between time spent on homework
and grade level).
1.3 Understand the meaning of, and be able to compute, the minimum, the lower
quartile, the median, the upper quartile, and the maximum of a data set.
Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1* Analyze problems by identifying relationships, distinguishing relevant
from irrelevant information, identifying missing information, sequencing
and prioritizing information, and observing patterns.
1.2* Formulate and justify mathematical conjectures based on a general
description of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.
California Mathematics Standards, Grade 7 (continued)
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Bviii California Mathematics, Grade 7, Standards Practice
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1* Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex
problems.
2.3* Estimate unknown quantities graphically and solve for them by using
logical reasoning and arithmetic and algebraic techniques.
2.4* Make and test conjectures by using both inductive and deductive
reasoning.
2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs,
tables, diagrams, and models, to explain mathematical reasoning.
2.6 Express the solution clearly and logically by using the appropriate
mathematical notation and terms and clear language; support solutions with
evidence in both verbal and symbolic work.
2.7 Indicate the relative advantages of exact and approximate solutions to
problems and give answers to a specified degree of accuracy.
2.8 Make precise calculations and check the validity of the results from the
context of the problem.
3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original
situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual
understanding of the derivation by solving similar problems.
3.3* Develop generalizations of the results obtained and the strategies used and
apply them to new problem situations.
All Mathematical Reasoning Standards are embedded in the questions on the Grade 7 CST.
California Mathematics Standards, Grade 7 (continued)
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Number of Subscribers by Month
Num
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Month
7000600050004000300020001000
0 Jan Feb Mar Apr May Jun
California Mathematics, Grade 7, Standards Practice B1
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Practice by ChapterChapter 1 Algebra: Integers
1 If x = 6 and y = 2, then 8(x - 4 ) y =
A 16.
B 32.
C 64.
D 256.
2 Which of the following expressions is equivalent to 9(a + b)?
F 9a + bG a + 9bH 9(b + a)
J 9(a × b)
3 Which of the following statements is true about 8x + 3y = 14?
A 8x + 3y is an equation, and 14 is
a term.
B 8x + 3y is a term, and 14 is an
expression.
C 8x + 3y = 14 is an expression, and
14 is an equation.
D 8x + 3y = 14 is an equation, and
8x + 3y is an expression.
4 If a = 6 and b = 7, then which of the following statements is true?
F ⎪a - b⎥ > ⎪b - a⎥
G ⎪a - b⎥ < ⎪b - a⎥
H ⎪a - b⎥ = ⎪b - a⎥
J ⎪a - b⎥ = - ⎪b - a⎥
5 The graph below shows the number of subscribers to a magazine in the first 6 months of the year. Which of the following statements is true?
A The increase in the number of
subscribers was the same from January to
February as it was from May to June.
B The increase in the number of
subscribers was larger from January to
February than it was from May to June.
C If the trend continues, the increase in
the number of subscribers from June to
July will be smaller than it was from
May to June.
D If the trend continues, the increase in
the number of subscribers from June to
July will be larger than it was from
May to June.
6 ( 4 _ 7 )
3 =
F 64
_ 343
G 16
_ 49
H 12
_ 21
J 7 _
10
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80007000600050004000300020001000
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Ope
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(Dol
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1 2 3 4 5 6
Number of Children
B2 California Mathematics, Grade 7, Standards Practice
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Practice by ChapterChapter 1 (continued)
7 The product of 9 and y is subtracted from the product of 4 and x, and the difference is 3. Which of the following equations shows that relationship?
A 4x - 9y = 3
B 9y - 4x = 3
C 4 _ x -
9 _ y = 3
D 9 _ y -
4 _ x = 3
8 If a = 3 and b = 4, then ab _
9 =
F 1 _
81 . H 1.
G 1 _
3 . J 9.
9 Which of the following is an example of the Associative Property of Addition?
A (a + b) + c = (b + a) + cB (a + b) + c = a + (b + c)
C a(b + c) = ab + acD (a + b) × 1 = a + b
10 ( 3 _ 4 ÷ 5 _
6 ) ÷ ( 9 _
8 ÷ 7 _
6 ) =
F 11
_ 15
H 13
_ 15
G 4 _
5 J
14 _
15
11 When simplified, which of the following expressions is farthest from zero on a number line?
A ⎪(-3 ) 2 ⎥
B ⎪3 - 10⎥
C ⎪(-2 ) 3 ⎥
D ⎪-8 + 2⎥
12 The monthly operating cost, in dollars, of a small daycare center is shown in the graph below.
What is the monthly cost for each additional child?
F $5
G $100
H $500
J $1000
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California Mathematics, Grade 7, Standards Practice B3
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Practice by ChapterChapter 2 Algebra: Rational Numbers
1 Mariah has only 3 _ 8 the amount of free
time that Romario has. If the amount of free time that Romario has is
represented by x, which of the following expressions represents how much free time Mariah has?
A 0.25xB 0.375xC 0.5xD 0.675x
2 Gina has 2.65 times as many pairs of shoes as the average person. If the average person has y pairs of shoes, which of the following expressions is equal to the number of pairs of shoes that Gina has?
F 20y
_ 53
G 20y
_ 33
H 33y
_ 20
J 53y
_ 20
3 How many terms are in the expression 5x7 + 4y6 + 8?
A 2
B 3
C 4
D 5
4 Which list of rational numbers is in order from least to greatest?
F 1 _
500 ,
1 _
50 , 0.00002, 0.0002, 0.2
G 0.00002, 0.0002, 1 _
500 ,
1 _
50 , 0.2
H 0.2, 1 _
50 ,
1 _
500 , 0.0002, 0.00002
J 0.2, 0.0002, 0.00002, 1 _
50 ,
1 _
500
5 Rodney had 5 _ 7 of a pie left over from
last night’s dessert. After tonight’s
dessert, Rodney has 2 _ 3 of the pie that
remained from last night’s dessert. How much of the original pie does Rodney now have?
A 10
_ 21
C 7 _
10
B 11
_ 21
D 14
_ 15
6 Kimberly is a softball pitcher, and she threw her first pitch at 1850 yards per minute, her second pitch at 100 feet per second, her third pitch at 30 yards per second, and her fourth pitch at 6060 feet per minute. Which of Kimberly’s pitches was the fastest?
F her first pitch
G her second pitch
H her third pitch
J her fourth pitch
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B4 California Mathematics, Grade 7, Standards Practice
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Practice by ChapterChapter 2 (continued)
7 To simplify 17 _ 20
+ 2 _ 15
, which of the
following operations must be done first?
A Multiply 17
_ 20
by 4 _
3 , and then
multiply 2 _
15 by
3 _
4 .
B Multiply 17
_ 20
by 4 _
4 , and then
multiply 2 _
15 by
3 _
3 .
C Multiply 17
_ 20
by 3 _
3 , and then
multiply 2 _
15 by
4 _
4 .
D Multiply 17
_ 20
by 3 _
4 , and then
multiply 2 _
15 by
4 _
3 .
8 The sum of a and 7 is equal to 8 times the product of b and c. Which of the following equations shows this relationship?
