Download 7th Grade Math Review

Spring 2013 MSM2 CCPS SOL Review Items
7.1
The student will
a) investigate and describe the concept of negative exponents for powers of ten;
b) determine scientific notation for numbers greater than zero;
c) compare and order fractions, decimals, percents, and numbers written in scientific
notation;
d) determine square roots; and
e) identify and describe absolute value for rational numbers.
7.1a
1. Which fraction and decimal are equivalent to 10-1
1
and -0.01
10
1
B. –
and -0.1
10
1
C.
and 0.01
10
1
D.
and 0.1
10
A. –
Write the base in the larger box and the power in the raised smaller box.
2. Many prefixes are used in mathematics and science. The prefix giga in
gigameter represents 1,000,000,000 meters. Write this prefix as a power of
ten.
7.1b
Circle all the planets that you want to select. You must select all correct planets.
1. Use the table to answer the question.
Which planets have a diameter larger
than the Earth’s diameter?
Planet
Earth
Jupiter
Mars
Mercury
Neptune
Saturn
Uranus
Venus
Diameter
(km)
1.3 x 104
1.4 x 105
6.8 x 103
4.8 x 103
5.0 x 104
1.2 x 105
5.1 x 104
1.2 x 104
2. The weight of an average grain of sand is
1.3 x 10-7grams. Which of the following numbers is equivalent to this
value?
A. 13,000,000 B. 1,300,000 C. 0.000000013
D 0.00000013
Spring 2013 MSM2 CCPS SOL Review Items
3. If the length of one side of a square park is 5.9 x 102 feet, then the area is
_______ square feet.
A
B
C
D
7.1c
2.3 x 101
1.18 x 103
3.48 x 104
3.48 x 105
1. Which list of rational numbers contains numbers that are all greater
than 1.8 x 10-1?
1
1
A
20%, , 0.19
C
2%, , 0.2
8
5
1
1
B
20%,
, 0.15
D
2%,
, 0.125
9
10
Circle all the numbers you want to select. You must circle all correct numbers. You may not use a
calculator.
2. Select all of the rational numbers that are equivalent to 5/2
5.2
250%
2.5
2.5 x 100
25%
5½
Write the numbers in the blanks provided. You must write all the numbers. You may not use a
calculator.
3.
7.1d
Arranged the numbers from greatest to least.
1
0.25,
,
2.5%,
5
2.5 x 101
1. Which of the following is NOT a square root of a perfect square?
A.
25
C.
200
B.
169
D
289
Spring 2013 MSM2 CCPS SOL Review Items
2. The area of a square room is 256 square feet. What is the perimeter
of the room?
A. 32 feet
B. 64 feet
7.1e
C. 128 feet
D. 512 feet
Circle all the equations that you want to select. You must select all correct equations.
1. Select all of the equations that are true.
1
1
=2
2
-2 =2
0.5 =-0.5
9= -9
-6= 6
-8 = -8
7.2
The student will describe and represent arithmetic and geometric sequences, using variable
expressions.
7.2
1. Let p represent any number in this sequence.
1000, 100, 10, 1…
Which of these can be used to determine the next number in this sequence?
A.
10p
p
10
C. p – 900
D. p – 100
B.
Circle all the descriptions that you want to select. You must select all correct descriptions.
2. Use the following sequence to answer the question.
5, 25, 125, 625,…
Circle all of the following that correctly describe the sequence.
Common ratio of 5
Arithmetic Sequence
Common difference of
20
5n
Geometric Sequence
n + 20
Spring 2013 MSM2 CCPS SOL Review Items
7.3
7.3a
The student will
a) model addition, subtraction, multiplication, and division of integers; and
b) add, subtract, multiply, and divide integers.
1. Which equation is represented by the model?
A.
B.
C.
D.
4
4
4
4
+ (-3) = -3
– (-3) = -3
+ (-7) = -3
– (-7) = -3
2. Which of the following models represents the expression 2(-3)?
Key
= -1
= 1
7.3b
A
C
B
D
1. Which of the following sets of numbers, when placed in the blank
make the value of this expression a negative number?
(15) + ____
A {-20, -18, -17}
B {-18, -15, -14}
C
D
{-10, -8, -7}
{-2, -1, 0}
Spring 2013 MSM2 CCPS SOL Review Items
Write the number in the blank provided. You may not use a calculator
2.
Simplify: -3 + 5(-2) – 15
3.
A city’s daily low temperatures in January fluctuated between -7oF and 2°F.
What was the temperature range?
4.
A 2°F
C 7°F
B 5°F
D 9°F
Two numbers are represented by the points P and Y on the number line
P
Which statement is false?
