Download Released Test - Solutions

Released Form
EA
SE
D
North Carolina
READY End-of-Grade
Assessment
Mathematics
R
EL
Grade 8
Student Booklet
Academic Services and Instructional Support
Division of Accountability Services
Copyright ã 2013 by the North Carolina Department of Public Instruction. All rights reserved.
GRADE 8 MATHEMATICS—RELEASED FORM
Sample Questions
A
10 miles
B
14 miles
C
21 miles
D
24 miles
3 X 7 = 21
D
S2
Kerry walks 3 miles each day. How far will she walk in 7 days?
What number is represented by point P on the number line below?
P
SE
S1
0
P = -7
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What fraction of the circle is shaded?
R
S3
EA
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
3/4 =.75
1
GRADE 8 MATHEMATICS—RELEASED FORM
The area of the surface of the Atlantic Ocean is approximately 31,830,000 square
miles. How is this area written in scientific notation?
3.183 × 104
B
3.183 × 105
C
3.183 × 106
D
3.183 × 107
3.183 x 10^7
Choice D
Concept = Scientific Notation
1 <= n < 10 (10)^x
Expressions and Equations
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EA
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D
A
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1
2
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GRADE 8 MATHEMATICS—RELEASED FORM
2
In which graph do all of the plotted points lie on the line y = x + 2?
A
B
Y = mx +b Expressions and Equations
Choice B
y
y
+8
+7
+6
+6
+5
+5
+4
+4
+3
+3
+2
+2
+1
+1
–8 –7 –6 –5 –4 –3 –2 –1 0
–1
+1 +2 +3 +4 +5 +6 +7 +8
D
+8
+7
x
SE
–2
–8 –7 –6 –5 –4 –3 –2 –1 0
–1
–3
–4
–5
–6
EA
–7
–8
+1 +2 +3 +4 +5 +6 +7 +8
x
–2
–3
–4
–5
–6
–7
–8
D
C
+8
+7
+6
+5
y
+8
+7
+6
+5
+4
R
+4
EL
y
+3
+3
+2
+2
+1
+1
–8 –7 –6 –5 –4 –3 –2 –1 0
–1
+1 +2 +3 +4 +5 +6 +7 +8
x
–8 –7 –6 –5 –4 –3 –2 –1 0
–1
–2
–2
–3
–3
–4
–5
–4
–5
–6
+1 +2 +3 +4 +5 +6 +7 +8
–6
–7
–7
–8
–8
3
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x
GRADE 8 MATHEMATICS—RELEASED FORM
3
Which choice is a correct equation for the line graphed below?
y
+6
+5
+4
+3
+2
+1
–6 –5 –4 –3 –2 –1 0
–1
+1 +2 +3 +4 +5 +6
D
–2
x
–3
SE
–4
–5
A
y = 3x + 1
B
y = 2x + 1
C
y =
1
2
D
y = 1x +1
R
3
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x +1
EA
–6
4
Which function is nonlinear?
A
y = 3x + 1
2
B
y = –x
C
y = 2x(x − 4)
D
y = 1x −7
2
slope = y/x
= 3/1
Y-intercept
=1
y= 3x+1 Choice A
Expressions and Equations
Linear
x raised to the first power - first degree
non-linear
exponential= 3^x ---> x is the exponent
quadratic = x^2 ---> the equation in the 2nd degree
Cubic = x^3 ---> the equation in the first degree
Rational = 3/x --> x is in the denominator
Choice is c ---> quadratic ( DPM) --> x^2 ( Laws of Exponents)
Functions -- Types of Functions
4
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GRADE 8 MATHEMATICS—RELEASED FORM
In which choice do all the points lie on the same line?
A
(0,
−
2 ) , (1, −1) , (2, 2 ) , (3, 7 )
( 0, 0 ) , (1, 1) , (2, 4 ) , (3, 9 )
C
(0, 0 ) , (1, 1) , (2, 8 ) , (3, 27 )
D
(0, 0 ) , (1, 2 ) , (2, 4 ) , (3, 6 )
EL
EA
SE
D
B
Points are on the same line if and only if
1) Change in Y is the same / change in x is the same in
all the ordered pair --> perfect correlation = 1 = r^2
Choice D
Linear Function ( first difference is the same)
R
5
5
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GRADE 8 MATHEMATICS—RELEASED FORM
Sharon made a scatterplot comparing the shoulder heights of dogs to their
weights.