F a + 7 = 8bcG 7a = 8(b + c)
H a + 7 = 8(b + c)
J 7a = 8bc
9 x-1 _
y-2 · ( x - y ) -3 =
A x4
_ y5 C
x3
_ y6
B y5
_ x4 D
y6
_ x3
10 Which of the following expressions has the same value as 9-7?
F 9 ÷ 9 ÷ 9 ÷ 9 ÷ 9 ÷ 9 ÷ 9
G 1 × 9 ÷ 9 ÷ 9 ÷ 9 ÷ 9 ÷ 9 ÷ 9
H 1 ÷ 9 ÷ 9 ÷ 9 ÷ 9 ÷ 9 ÷ 9
J 1 ÷ 9 ÷ 9 ÷ 9 ÷ 9 ÷ 9 ÷ 9 ÷ 9
11 Conrad and Yufi both built sand
castles. Conrad’s sand castle is 5 _ 4 as big
as Yufi’s sand castle. If the size of Yufi’s sand castle is represented by m, which expression represents the size of Conrad’s sand castle?
A 0.8mB 0.9mC 1.25mD 1.35m
12 The bean plants in Mesha’s garden produced 0.3125 times the number of beans that they produced last year. Let z equal the number of beans produced by Mesha’s bean plants last year. Which of the following expressions represents the number of beans produced by Mesha’s bean plants this year?
F z _
16
G z _
8
H 5z
_ 16
J 5z
_ 8
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1 2 3 4 5 6 7 8
(2, 7)
(5, 3)
California Mathematics, Grade 7, Standards Practice B5
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Practice by ChapterChapter 3 Real Numbers and the Pythagorean Theorem
1 √ ����� 144a6b18c12 =
A 12a2b6c4
B 12a3b9c6
C 14a2b6c4
D 72a3b9c6
2 Desmond bought 3 gallons of milk at $2.45 per gallon and 5 cartons of eggs at $1.79 per carton. What was the total amount of money that Desmond spent?
F $7.35
G $8.95
H $14.70
J $16.30
3 Which of the following is a false statement about the inequality 5x3 - 7 < 33?
A Five is a coefficient of one of the terms
in the inequality.
B There is an expression on both sides of
the inequality.
C One of the terms in the inequality
includes a constant raised to the power 3.
D One of the terms in the inequality
includes a variable raised to the power 3.
4 Which of the following is an irrational number?
F 3.31662479…
G 3.60555127
H √ �� 169
J 7 _
11
5 The measure of the hypotenuse of an isosceles right triangle is 16. What is the measure of one of the legs?
A 8
B 8 √ � 2
C 16
D 16 √ � 2
6 What is the straight-line distance between the two points plotted on the coordinate graph shown below?
F 5
G 9
H 16
J 25
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B6 California Mathematics, Grade 7, Standards Practice
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Practice by ChapterChapter 3 (continued)
7 Which of the following expressions is equal to ( √ � 25 )2?
A √ � 52
B √ �� 252
C √ �� 1252
D √ �� 6252
8 A crate containing 525 apples weighs 80.3 kilograms. The weight of the crate itself is 6.8 kilograms. If each of the apples has the same weight, how much does one apple weigh?
F 0.007 kilograms
G 0.014 kilograms
H 0.07 kilograms
J 0.14 kilograms
9 An expression consists of three terms that are added together. The first term has a coefficient of 5, the second term consists of two variables that are multiplied together, and the third term is a constant. Which of the following expressions could this be a description of?
A 5x2 + xy + 18
B 2x5 + xy + 18
C 5x2 + xy + yD 5x2 + xy + 18y
10 Which of the following is a rational number?
F π
G π × 2
H 3.14159265…
J 22
_ 7
11 The measure of one leg of a right
triangle is 3 _ 4 the length of the other leg
of the right triangle. If the measure of the second leg of the right triangle is z, what is the measure of the hypotenuse of the right triangle in terms of z?
A z _
4
B 3z
_ 4
C 5z
_ 4
D 7z
_ 4
12 The straight-line distance between the points (10, 2) and (x, 12) on a coordinate graph is 12. If x is positive, what is the value of x?
F -10
G -2
H 14
J 22
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0
Perim
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Side Length
California Mathematics, Grade 7, Standards Practice B7
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Practice by ChapterChapter 4 Proportions and Similarity
1 For the first 4 hours of a 6-hour flight, an airplane traveled at 480 miles per hour. Then the wind changed, and the airplane traveled at 420 miles per hour for the remaining 2 hours of the flight. What was the airplane’s average speed?
A 440 miles per hour
B 450 miles per hour
C 460 miles per hour
D 470 miles per hour
2 To qualify for a marathon, Ndudi must run 26 miles at a pace of 8 miles per hour. If Ndudi runs the 26 miles at 11 feet per second, will Ndudi qualify?
F Yes, he’ll qualify with less than
10 minutes to spare.
G Yes, he’ll qualify with more than
10 minutes to spare.
H No, he’ll miss qualifying by less than
10 minutes.
J No, he’ll miss qualifying by more than
10 minutes.
3 So far, Dahlia has raised 19 _ 20
of the
money that she needs to raise for a walk-a-thon. Let w represent the amount of money that she needs to raise for the walkathon. Which of the expressions represents the amount of
money she has raised so far?
A 0.19w C 0.91wB 0.9w D 0.95w
4 Mina’s toy box has a volume of 7 cubic feet. What is the volume of Mina’s toy box in cubic inches?
F 84
G 1,728
H 12,096
J 20,736
5 The following graph shows the relationship between the perimeter of a regular geometric figure and the length of one of its sides. How many sides does the figure have?
A 3 C 5
B 4 D 6
6 Which of the following measurements is the greatest: 3.75 square feet, 500 square inches, 3250 square centimeters, or 0.3 square meters?
F 3.75 ft2
G 500 in2
H 3250 cm2
J 0.3 m2
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B8 California Mathematics, Grade 7, Standards Practice
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Practice by ChapterChapter 4 (continued)
7 Marcella has a dollhouse that was modeled after, and built to the scale of, a real house. The height of the garage door on Marcella’s dollhouse is 1 foot. If 1 inch on Marcella’s dollhouse is equal to 0.75 foot on the real house that it is modeled after, what is the height of the garage door on the real house?
A 0.75 foot
B 3 feet
C 4 feet
D 9 feet
8 A group of tourists rented two canoes. The first canoe traveled at 12 miles per hour for 35 minutes, while the second canoe traveled at 8 miles per hour for 45 minutes. Which of the following statements is true?
F The first canoe traveled 1 mile more
than the second canoe.
G The second canoe traveled 1 mile more
than the first canoe.
H The first canoe traveled 4 miles more
than the second canoe.
J The second canoe traveled 4 miles
more than the first canoe.
9 How many cubic millimeters are in 10 cubic kilometers?
A 106
B 107
C 1018
D 1019
10 A map is drawn to a scale of 1:2400. How long would the image be on the map of a soccer field that is 120 yards long?
F 0.5 inch
G 1.8 inches
H 2.0 inches
J 3.6 inches
11 An ice-cream shop did 9 _ 4 the amount in
sales last year as it did the year before. If the shop did $350,000 in sales the year before last, which of the following expressions represents the amount in sales it did last year in dollars?
A 350,000 × 1.25
B 350,000 × 1.5
C 350,000 × 2.25
D 350,000 × 2.5
12 A scientist calculated the density of a substance to be 3000 kilograms per cubic meter. What is the density of the substance in kilograms per cubic kilometer?