A
B
C
D
P ÷Y < 0
P–Y<0
P •Y < 0
P +Y <0
Y
Spring 2013 MSM2 CCPS SOL Review Items
7.4
The student will solve single-step and multistep practical problems, using proportional
reasoning.
Write your answer in the blank next to each ingredient. You may use a calculator.
1.
Darcia made a snack mix using the following recipe.
1 ¼ cups granola, ¾ cup peanuts, ½ cup raisins, ¼ cup chocolate chips. If
she used 3 cups of granola and wanted to keep the ingredients proportional,
how much would she use of each of the other ingredients.
____________ cup(s) peanuts
____________ cup(s) raisins
____________ cup(s) chocolate chips
2.
Juanita wants to purchase a jacket that cost $231. If Juanita earns $66 for
every 3 hours she works, about how many hours will it take her to earn
enough to purchase the jacket?
A 1.5 hours
B 3.5 hours
3.
Mr. Callaway needs to purchase enough grass seed to cover a 3000-squarefoot lawn and a 4200-square-foot lawn. If 40 ounces of grass seed will seed
a 2400-square-foot lawn, how many ounces does he need to seed both
lawns?
A 3
B 50
4.
C 5.5 hours
D 10.5 hours
C 120
D 180
At a discount furniture store, Chris offered a salesperson $600 for a couch
and a chair. The offer includes the 8% sales tax. If the salesperson accepts
the offer, what would be the price of the furniture, to the nearest dollar,
before tax?
A $552
B $556
C $592
D $648
Spring 2013 MSM2 CCPS SOL Review Items
5.
A scale drawing for a construction project uses a scale of 1 inch = 4 feet.
The dimensions of the rectangular family room on the scale drawing are
7.5 inches by 12 inches. What will be the actual area of the floor of the
family room after the construction project is completed?
A 90 square feet
B 156 square feet
C 360 square feet
D 1440 square feet
Select the numbers from the table. Write the numbers in the blanks provided. You must use all
numbers. You may use a calculator.
6.
A truck has traveled 75 miles in 1.5 hours of driving. At the same speed,
create a proportion that can be used to determine how long, T (in hours),
it would take the truck to travel 325 miles?
75
1.5
325
=
t
7.5
The student will
a) describe volume and surface area of cylinders;
b) solve practical problems involving the volume and surface area of rectangular prisms
and cylinders; and
c) describe how changing one measured attribute of a rectangular prism affects its volume
and surface area.
7.5a
1.
Grant is creating a new solid cylindrical pole for the sail on his boat. He will
melt the metal down to form the pole and then paint it. The pole will be 16
feet tall and have a diameter of 6 inches. Which of the following statements
are correct?
Grant needs to_________
Find the surface area to
figure out how much
metal to buy.
Find the volume to
know how much paint
he will need to paint the
outside.
Find the surface area to
know how much paint
he will need to paint the
outside.
Find the volume to
know how much space
the pole will take up on
the deck.
Find the surface area to
know how much space
the pole will take up on
the deck.
Find the volume to
figure out how much
metal to buy.
Spring 2013 MSM2 CCPS SOL Review Items
7.5b
1.
A swimming pool is 50 meters long, 25 meters wide and 3 meters deep. A
liter is the same as 0.001 cubic meters. How many liters of water are
needed to fill the pool?
A 3,750 liters
B 37,500 liters
C 375,000 liters
D 3,750,000 liters
Write the answer in the box provided. Round your answer to the nearest tenth. You may use a
calculator.
2.
7.5c
As a project in tech class, the students are making aluminum flower pots
shaped like cylinders. There is a bottom on each pot, but no top. If the pots
are 9 inches in height and have a diameter of 12 inches, how many square
inches of aluminum are needed for each pot?
1. The rectangular prism shown has a volume of 60 cm3.
If the height of the prism is increased to 15 cm and the other
dimensions remain the same, the volumeA
B
C
D
Doubles
Triples
Increases by 15 cm3
Increases by 900 cm3
2. What happens to the volume of a prism if all three dimensions are doubled?
The Volume_____ .
A
B
C
D
doubles
triples
gets 6 times bigger
gets 8 times bigger
Spring 2013 MSM2 CCPS SOL Review Items
7.6
7.6
The student will determine whether plane figures—quadrilaterals and triangles—are similar and
write proportions to express the relationships between corresponding sides of similar figures.
ABC ~ DEF
1.
F
B
A
E
C
D
Which of the following statements are false?
Angle A is congruent to
AB is congruent to DE
angle F
Angle F is congruent to
3.
Angle B is congruent to
AC
AB
=
DE DF
angle A
2.