Line of Best fit - Statistics and Probability
120
110
100
90
80
70
60
D
50
40
30
20
10
2
4
6
8 10 12 14 16 18 20 22 24 26 28 30
EA
0
SE
Weight (pounds)
Height (inches)
EL
Sharon’s dog has a shoulder height of 28 inches. Using a linear model, which is
the best prediction of her dog’s weight?
A
85 pounds
B
90 pounds
C
105 pounds
D
120 pounds
Rate of Change
(18,60) ; (24,82)
22/6= 3.66
(3.6)(28)=100.8
Estimate (3.5) (30) = 105
C is the best choice
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6
6
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GRADE 8 MATHEMATICS—RELEASED FORM
Questions 7 through 15 require you to write your answers in the boxes
provided on your answer sheet. Write only one number or symbol in each box
and fill in the circle in each column that matches what you have printed. Fill in
only one circle in each column.
7
What is the value of 0.36 • 11 ?
8
let x = .3636
100x = 36.36
Subtract
99x=36
x= 36/99
11/2 (36/99) = 18/9 = 2
What is the sum of all the integers between 19 and
D
2
SE
EL
On a number line, let point P represent the largest integer value that is less than
−
407. Let point Q represent the largest integer value that is less than 68 . What
is the distance between P and Q?
Sq Root
Sq Root
-64 -68 -81
400 407 441
-8
-9
20
21
-8 4/17
20 7/41
-8.24
20.171
20
-9 is less than -8 on the number line
R
9
Sq root of 77
between 8 and 9
5+6+7+8=26 The number system
EA
Sq root of 19
between 4 and 5
77 ?
20- (-9) = 29
or
20-.17-(-8.24) = -28.58 abs value for distance positive number --> 29
The number System
7
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GRADE 8 MATHEMATICS—RELEASED FORM
−
10
11
−
3
1
2
What is the value of 4 4 • 4 − 3 • 5 0 ?
4 •5 •5
Negative exponemts ; Zero exponents , add exp. keep the bas, subtract exp
keep the base
-2+3-0= 5
Expressions and equations
base 4
3-1=2 /4 1/4^2 5/16 = .3125
When 8 is added to the number that is produced by doubling the number x, the
result is equal to 8 times the number that is 5 less than x. What is the value of x?
In
-6x=-48 x = 8 Expressions and Equations
WXY , WY is congruent to XY . The perimeter of WXY
m
EA
W
EL
3m-4
R
12
SE
8+2x = 8( x-5)
8+2x=8x-40
D
let the number = x
How many inches long is WX ?
is 76 inches.
X
3m – 4
Y
3m-4+3m-4+m=76
7m-8=76
7m=84
m= 12
8
Expression and Euation
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GRADE 8 MATHEMATICS—RELEASED FORM
13
Kyle is a salesman. His monthly earnings include a fixed monthly salary and a
commission that is a fixed percentage of his total sales for the month.
•
Kyle’s total sales for the month of January were $15,000, and his total
earnings for that month were $2,550.
•
Kyle’s total sales for the month of February were $25,000, and his
total earnings for that month were $3,050.
What is Kyle’s fixed monthly salary in dollars?
(15,000, 2550); (25,000, 3050)
slope = (3050-2550)/(25000-15000) = .05
Y=mx+b
2550=(.05*15000)+b
b= 1800
Linear
SE
In the table below, y is a linear function of x.
x
y
3
5
EA
Linear
Function
5
–
3
11
EL
7
–
What is the value of y when x = 0?
Linear function y-change = -8 ( constant)
x-change = 2 (constant)
Y = mx + b
5 = -4(3)+ b
B= 17
Y= -4x+17
Y= 17
R
14
D
Function
9
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GRADE 8 MATHEMATICS—RELEASED FORM
Beginning in 2000, a sports team increased its ticket price by a constant amount
each year until 2010.
•
A ticket cost $48 in 2005.
•
A ticket cost $55.50 in 2008.
How much did a ticket cost in 2000?
Express the answer as dollars.cents.
D
EL
EA
SE
Linear Function
ordered pair
(2005,48); (2008, 55.5)
(55.5-48)/(2008-2005)
7.5/3 = 2.5
Y = mx +b
55.5-(8*2.5)=35.5
Or y=mx+b and substitute x for 2000 ( try it)
R
15
10
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GRADE 8 MATHEMATICS—RELEASED FORM
This is the end of the calculator inactive test questions.