F 3 × 106
G 3 × 109
H 3 × 1012
J 3 × 1015
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California Mathematics, Grade 7, Standards Practice B9
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Practice by ChapterChapter 5 Percent
1 In a jellybean jar, 3 _ 40
of the jellybeans
are green. What percent of the
jellybeans in the jar are green?
A 0.075%
B 0.75%
C 7.5%
D 75%
2 Hakeem, Ted, Roberto, and Fred will
all soon wed. They all purchased the
same type of tuxedo with the same
original price at a discount, but since
they bought their tuxedos at different
stores, their discounts were different.
Hakeem got 30 percent off, Ted got 2 _ 5
off, Roberto purchased his tuxedo for
0.65 of the original price, and Fred
purchased his tuxedo for 3 _ 4 of the
original price. Who paid the most for
his tuxedo?
F Hakeem
G Ted
H Roberto
J Fred
3 Which term in the expression on the right side of the equation x ÷ 8 = y - 3 is a variable?
A xB x ÷ 8
C yD y - 3
4 A used car salesman receives a 15-percent commission on any cars he sells. If he sold 1 car for $12,500 and another car for $16,000 last month, how much did he make in commissions last month?
F $1,875
G $2,400
H $4,275
J $4,800
5 The number of students in a yoga class increased from 14 to 42. What is the percent increase in the number of students in the yoga class?
A 100%
B 200%
C 300%
D 400%
6 Charmain needs to score 90 percent on her final exam to get an A, 80 percent to get a B, 70 percent to get a C, and 60 percent to get a D. If there are 3 sections on the exam, and she scored
13 _ 16
on the first section, 7 _ 8 on the second
section, and 3 _ 4 on the third section, what
grade did she receive on the exam?
F A
G B
H C
J D
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B10 California Mathematics, Grade 7, Standards Practice
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Practice by ChapterChapter 5 (continued)
7 Sari, Rakim, Candy, and Amos each invested $1000. After one year, Sari
had 31 _ 20
of her initial investment, Rakim
had 108% of his initial investment, Candy had 1.7 of her initial investment,
and Amos had 3 _ 2 of his initial
investment. Who had the most money after 1 year?
A Sari
B Rakim
C Candy
D Amos
8 Which of the following might not be present in an equation?
F variable
G term
H equal sign
J expression
9 Bethany bought a computer scanner from an online auction site for $280.00, and then sold it on the same auction site for a 22-percent profit. How much did Bethany sell the computer scanner for?
A $61.60
B $218.40
C $246.40
D $341.60
10 In order to become more physically active, Morris decreased the number of hours of television he watches per week from 18 hours to 13.5 hours. What is the percent decrease in the number of hours of television that Morris watches per week?
F 20%
G 25%
H 50%
J 75%
11 Ivy received 416 votes for class president out of 520 votes cast. What percent of the vote did Ivy receive?
A 80%
B 82%
C 84%
D 86%
12 Yesterday the price of gas was $2.20 per gallon, and today it is $2.53 per gallon. What was the percent of increase in the price of gas from yesterday to today?
F 15%
G 20%
H 115%
J 120%
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1
y
xO
12345678
1 2 3 4 5 6 7 8
(5, 8)
(5, 2)
(8, 6)(2, 6)
California Mathematics, Grade 7, Standards Practice B11
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1 A line segment has endpoints of (5, 9) and (13, 21) on a coordinate graph. What is the midpoint of the line segment?
A (8, 15)
B (9, 15)
C (9, 16)
D (8, 16)
2 The circle below is divided into eighths.
Which of the following expressions represents the measure of ∠1?
F (180 × 0.125)˚
G (180 × 0.375)˚
H (360 × 0.125)˚
J (360 × 0.375)˚
3 A regular decagon is a polygon with 10 sides, all of which are equal in length. The perimeter of a certain regular decagon is y. Which of the following expressions represents the length of one of the sides of the regular decagon?
A y × 10
B y ÷ 10
C y + 10
D y10
4 �ABC and �DEF are congruent. If the area of �ABC is 80, what is the area of �DEF?
F 40
G 80
H 120
J 160
5 Point P is located at (2, 5). What is the image of point P under a translation of 3 units right and 2 units down?
A (5, 3)
B (5, 7)
C (-1, 3)
D (0, 8)
6 Which of the following is true about −−
AB and
−− CD , as shown below?
F −−
AB is a perpendicular bisector of −−
CD .
G −−
CD is a perpendicular bisector of −−
AB .
H −−
AB is the midpoint of −−
CD .
J −−
CD is the midpoint of −−
AB .
Practice by ChapterChapter 6 Geometry and Spatial Reasoning
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xO
y
B12 California Mathematics, Grade 7, Standards Practice
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7 Juwan has drawn a circle with 2
chords. The first chord has a length
that is 1 _ 2 the length of the second chord.
The length of the second chord is m.
Which of the following expressions
represents the length of the first
chord?
A 0.05 C 0.5
B 0.05 × m D 0.5 × m
8 The perimeter of Yorba’s garden is 2 feet less than 3 times the perimeter of Ming’s garden If the perimeter of Ming’s garden is P, what is the perimeter of Yorba’s garden?
F P - 2
G 2P - 3
H 3P - 2
J 3P + 2
9 Are any two squares always congruent? If not, why?
A No, the sides of one square aren’t
always equal in length to the sides of
another square.
B No, the angles of one square aren’t
always equal in measurement to the
angles of another square.
C No, the sides of one square aren’t always
equal in length to the sides of another
square, and the angles of one square
aren’t always equal in measurement to
the angles of another square.
D Yes, two squares are always congruent.
10 The two triangles shown below are reflections of each other. What is the line of symmetry?
F the x-axis H the y-axis
G the line m J the line n
11 Rochelle has drawn two circles.
The diameter of the first circle is 1 _ 5
the diameter of the second circle. If the diameter of the second circle is d, which of the following expressions represents the area of the first circle?
A π × 0.01 × dB π × 0.1 × dC π × 0.01 × d2
D π × 0.1 × d2
12 The area of a rectangle is 96 square centimeters. If the height of the rectangle is h centimeters, which of the following expressions represents the length of the base of the rectangle in centimeters?
F 96 + hG 96 - hH 96 × hJ 96 ÷ h
Practice by ChapterChapter 6 (continued)
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2 in.
3 in.
1 in.
4 m
12 m
California Mathematics, Grade 7, Standards Practice B13
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Practice by ChapterChapter 7 Measurement: Area and Volume
1 The surface area of a rectangular solid is 22 square inches. The lengths of the sides of a similar rectangular solid are 3 times the side lengths of the first rectangular solid. What is the surface area of the second rectangular solid?
A 25 in2
B 66 in2
C 198 in2
D 484 in2
2 The length of a side of the larger square is 4 meters. What is the area of the shaded portion of the figure?
F 5.66 m2
G 8 m2
H 11.31 m2
J 12 m2
3 Which statement about two lines in three-dimensional space is not true?
A The intersection of the lines could be a
single point.
B The intersection of the lines could be a
segment.
C The lines could be parallel.
D The lines could be skew lines, which
are neither intersecting nor parallel.
4 If it takes the pilot of a jet aircraft 1 minute to correct her course, what is the minimum distance that must be maintained between any two jets that are traveling at 300 miles per hour?