AB AC
=
DE DF
angle E
If Quadrilateral DOGS is similar to Quadrilateral BEAR, then ___
A
GS
AR
=
DO BE
B
DO BE
=
SD
AR
C
OG AR
=
DS BR
D
SD OG
=
AR
EA
If Triangle A is similar to triangle B, then what is the scale factor from
triangle A to triangle B?
10.2 in
8.1 in
3.4 in
2.7 in
A
7.5 in
A 3
B 2
B
2.5 in
1
2
1
D
3
C
Spring 2013 MSM2 CCPS SOL Review Items
7.7
The student will compare and contrast the following quadrilaterals based on properties:
parallelogram, rectangle, square, rhombus, and trapezoid.
7.7
.
Circle all the statements that you want to select. You must select all correct statements.
1.
Select all statements that are true about all parallelograms?
all 4 sides are
congruent
all angles are
congruent
the sum of all the
angles is 360o
opposite sides are
parallel
diagonals are
congruent
diagonals bisect
each other
Which answer choice best describes the Quadrilateral pictured?
A
B
C
D
7.8
7.8
quadrilateral, parallelogram
rhombus, parallelogram
rectangle, rhombus
trapezoid, isosceles trapezoid
The student, given a polygon in the coordinate plane, will represent transformations (reflections,
dilations, rotations, and translations) by graphing in the coordinate plane.
A
1. The triangle to the right is a pre-image. If it is
rotated about the origin 180o clock wise. Plot the
B
location of B ′ ?
3
2
1
-3
-2
-1
0
-1
-2
2.
If rectangle T’E’X’S’ represents the
image after a translation of 3 units to
the right and 2 units down, which of
the following ordered pairs would
represent the coordinates for point T?
A
B
C
D
(-1, 2)
(-1, 6)
(-7, 6)
(-7, 2)
T’
E’
S’
X’
C
1
2
3
4
Spring 2013 MSM2 CCPS SOL Review Items
7.9
7.9
The student will investigate and describe the difference between the experimental probability and
theoretical probability of an event.
Place the two words in the boxes so that the inequality represents the relationship.
1.
Mark rolled two fair number cubes 50 times and got the sum of 7, eight
times. Complete the inequality below to show the relationship between the
experimental probability and theoretical probability of Marks situation.
Experimental Probability
Theoretical Probability
>
2.
Which of the following statements is true?
When rolling a fair number cube ____________
A the theoretical probability is always greater than the experimental probability.
B the theoretical probability is always less than the experimental probability.
C the more times the cube is rolled the closer the experimental probability gets to
theoretical probability.
D the number 7 will appear more than the number 1.
Spring 2013 MSM2 CCPS SOL Review Items
7.10
7.10
The student will determine the probability of compound events, using the Fundamental (Basic)
Counting Principle.
Select an event and probability from each table. Write the event and probability in the blank
provided below each table.
1.
A deck of cards contained 3 red cards, 9 purple cards, 4 green cards
and 2 blue cards. If two cards are selected with replacement, what is
the probability that the first card was a purple and the second card
was also purple. Select the type of event and the probability then write
each selection in the line below the tables.
Type of Event
Dependent Event
Independent Event
Simple Event
Probability
90%
50%
25%
______________________
2.
__________________
A combination lock opens when the user moves the
three dials to three set numbers. If each dial can be set
at any number 1 through 9, how many lock
combinations are possible?
A
B
C
D
1,000
729
30
27
Spring 2013 MSM2 CCPS SOL Review Items
7.11
7.11a
The student, given data for a practical situation, will
a) construct and analyze histograms; and
b) compare and contrast histograms with other types of graphs presenting information
from the same data set.
1. About what percent of the cars have an average of 25 to 45 miles per gallon?
A
B
C
D
6%
10%
35%
50%
Average Miles per Gallon for Military Vehicles
Spring 2013 MSM2 CCPS SOL Review Items
11b
1. Which histogram could be
Points Scored in the City Tournament
used to represent the circle
30 to 39
7%
graph to the right?
39 to 40
8%
0 to 9
31%
20 to 29
23%
10 to 19
31%
Points Scored in the City
Tournament
Points Scored in the City
Tournament
5
A
5
C
Number of Players
Number of Players
4
3
2
1
0
0-9
10-19
20-29
30-39
4
3
2
1
0
40-49
0-9
Points Scored
20-29
30-39
40-49
Points Scored
B
D
Points Scored in the City
Tournament
Points Scored in the City
Tournament
5
5
4
4
Number of Players
Number of Players
10-19
3
2
1
0
0-9
10-19
20-29
30-39
Points Scored
40-49
3
2
1
0
0-9
10-19
20-29
30-39
Points Scored
40-49
Spring 2013 MSM2 CCPS SOL Review Items
7.12
The student will represent relationships with tables, graphs, rules, and words.