Directions:
1. Look back over your answers for the calculator inactive questions. You
will not be able to go back and work on these questions once you are
given a calculator.
2. Raise your hand to let your teacher know you are ready to begin the
calculator active test questions.
R
EL
EA
SE
D
3. Do not begin work on the calculator active test questions until your
teacher has given you a calculator.
11
GRADE 8 MATHEMATICS—RELEASED FORM
Suppose that a scientist estimates that every square mile of the ocean contains an
average of 4.6 × 104 pieces of trash. The area of the Earth’s surface that is
covered by oceans is approximately 1.2 × 108 square miles. Using the estimate,
how many pieces of trash are in the Earth’s oceans?
A
5.5 × 1012
B
1.2 × 108
C
3.4 × 104
D
3
Expressions and Equations
Scientific notation
4.6x1.2 = 5.52 x 10^12
Choice A
EL
EA
SE
D
2.6 × 10
R
16
12
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GRADE 8 MATHEMATICS—RELEASED FORM
On Monday, Mr. James made an eight-hour trip to his mother’s house in his car.
The graph below shows the distance he had traveled at different times.
y
500
400
350
300
D
250
200
SE
Distance (miles)
450
150
100
0
EA
50
1
2
3
4 5 6 7 8
Time (hours)
9 10
x
EL
On Tuesday, he drove home. His speed on Tuesday was 5 miles per hour faster
than for the trip on Monday. Which equation would model the distance, d, that
Mr. James had traveled on his return trip after t hours?
A
d = 45t
B
d = 50t
C
d = 55t
D
d = 60t
R
17
slope =50
faster = 50+5 = 55
Choice is C
Expressions and Equations
13
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GRADE 8 MATHEMATICS—RELEASED FORM
A
–
B
–
C
0
D
4
−
4x − 2
= −6 ?
3
16
Cross porducts
-4x -2 = -18
-4x = -16
x=4
Choice is D
Expressions and Equations
12
$6.75
B
$7.75
C
$19.25
D
$22.00
let x = shrub
let y = Tree
15x + 5y = 211.25
Y= x+15.25
-x+y =
15.25
15 5 211.25
-1 1
15.25
Use Matrices
A ^-1 B = ( 6.75,22)
EA
A
SE
D
A company charges $211.25 for 5 trees and 15 shrubs. The company charges
$15.25 more for a tree than a shrub. How much does each shrub cost?
EL
19
What value of x satisfies the equation
R
18
14
Expressions and Equations
Systems of Equations
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GRADE 8 MATHEMATICS—RELEASED FORM
Two stores sell cherries at different prices per pound.
•
Store P sells 3.5 pounds of cherries for $13.30.
•
The graph below shows the cost to purchase different weights of
cherries at Store Q.
Expressions and Equations
9
8
(3.5,13.30) ; (1.25,4)
Price per pound = 3.8
3.20
6
EA
R
EL
3
1
$32
38-32=6
4
2
$38
Choice is D
5
Store Q
SE
7
10 pounds
Store P
D
Slope = y/x
Cost (dollars)
20
0
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
Weight (pounds)
Phillip needs to purchase 10 pounds of cherries. Which statement below is true?
A
Phillip will spend $8.00 less on cherries at Store P than at Store Q.
B
Phillip will spend $8.00 more on cherries at Store P than at Store Q.
C
Phillip will spend $6.00 less on cherries at Store P than at Store Q.
D
Phillip will spend $6.00 more on cherries at Store P than at Store Q.
15
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GRADE 8 MATHEMATICS—RELEASED FORM
Function from equation and table
Limousine Company P and Company R both charge a rental fee plus an additional
charge per hour.
•
The equation y = 50 + 30x models the total cost (in dollars), y, of
renting a limousine from Company P for x hours.
•
The table below shows the cost to rent a limousine from Company R
for different lengths of time. y= 25x+75 -- > Company R
Company R
Compare slopes 25 and 30
2
3
4
5
$100 $125 $150 $175 $200
SE
Total Cost
1
D
Time (hours)
Which statement accurately compares the per hour charges of the two companies?
Company P charges $5 less per hour than Company R.
B
Company P charges $5 more per hour than Company R.
C
Company P charges $25 less per hour than Company R.