F 60 miles
G 30 miles
H 10 mile
J 1 mile
5 What is the area of the parallelogram shown below? (A = b × h)
A 96 m2
B 48 m2
C 24 m2
D 16 m2
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2 cm
4 cm
3 cm
2.5 cm
2.5 cm
5 in.
4 in.4 in. 6 in.
7 in.
B14 California Mathematics, Grade 7, Standards Practice
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Practice by ChapterChapter 7 (continued)
6 What is the shaded part of the figure shown below called?
F vertex
G edge
H face
J diagonal
7 Nancy’s car will travel 38 miles on a gallon of gasoline. The price of gasoline is $2.50 per gallon. How much money will Nancy need for gasoline to make the 2800-mile drive from San Diego to New York?
A $200.00
B $300.00
C $400.00
D $500.00
8 What is the surface area of the rectangular prism shown below?
F 52 cm2
G 26 cm2
H 24 cm2
J 9 cm2
9 Which line segment bisects −−
BC in the triangle shown below?
A −−
AD
B −−
CD
C −−
AE
D −−
BD
10 What is the volume of the solid figure shown below?
F 390 in3
G 430 in3
H 550 in3
J 3360 in3
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California Mathematics, Grade 7, Standards Practice B15
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1 Which of the following terms most accurately describes the 3 in the expression below?
2x - 5y3 + 12
A variable
B coefficient
C exponent
D term
2 Which of the following expressions
describes a variable (y) that equals
4 more than 1 _ 5 of that variable?
F (4 + y)
_ 5 = y
G y = 4 + y _
5
H y _
5 = y + 4
J 4 + y = y _
5
3 Which of the following expressions is equivalent to 3x + 12?
A 1 _
4 (48 + 12x)
B 3(x + 12)
C 4(3x + 3)
D (12 + 3)x
4 Which of the following operations will not change the value of any number?
F multiplication by zero
G division by 1
H division by zero
J adding 1
5 Solve the following equation.
5x - 2 = 7
A x = 1
B x = 5
_ 9
C x = 9 _
5
D x = 4
6 Cube A has side length s. The sides of cube B are half the length of the sides of cube A. Which of the following expressions represents the difference in their volumes?
F s3 - 2
G (s - 2)3
H s3 - ( s _ 2 ) 3
J s3 - s3
_ 2
Practice by ChapterChapter 8 Algebra: More Equations and Inequalities
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B16 California Mathematics, Grade 7, Standards Practice
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Practice by ChapterChapter 8 (continued)
7 Solve the following equation for x.
3x - 9 = 2x - 8
A x = 17
B x = 3.4
C x = 3
D x = 1
8 What is the coefficient of the variable y in the following equation?
3x + y = 7
F The variable y has no coefficient.
G 0
H -1
J 1
9 Which of the following properties of real numbers is used in the equation below?
12x(x - 3y - 7) = 12x(x - 7 - 3y)
A Commutative Property of Subtraction
B Reflexive Property
C Commutative Property of Addition
D Distributive Property
10 Which inequality shows the following relationship?
3 less than 4 times a number is greater than or equal to 2 times that number.
F 3 - 4x ≥ 2xG 4x - 3 ≥ 2xH 4x ≥ 2x -3
J 4x - 3 = 2x
11 In the expression below, which of the following coefficients is shown in exactly two terms?
2x3 + 9y - 3y3 + 9x2
A 2
B 3
C 9
D x
12 Solve the following inequality for y.
3y + 9 ≥ 2
F y ≥ - 7 _
3
G y ≤ - 7 _
3
H y ≥ - 3 _
7
J y ≤ - 7 _
3
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California Mathematics, Grade 7, Standards Practice B17
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Practice by ChapterChapter 9 Algebra: Linear Functions
1 Which equation is represented by the following graph?
A y = 2x - 1
B y = -2x - 1
C y = 2x + 1
D y = -x + 1
2 A train travels at 90 miles per hour for 315 miles, and then reduces its speed to 80 miles per hour for 560 miles. About how long has the train been traveling for?
F 5 hours
G 7 hours
H 9 hours
J 11 hours
3 When a number x is multiplied by 3, the result is greater than when 2 is added to x. Which of the following inequalities represents this?
A 3x > 2 + xB x > 2 + 3xC 3x + 2 > xD 3x < 2 + x
4 Oranges can be purchased from the grocery store at a price of 5 for $2. Which of the following graphs represents this relationship?
F
G
H
J
O
-2-3-4
21 43-2-3-4
1234
y
x
$8
$6
$4
$2
0
Tota
l Cos
t
2 4 6 8 10 12 14 16 18
Number of Oranges
2 4 6 8 10 12 14 16 18
Number of Oranges
$8
$6
$4
$2
0To
tal C
ost
2 4 6 8 10 12 14 16 18
Number of Oranges
$8
$6
$4
$2
0
Tota
l Cos
t
2 4 6 8 10 12 14 16 18
Number of Oranges
$8
$6
$4
$2
0
Tota
l Cos
t
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1 2 3 4 5 6 7 8 9 10
Minutes
$8
$6
$4
$2
0
Tota
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t
y
xO
Am
ou
nt
Sold
(gal
lon
s)
Price
B18 California Mathematics, Grade 7, Standards Practice
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Practice by ChapterChapter 9 (continued)
5 The following graph shows the monthly cost of a long-distance calling plan, based on how many minutes are used. What does the slope of the graph represent?
A the cost of zero minutes of
long-distance calls
B the cost per additional minute of
long-distance calls
C the total cost of long-distance calls
D the number of minutes $1 can buy
6 Adam is running in a 5-mile race. He runs the first mile in 8 minutes. What must his average speed be for the last 4 miles in order for his overall average speed for the race to be 7 minutes per mile?
F 6 minutes per mile
G 6.5 minutes per miles
H 6.75 minutes per miles
J 7 minutes per mile
7 The following scatter plot shows the relationship between the price of gasoline and the number of gallons sold at a particular gas station.
Which of the following statements best describes the relationship between the price of gasoline and the number of gallons sold?
A As the price increases, the number of
gallons sold increases.
B As the price increases, the number of
gallons sold stays the same.
C As the price increases, the number of
gallons sold decreases at first and then
increases.
D As the price increases, the number of
gallons sold decreases.
8 If 3 is added to some number x, and the resulting quantity is then squared, the result is 15. Which of the following equations represents this relationship?
F 3 + x = 152
G 3 + x2 = 15
H (3 + x)2 = 15
J 32 + x2 = 15
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Boat Rentals
1 2 3 4 5
3530252015105
0
Cost
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
California Mathematics, Grade 7, Standards Practice B19
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Practice by ChapterChapter 10 Algebra: Nonlinear Functions and Monomials
1 The table below shows the cost of renting a boat at a lake.
How much does each additional hour add to the price?
A $5
B $10
C $15
D $20
2 Which of the following expressions is equivalent to 9-3 × 9-6?
F 9-18
G 9-9
H 9-6
J 9-3
3 Which of the following expressions is
equivalent to 12x3y5
_ 4x2y
?