7.12
Plot the point on the graph then write the order pair in the blanks provided.
1.
Plot a point that would be a solution to the
graphed line and write the order pair.
( _____, _____ )
2.
Which of the following equations best represents the data in the table?
X
-2
0
1
3
A
B
7.13
y = -4x + 2
y = -5x
Y
10
2
-2
-10
C y = -2x + 6
D y = -7x - 4
The student will
a) write verbal expressions as algebraic expressions and sentences as equations and vice
versa; and
b) evaluate algebraic expressions for given replacement values of the variables.
7.13a
Circle all the phrases that you want to select. You must select all correct phrases.
1.
Select all the phrases that could represent the following expression:
2x + 10
Double a number and
ten
Double the sum of a
number and ten
The difference between
twice a number and ten
Two times a number and
ten
Two and a number plus
10
Twice a number plus ten
Spring 2013 MSM2 CCPS SOL Review Items
7.13b
Write the answer in the blank provided. You may use a calculator.
1.
Simplify the following expression when b= -3 and v =
2
. Write your answer
3
in the box provided below the expression.
-3v – b2 + bv
2.
Which number could replace the variable to make the expression equivalent
to 6?
1
(4r2 – 2r)
2
A
B
C
D
-2
-1
1
2
7.14
The student will
a) solve one- and two-step linear equations in one variable; and
b) solve practical problems requiring the solution of one- and two-step linear equations.
7.14a
Use the model to answer the question.
Key
=
=x
= -x
Which equation and solution is represented by the model?
A
2x – 3 = 9,
x=6
B
2x – 3 = 9,
x=3
C
-2x + 3= 9,
x=6
D
-2x – 3 = 9,
x=3
=1
-1
Spring 2013 MSM2 CCPS SOL Review Items
7.14b
Select an equation and solution from each table. Write the equation and solution in the blank
provided below each table.
1. Quami earns $10 helping his friend clean windows during his summer
vacation. He charges $1 for the first window and $0.50 for each
addition window (x) he washes. Select the correct equation and solution
then write each selection in the line below the tables?
7.15
7.15a
Equation
0.5x + 1 = 10
0.5x = 10
x + 1 = 10
x + 0.5 = 10
Solution
x = 4.5
x=9
x = 9.5
x = 18
__________________
_______________
The student will
a) solve one-step inequalities in one variable; and
b) graph solutions to inequalities on the number line.
Circle all the numbers that you want to select. You must select all correct numbers.
1. Select all numbers that would satisfy the inequality -10x > 5.
-
3
4
-1
1
4
1
2
-
1
0
Spring 2013 MSM2 CCPS SOL Review Items
7.15b
Circle all the inequalities that you want to select. You must select all correct inequalities.
1. Select all of the inequalities that could be represented by the following
graph.
7.16
7.16a
x
≤9
-3
-2 x ≤6
-3 ≥- x
x + 6 ≥3
x + 6 ≥-9
6 ≤x - 3
The student will apply the following properties of operations with real numbers:
a) the commutative and associative properties for addition and multiplication;
b) the distributive property;
c) the additive and multiplicative identity properties;
d) the additive and multiplicative inverse properties; and
e) the multiplicative property of zero.
1. Rachel noticed that for her rectangular backyard had a width of 7 yards and a
length of 15 yards, she knew she could either multiply 7 times 15 or 15 times
7 to get the area of the back yard. What property allows her to do this?
A
B
C
D
Commutative property of addition
Commutative property of multiplication
Associative property of addition
Associative property of multiplication
7.16b
1. Is the equation 0.2(10x – 5) = -8 equivalent to 2x – 1 = -8?
A
B
C
D
Yes, the equations are equivalent by the associative property of multiplication.
Yes, the equations are equivalent by the commutative property of multiplication.
Yes, the equations are equivalent by the distributive property
No, the equations are not equivalent.
Spring 2013 MSM2 CCPS SOL Review Items
7.16c
1. The multiplicative identity property was applied in which equation?
1 2
• =1
2 1
1 2 2
B
• =
2 3 6
1 3 3
C
• =
2 3 6
1 1 1
D
• =
2 2 4
A
7.16d
Write the number in the blank provided. You may use your calculator.
1. What number should be placed in the blank to make the following equation
true?
1
(10 + ___)= 0
3
7.16e
Circle all the equations that you want to select. You must select all correct equations. You may use
a calculator.
1.
Select all the equations that illustrate the zero property of multiplication.
1
•3 – 3 = 4
3
1
0•9• =0
9
4 + 3(0) = 4
-5 +5+0 = 0
1
1
+2 – 2 =
+0
2
2
1
(9 + 3) = 3 + 1
3