A 48x5y6
B 8xy4
C 3xy6
D 3xy4
4 Which of the following graphs shows the expression shown below?
y = - 1 _ 2 x2
F
G
H
J
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1 2 3 4 5 6
Liters of Water
654321
0
Mas
s (k
g)
1 2 3 4 5 6
Liters of Water
654321
0
Mas
s (k
g)
1 2 3 4 5 6
Liters of Water
654321
0
Mas
s (k
g)
1 2 3 4 5 6
Liters of Water
654321
0
Mas
s (k
g)
B20 California Mathematics, Grade 7, Standards Practice
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5 Which of the following expressions is equivalent to 3-2 × 3-5 ÷ 34?
A 3-11
B 3-3
C 310
D 340
6 Which of the following expressions is equivalent to the following expression?
5a2 ∙ 7ab2
F 12a2b2
G 12a3b2
H 35a2b2
J 35a3b2
7 Which of the following expressions has the same value as n-4?
A n _ 4
B 1 _
4n
C 1 _ n ∙ 1 _ n ∙ 1 _ n ∙ 1 _ n
D n ∙ n ∙ n ∙ n
8 The table below shows the mass of a 5-gallon bucket filled with different amounts of water.
Liters of Water 0 1 2 3 4 5
Mass in Kilograms 0.5 1.5 2.5 3.5 4.5 5.5
Which of the following graphs best represents the data shown in the table?
F
G
H
J
Practice by ChapterChapter 10 (continued)
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60° 70° 80° 100°90°
Points Scored
Key: 1 3 represents 13
Stem Leaves
012
5 8 90 0 1 2 2 2 3 4 5 80 0
50 55 60 65
50 55 60 65
50 55 60 65
50 55 60 65
California Mathematics, Grade 7, Standards Practice B21
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Practice by ChapterChapter 11 Statistics
1 The box-and-whisker plot below represents the daily high temperatures in degrees Fahrenheit at an amusement park during the summer.
What was the highest temperature recorded at the amusement park during the summer?
A 62°
B 78°
C 96°
D 100°
2 The stem-and-leaf plot below shows the number of points Carlos scored in each basketball game he has played in this season.
What is the median number of points scored?
F 5
G 8
H 12
J 15
3 Angelina measured the heights in inches of her friends and recorded the data below:
58, 50, 52, 55, 64, 55,53, 58, 57, 57, 60, 53
Which of the following box-and-whisper plots represents Angelina’s data?
A
B
C
D
4 A group of twenty students received the following grades on a math test: four received an 84, five received an 88, six received a 90, three received a 94, and two received a 98. What is the median grade?
F 88
G 90
H 92
J 98
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50 10 15 20
Chicago weekly snowfall
New York weekly snowfall 50 55 60
Points Scored
Key: 6 0 = 60 inches
Stem Leaves
56
5 6 8 90 0 1 2 2 2 3 4 5 5 7
B22 California Mathematics, Grade 7, Standards Practice
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Practice by ChapterChapter 11 (continued)
5 The amount of snow each week was measured in New York City and Chicago over a certain winter. The data are represented in the two box-and-whisker plots below. Which city had the higher median snowfall?
A New York City
B Chicago
C They are the same.
D It is impossible to determine from
these plots.
6 A group of fifteen dogs were weighed with the following results: three weighed 5 pounds, four weighed 8 pounds, five weighed 10 pounds, two weighed 12 pounds, and one weighed 15 pounds. What is the upper quartile of these data?
F 8 pounds
G 10 pounds
H 12 pounds
J 15 pounds
7 A farmer measured the heights of his ten horses and ponies. The results of the data are summarized in the box-and-whisker plot below.
What is the difference in height between the tallest horse and the shortest pony?
A 2 inches
B 6 inches
C 8 inches
D 12 inches
8 The stem-and-leaf plot below shows the heights in inches of boys in Justin’s class.
How tall is the shortest boy?
F 50 inches
G 55 inches
H 59 inches
J 60 inches
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California Mathematics, Grade 7, Standards Practice B23
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1 Which expression below has the same value as z4?
A 4zB z ÷ 4
C z × z × z × zD 4z × 4z × 4z × 4z
2 Which of the following fractions is the same as 0.16?
F 4 _
100
G 4 _
25
H 16
_ 25
J 4 _
5
3 Which of the following has the same value as 3-4 ÷ 35?
A 3-20 C 31
B 3-9 D 39
4 Kishore owns 12 DVDs. He goes shopping and buys d DVDs, giving him a total of 16 DVDs. Which of the following equations shows this relationship?
F 12 + d = 16
G 12d = 16
H 12 - d = 16
J 16 + d = 12
5 ⎪8 - 14⎥ + ⎪9 - 12⎥ =
A -9
B 1
C 9
D 43
6 Lisa paid $1.75 for a slice of pizza. If there are 8 slices in one pizza, how much does one pizza cost?
F $8.00
G $8.75
H $9.75
J $14.00
7 What is the coefficient (or coefficients) in the following expression?
25 + 5h
A 25, 5
B hC +
D 5
8 Tyrone is buying a new jacket that
regularly costs $45, but is on sale for
1 _ 5 off. Which expression can he use to
find the discount on the jacket?
F 0.02 × $45
G 0.15 × $45
H 0.20 × $45
J 0.50 × $45
Periodic Assessment 1
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Pric
e (d
olla
rs)
0 2
403530252015105
4 6 8 10 12 14 16 18 20
Number of Goldfish
Pric
e (d
olla
rs)
0 2
403530252015105
4 6 8 10 12 14 16 18 20
Number of Goldfish
Pric
e (d
olla
rs)
0 2
403530252015105
4 6 8 10 12 14 16 18 20
Number of Goldfish
Pric
e (d
olla
rs)
0 2
403530252015105
4 6 8 10 12 14 16 18 20
Number of Goldfish
B24 California Mathematics, Grade 7, Standards Practice
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9 Which of the following is not an irrational number?
A √ � 2
B √ � 7
C √ � 24
D √ � 25
10 Which of the following expressions is equivalent to 6x + 8y?
F 48(x + y)
G 14xyH 6(x + 2y)
J 2(3x + 4y)
11 54 · 23 · 42
_ 53 · 22 · 43
=
A 2 _
5
B 1
C 5 _
2
D 10
12 José is considering buying some goldfish. The table below shows the prices for buying various numbers of goldfish.
Number of Goldfi sh 0 5 8 12 17 20
Price (dollars) 0 10 16 24 34 40
Which of the following graphs best represents these prices?
F
G
H
J
Periodic Assessment 1 (continued)
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y
xO
-2-3
-2-3
12345
621 43 5 7
California Mathematics, Grade 7, Standards Practice B25
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13 Which of the following expressions shows the number 0.000012 in scientific notation?
A 1.2 × 10-6
B 1.2 × 10-5
C 12 × 10-5
D 1.2 × 105
14 Jack is buying motor oil for his car. What is the least amount of money he can pay if he wants to buy 12 quarts?
Motor Oil Description
Brand 1 $1.00 per quart
Brand 2 $3.00 per 4 quarts
Brand 3 $2.50 per 2 quarts
Brand 4 $5.00 per 6 quarts
F $3.00 H $9.00
G $5.00 J $15.00
15 Which of the following is equivalent to 3.2?
A 5 _
16
B 1 _
2
C 3 _
2
D 16
_ 5
16 Mary is using a recipe that calls for
3 _ 4 cup of flour and 5 _
6 cup of sugar.
Which of the following shows the next
step using the least common
denominator to simplify 3 _ 4 + 5 _
6 ?
F ( 3 _
4 ×
5 _
5 ) + (
5 _
6 ×
3 _
3 )
G ( 3 _
4 ×
3 _
3 ) + (
5 _
6 ×
2 _
2 )
H ( 3 _
4 ×
4 _
4 ) + (
5 _
6 ×
6 _
6 )
J ( 3 _
4 ×
2 _
2 ) + (
5 _
6 ×
3 _
3 )
17 What is the area of the rectangle plotted on the graph below? The units are meters.
A 4 m2
B 5 m2
C 15 m2
D 56 m2
Periodic Assessment 1 (continued)
B23-B26_Gr7_PA-879533-8.indd 25B23-B26_Gr7_PA-879533-8.indd 25 2/16/07 7:54:56 PM2/16/07 7:54:56 PM
5 ft
13 ft
B26 California Mathematics, Grade 7, Standards Practice
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18 A 13-foot ladder rests against the side of a building. The base of the ladder is 5 feet from the building.
What is the distance from the top of the ladder to the ground?
F 11.3 ft
G 12.0 ft
H 13.0 ft
J 14.3 ft
19 If x = 5 and y = 4, then 8x - 2xy =
A 0.
B 6.
C 70.
D 80.
20 √ �� 169 =
F 13
G 23
H 33
J 43
21 Minh is buying shoes that are regularly $59.00. The shoes are on sale for 2 _
5 off.
a. What is the discount written as a
percent?
b. Write an expression that Minh can use
to find the discount on the shoes.
c. Find the amount of the discount.
Periodic Assessment 1 (continued)
B23-B26_Gr7_PA-879533-8.indd 26B23-B26_Gr7_PA-879533-8.indd 26 2/14/07 10:26:13 PM2/14/07 10:26:13 PM
12 in. 12 in.
28 in.
28 in.
6 in. 6 in.
14 in.
14 in.
12 in. 12 in
28 in.
28 in.
12 in. 12 in.
12 in.
12 in.
10 in. 10 in.
28 in.
28 in.
California Mathematics, Grade 7, Standards Practice B27
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Periodic Assessment 2
1 Which of the following rectangles is congruent to the rectangle below?
A
B
C
D
2 The chart below describes the speeds of four frogs.
Frog Description
#1 travels 40 feet in 3 minutes
#2 travels 9 feet in 1 minute
#3 travels 20 feet in 120 seconds
#4 travels 3 feet in 15 seconds
Which frog is the fastest?
F Frog #1 H Frog #3
G Frog #2 J Frog #4
3 A store buys television sets from the factory for $280 each. The store then sells the sets with a markup of 35%. How much does the store charge for a television set?
A $98 C $315
B $182 D $378
4 Sean drives 15 miles to work each way. How many miles does he drive to and from work in a week if he works Monday through Friday?
F 60 H 210
G 150 J 300
5 Keisha is buying a pair of shoes. The shoes are regularly $60, but are on sale for 20% off. How much was deducted from the original price?
A $1.20 C $12.00
B $6.00 D $20.00
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3 cm 3 cm
4 cm
4 cm
B28 California Mathematics, Grade 7, Standards Practice
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6 A construction manager estimates a project will require 42 workdays in order to be completed. How many workdays will it take to complete the project if the construction manager uses a crew of 6 workers?
F 7 H 48
G 36 J 256
7 Rebecca is buying a television that is
regularly $500 but is on sale for 1 _ 4 off.
Which expression can she use to find
the discount on the television?
A 0.0025 × $500
B 0.14 × $500
C 0.25 × $500
D 0.40 × $500
8 The following is a scale drawing of a plot of land. Each centimeter is equal to 1,000 meters. How many square meters is the plot of land?
F 1,000,000
G 7,000,000
H 7,500,000
J 12,000,000
9 In which of the following triangles does the line segment CD bisect ∠ACB?
A
B
C
D
10 Gabrielle’s car gets an average of 36 miles per gallon of gas. She plans to drive 198 miles today and 234 miles tomorrow. How many gallons of gas should she expect to use in all?
F 6 H 12
G 8 J 18
Periodic Assessment 2 (continued)
B27-B30_Gr7_PA-879533-8.indd 28B27-B30_Gr7_PA-879533-8.indd 28 2/14/07 10:26:54 PM2/14/07 10:26:54 PM
y
xO
-2-3
-2-3
1234567
621 43 5 7
(6, 6)(-2, 5)
(-2, -2) (6, -2)
California Mathematics, Grade 7, Standards Practice B29
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11 A 300-gallon tank is drained at a rate of 5 quarts per minute. How long will it take for the tank to drain?
A 4 seconds
B 4 minutes
C 4 hours
D 4 days
12 A garden measures 180 square feet. How many square inches does the garden measure?
F 1.25
G 15
H 2,160
J 25,920
13 Carmen borrowed $1200 at 8% simple interest for one year. She made no payments that year. How much interest did she owe at the end of the year?
A $96
B $120
C $192
D $960
14 Alex earns $56 for 4 hours of work. At that rate, how long would he have to work to earn $630?
F 11 hours
G 45 hours
H 90 hours
J 158 hours
15 Mark works as a sales representative, and he is paid 15% commission on his sales. In March, his sales total was $5525.00. To the nearest penny, how much of a commission did Mark earn in March?
A $15.00
B $82.88
C $552.50
D $828.75
16 What is the area of the rectangle shown on the graph below?
F 16 units2
G 32 units2
H 64 units2
J 128 units2
17 Amber planted a tree 9 years ago. It grew 24 inches per year for the first 5 years, and then it grew 18 inches per year for the next 4 years. How many inches has the tree grown in all?
A 192
B 210
C 264
D 288
Periodic Assessment 2 (continued)
B27-B30_Gr7_PA-879533-8.indd 29B27-B30_Gr7_PA-879533-8.indd 29 2/14/07 10:26:56 PM2/14/07 10:26:56 PM
8 cm
8 cm
4 cm
4 cm
7 cm7 cm
30
8961
B30 California Mathematics, Grade 7, Standards Practice
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18 What is m∠C?
F 30˚
G 61˚
H 89˚
J 90˚
19 How many feet are in 3 miles?
A 3,000
B 9,000
C 15,840
D 21,120
20 Armando bought an MP3 player that was on sale for 25% off the original price. As a special promotion, the salesperson discounted the MP3 player an additional 20% off the sale price. If the MP3 player originally cost $200, what was the final sale price that Armando paid for it?
F $80
G $110
H $120
J $155
21 Ty’s TV Shop sells a particular television set for $349.00. The set is on sale this week for 30% off. The same television set is on sale at Elena’s Electronics for 20% off the regular price of $329.00.
a. Which store offers the better price on
the television set?
b. How much less does it cost at that
store?
c. There are coupons in the Sunday
newspaper offering an additional
$20.00 off at Ty’s or an additional
$30.00 off at Elena’s. If you were to
use the coupon, then which would
have the better price?
Periodic Assessment 2 (continued)
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O
-2-3-4
21 43-2-3-4
y
x
123456
Beat
s pe
r Min
ute
7080
5060
40
90100
100 20 30 40 50 60Minutes of Exercise
Exercise Heart Rate
Pric
e (d
olla
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0 2
2015105
4 6 8 10 12 14
Pounds of Grapes
y
x
Pric
e (d
olla
rs)
0 2
2015105
4 6 8 10 12 14
Pounds of Grapes
y
x
Pric
e (d
olla
rs)
0 2
2015105
4 6 8 10 12 14 16 18 20
Pounds of Grapes
y
x
Pric
e (d
olla
rs)
0 2
2015105
4 6 8 10 12 14
Pounds of Grapes
y
x
California Mathematics, Grade 7, Standards Practice B31
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Periodic Assessment 3
1 What is the slope of the line graphed below?
A -3 C 1 _
3
B - 1 _
3 D 3
2 The scatter plot below shows heart rates recorded after exercising for different amounts of time.
Which of the following statements best describes the relationship between minutes of exercise and heart rate as shown on the scatter plot?
F As exercise time increases, the heart
rate decreases.
G As exercise time increases, the heart
rate decreases at first, then increases.
H As exercise time increases, the heart
rate stays about the same.
J As exercise time increases, the heart
rate increases.
3 The table below shows prices for buying various amounts of grapes at a grocery store.
Pounds 1 5 12 14
Price(dollars) 1.50 7.50 18.00 21.00
Which of the following graphs best represents these prices?
A
B
C
D
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9 cm
6 cm5 cm
13 m
8 m
B32 California Mathematics, Grade 7, Standards Practice
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4 What is the surface area of the rectangular solid shown below?
F 258 cm2 H 540 cm2
G 360 cm2 J 648 cm2
5 Raya earns $52 for 4 hours of work. At that rate, how many hours would she have to work to earn $364?
A 7 C 28
B 14 D 52
6 The product of a number (x) squared and 2 is added to the product of a number (x) and 5. The total of this expression is 18. Which of the following equations shows this relationship?
F 2x + 5x = 18
G (x + 5) + (x + 2) = 18
H 5x2 + 2x = 18
J 2x2 + 5x = 18
7 Which of the following is a coefficient in the expression 7y2 + x + 30?
A y C 7
B x D 30
8 What is the area of parallelogram WXYZ?
F 21 m 2 H 104 m 2
G 64 m 2 J 169 m 2
9 The amount of dough that a bakery uses to make cookies is proportional to the number of cookies made. If 120 pounds of dough makes 2,880 cookies, how much dough is required to make 4,104 cookies?
A 24 pounds
B 34.2 pounds
C 171 pounds
D 195 pounds
10 Which of the following properties is used in the equation shown below?
3a × (2b × 5c) = (3a × 2b) × 5c
F Associative Property of Multiplication
G Commutative Property of
Multiplication
H Distributive Property
J Reflexive Property
Periodic Assessment 3 (continued)
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Pric
e (d
olla
rs)
0 1
108642
2 3 4 5 6 7
Pounds of Apples
y
x
Pric
e (d
olla
rs)
0 1
108642
2 3 4 5 6 7
Pounds of Apples
y
x
Pric
e (d
olla
rs)
0 1
108642
2 3 4 5 6 7
y
x
Pric
e (d
olla
rs)
0 1
108642
2 3 4 5 6 7
Pounds of Apples
y
x
California Mathematics, Grade 7, Standards Practice B33
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11 Which of the possible values for x makes the equation below true?
x _ 8 + 3 = 11
A 0 C 32
B 8 D 64
12 Which of the following rectangles displays a diagonal?
F
G
H
J
13 Apples are on sale for 2 pounds for $3.00. Which of the following graphs shows the relationship between the number of pounds of apples bought and the total cost?
A
B
C
D
Periodic Assessment 3 (continued)
B31-B35_Gr7_PA-879533-8.indd 33B31-B35_Gr7_PA-879533-8.indd 33 2/14/07 10:24:12 PM2/14/07 10:24:12 PM
Pounds of Apples
14 in.
3 in.
4 in.
O
-2-3-4
-2-3-4
y
x
1234
21 43
O
-2-3-4
-2-3-4
y
x
1234
21 43
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
B34 California Mathematics, Grade 7, Standards Practice
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Name Date
14 Which of the following expressions is equivalent to 6x + 18y?
F 6(3x + y) H 18(x + y)
G 6(x + 3y) J 6(x + y)
15 Which of the following expressions shows 1,284,000 written in scientific notation?
A 1.284 × 106 C 1.284 × 108
B 1.284 × 107 D 1.284 × 109
16 Megan cuts a triangle off one corner of a rectangle to make a trapezoid, as shown below.
What is the area of the shaded trapezoid?
F 44 in2 H 56 in2
G 50 in2 J 70 in2
17 Which of the following is the solution set to the inequality 3x - 2 < 7?
A {x | x > 3} C {x | x < 3}
B {x | x > 9} D {x | x < 9}
18 Which of the following graphs best represents the graph of y = -2x + 3?
F
G
H
J
Periodic Assessment 3 (continued)
B31-B35_Gr7_PA-879533-8.indd 34B31-B35_Gr7_PA-879533-8.indd 34 2/16/07 7:55:48 PM2/16/07 7:55:48 PM
0 1 2 3 4 5 6 7 8 9 101112
654321Pr
ice
(dol
lars
)
Number of Brownies
0 1 2 3 4 5 6 7 8 9 101112
654321Pr
ice
(dol
lars
)
Number of Brownies
0 1 2 3 4 5 6 7 8 9 101112
654321Pr
ice
(dol
lars
)
Number of Brownies
Pric
e (d
olla
rs)
0 1 2 3 4 5 6 7 8 9 101112
Number of Brownies
654321
California Mathematics, Grade 7, Standards Practice B35
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Periodic Assessment 3 (continued)
Name Date
19 Michelle baked brownies for a bake sale. She is selling 4 brownies for $1.00. Which of the following graphs shows the relationship between the number of brownies sold and the total cost?
A
B
C
D
20 How many vertices are there in the prism shown below?
F 5 H 15
G 10 J 25
21 Simplify the expression below and explain which property is used for each step in the process.
18x2 + 6xy + (3xy · 1)
B31-B35_Gr7_PA-879533-8.indd 35B31-B35_Gr7_PA-879533-8.indd 35 2/16/07 7:55:55 PM2/16/07 7:55:55 PM
Math Test Scores
Stem Leaves
89
10
0 3 5 8 93 50
Key: 8 3 represents 83
Math Test Scores
Stem Leaves
789
10
7980 83 85 8893 9510
Key: 8 3 represents 83
Math Test Scores
Stem Leaves
789
10
98 5 3 03 50
Key: 8 3 represents 83
Math Test Scores
Stem Leaves
789
10
90 3 5 83 50
Key: 8 3 represents 83
B36 California Mathematics, Grade 7, Standards Practice
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Name Date
Periodic Assessment 4
1 Which of the following expressions is equivalent to 5x + 10x + 4y + 6y + 20?
A 3x + 2y + 4
B 5x + 10y + 4
C 15x + 2y + 20
D 5(3x + 2y + 4)
2 What is the lower quartile of the following set of numbers?
{56, 72, 65, 120, 58, 64, 85, 92}
F 56 H 64
G 61 J 68.5
3 What would be the mean of the following data set if the outlier were removed from the calculation?
{45, 56, 58, 65, 66, 75, 76, 78, 84, 88, 159}
A 58 C 75
B 69.1 D 77.3
4 Which of the following expressions is
equivalent to 18m4 _
12m-2 ?
F 3m-8
_ 2
G 3m-6
_ 2
H 3m6
_ 2
J 3m8
_ 2
5 Shawn recorded the following math test scores from his first semester of college.
85, 83, 95, 93, 100, 80, 79, 88
Which of the following stem-and-leaf plots correctly displays this data?
A
B
C
D
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Pric
e (D
olla
rs)
0 2 4 6 8 10 12 14 16 18
Pounds of Carrots
1412108642
Pric
e (D
olla
rs)
0 2 4 6 8 10 12 14 16 18
Pounds of Carrots
1412108642
Pric
e (D
olla
rs)
0 2 4 6 8 10 12 14 16 18
Pounds of Carrots
1412108642
Pric
e (D
olla
rs)
0 2 4 6 8 10 12 14 16 18
Pounds of Carrots
1412108642
Volu
me
0 1 2 3 4 5 6
Side Length
140
120
100
80
60
40
20
California Mathematics, Grade 7, Standards Practice B37
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Periodic Assessment 4 (continued)
6 Lita pays $3 for 4 pounds of carrots. Which of the following graphs best displays this relationship?
F
G
H
J
7 Which of the following expressions is equal to 11-8 × 1112?
A 11-20 C 114
B 11-4 D 1120
8 What is the upper quartile of the following set of numbers?
{45, 56, 58, 65, 66, 75, 76, 78}
F 57
G 75
H 75.5
J 78
9 The graph below shows the relationship between the side length of a cube and the volume of the cube.
If the side length of the cube is 4 centimeters, what is the volume of the cube?
A 34 cm3
B 46 cm3
C 64 cm3
D 84 cm3
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Art Club Ages
Stem Leaves
012
6 6 7 8 82 2 3 4 4 4 40 1 2 2
Key: 1 2 represents 12 years
20 30 40 706050
Study Time y
xO
20406080
100120140160
1 2 3 4 5 6 7 8 9
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10 84 × 75 × 106 × 114 __
83 × 74 × 108 × 114 =
F 14
_ 25
H 28
_ 25
G 24
_ 25
J 56
_ 25
11 The stem-and-leaf plot below shows the ages of children in the art club.
What is the mode for this data?
A 2 C 13.5
B 4 D 14
12 The box-and-whisker plot below represents the amount of time a group of 7th graders spent studying.
What is the median of the data?
F 48.5 H 34.5
G 41 J 30
13 Which expression is equivalent to 6 8 × 6 9 ?
A 6 17
B 6 72
C 36 17
D 36 72
14 What is the range of the following data?
23.6, 45.5, 46.9, 65.3, 73.2, 75.8, 86.7, 134.8
F 23.6
G 65.3
H 73.2
J 111.2
15 Jeff wants to increase his savings account by depositing $10 each week from his lawn jobs. The graph below shows how much he money (y) he will have after x weeks.
How much did Jeff have in his account to start?
A $0 C $60
B $15 D $150
B38 California Mathematics, Grade 7, Standards Practice
Periodic Assessment 4 (continued)
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O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
Fish
Cau
ght
0 2 4 6 8 10 12 14 16 18
Time (hours)
108642
Fish
Cau
ght
0 2 4 6 8 10 12 14 16 18
Time (hours)
108642
Fish
Cau
ght
0 2 4 6 8 10 12 14 16 18
Time (hours)
108642
Fish
Cau
ght
0 2 4 6 8 10 12 14 16 18
Time (hours)
108642
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16 Which is the graph for y = (- 1 _ 2 ) x2?
F
G
H
J
17 14z-6 _
4z-3 =
A 7z-18
_ 2 C
7z-3
_ 2
B 7z-9
_ 2 D
7z18
_ 2
18 Jerome spent the weekend fishing at a nearby lake. The table below shows the number of hours he spent fishing and the number of fish that he caught.
Time (hours) 0 2 6 10 18
Fish 0 1 3 5 9
Which of the following graphs best represents the data?
F
G
H
J
California Mathematics, Grade 7, Standards Practice B39
Periodic Assessment 4 (continued)
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21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
-2-3-4
21 43-2-3-4
1234
y
x
O
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21 43-2-3-4
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y
x
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19 Which of the following is the graph for y = 3x2?
A
B
C
D
20 Which expression below has the same value as n · n · n · n?
F 4n
G n 4
H n + n + n + n
J n _
4
21 The following data shows the points scored by a local high school basketball team in each of 8 games.
65, 70, 83, 62, 54, 70, 74, 88
a. What is the upper quartile of the data?
b. What is the median of the data?
c. Construct a box-and-whisker plot to represent the data.
B40 California Mathematics, Grade 7, Standards Practice
Periodic Assessment 4 (continued)
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California Mathematics, Grade 7, Standards Practice B41
Periodic Assessment 1Student Answer Sheet
Record your answers by coloring in the appropriate bubble for the best answer to each question.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
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Write your answer for Question 21 in the space below. Show all your work or reasoning.
B41-B42_Gr7_PA-879533-8.indd 41B41-B42_Gr7_PA-879533-8.indd 41 2/14/07 10:26:32 PM2/14/07 10:26:32 PM
B41-B42_Gr7_PA-879533-8.indd 42B41-B42_Gr7_PA-879533-8.indd 42 2/14/07 11:25:15 PM2/14/07 11:25:15 PM
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California Mathematics, Grade 7, Standards Practice B43
Periodic Assessment 2Student Answer Sheet
Record your answers by coloring in the appropriate bubble for the best answer to each question.
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Write your answer for Question 21 in the space below. Show all your work or reasoning.
B43-B44_Gr7_PA-879533-8.indd 43B43-B44_Gr7_PA-879533-8.indd 43 2/14/07 10:25:25 PM2/14/07 10:25:25 PM
B43-B44_Gr7_PA-879533-8.indd 44B43-B44_Gr7_PA-879533-8.indd 44 2/14/07 11:25:33 PM2/14/07 11:25:33 PM
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California Mathematics, Grade 7, Standards Practice B45
Periodic Assessment 3Student Answer Sheet
Record your answers by coloring in the appropriate bubble for the best answer to each question.
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Write your answer for Question 21 in the space below. Show all your work or reasoning.
B45-B46_Gr7_PA-879533-8.indd 45B45-B46_Gr7_PA-879533-8.indd 45 2/14/07 10:23:41 PM2/14/07 10:23:41 PM
B45-B46_Gr7_PA-879533-8.indd 46B45-B46_Gr7_PA-879533-8.indd 46 2/14/07 11:24:38 PM2/14/07 11:24:38 PM
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California Mathematics, Grade 7, Standards Practice B47
Periodic Assessment 4Student Answer Sheet
Record your answers by coloring in the appropriate bubble for the best answer to each question.
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Write your answer for Question 21 in the space below. Show all your work or reasoning.
B47-B48_Gr7_PA-879533-8.indd 47B47-B48_Gr7_PA-879533-8.indd 47 2/14/07 10:25:53 PM2/14/07 10:25:53 PM
B47-B48_Gr7_PA-879533-8.indd 48B47-B48_Gr7_PA-879533-8.indd 48 2/14/07 11:25:00 PM2/14/07 11:25:00 PM