D
Company P charges $25 more per hour than Company R.
EL
EA
A
Choice is B ---> Linear Functions
R
21
16
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GRADE 8 MATHEMATICS—RELEASED FORM
In which function table do all of the points (x, y) lie on the line that has a slope of
3 and a y-intercept of 2?
Functions from table Y=mx+b ---> look for 1st difference y/x = slope multibply by x subtract
from B
y-value you'll get the b
x
y
x
y
A
–
1
–
–
1
–
1
9
3
2
7
10
3
5
17
9
3
5
17
9
3
8
26
9
3
–
1
2
3
3
5
8
–
1
9
8
8
26
SE
D
y
EA
x
EL
C
D
8
3*8=24+2 = 26
Choice is A
3
1
2
3
x
–
1
9
y
–
1
2
8
6
18
10
5
17
9
26
8
8
25
8
R
22
17
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GRADE 8 MATHEMATICS—RELEASED FORM
Modeling a linear function
Mr. Jones filled his swimming pool with water.
•
Mr. Jones began filling the pool at a constant rate. steep
•
He turned off the water for a while.
•
= zero slope = horizontal line
He then turned the water back on at a slower constant rate. = less steep
•
Mr. Jones turned off the water again for a while. = horizontal line
He then turned the water back on at the first rate. same slope as first slope
parallel slopes
Which graph best represents Mr. Jones filling the pool?
B
Gallons
SE
Choice is A - Functions
EA
Gallons
A
D
•
Time
Gallons
D
R
C
EL
Time
Gallons
23
Time
Time
18
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GRADE 8 MATHEMATICS—RELEASED FORM
XYZ will be translated so that the coordinates of X ′ are (5, 11)
Example:
x+3, y+3 each vertex x,y moves 3,3 move at the same
Y
Look for the chane in each coordinate,
then apply it to the other coordinates
x= (7,11)
x' =(5,11)
x-coordinate translated by -2 down
X
y-coordinates remained
the same
y
14
13
12
11
10
D
z= (8,7)
z'= (6,7)
9
8
7
Choice is B
Geometry
Translation
5
Z
SE
6
3
2
1
1
2
3
4
5
6
EL
0
EA
4
7
8
9 10 11 12 13 14
x
What will be the coordinates of Z ′ ?
A
(5, 8 )
B
(6, 7 )
C
(7, 6 )
D
(8, 5 )
R
24
19
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GRADE 8 MATHEMATICS—RELEASED FORM
Kim made soup which contains 75 total ounces of beans.
•
The soup has two kinds of beans, black and red.
•
There are 4 times as many ounces of black beans as red beans.
How many ounces of red beans are in the soup?
B
12
C
15
D
19
Expressions and Equations
Systems of Equations
let x = red
let y = black
x +y = 75
y=4x
x+4x=75
5x=75
x=15
Choice is C
D
5
EL
EA
SE
A
R
25
20
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GRADE 8 MATHEMATICS—RELEASED FORM
SE
D
The figure below shows a square inscribed in a circle. The area of the shaded
region is 2.5 square units.
Divide the square into parts
Geometry --> upper 2 congruent parts lower 4 congruent parts
s
Area of a triangle = 1/2 bh
1/2(2r)r= r^2
2r^-3/4r^2 = 2.25
r
5/4R^2 = 5/2
R^2=2
R=square root of 2
Area of the circle = pie r^2
= 3.13(2)
= 6.28
Choice is C
3.1 square units
B
4.7 square units
C
6.3 square units
D
7.9 square units
EL
A
EA
What is the approximate area of the circle?
R
26
21
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GRADE 8 MATHEMATICS—RELEASED FORM
27
Quadrilateral PQRS is graphed in the coordinate plane.
P
y
Q
+8
+7
+6
+5
+4
+3
+2
S
R
+1
–8 –7 –6 –5 –4 –3 –2 –1 0
–1
+1 +2 +3 +4 +5 +6 +7 +8
D
–2
x
SE
–3
–4
–5
–6
EA
–7
–8
To the nearest tenth, what is the perimeter of quadrilateral PQRS?
B
33.7 units
C
37.6 units
D
48.0 units
Pythagorean theorem -- Geometry
to find PS = 3^2+8^= 73-- sq root = 8.54
Pythagorean theorem to find RS = 2^2+11^2=125-- sq root 11.18
P = 6+8+11.18+8.54=33.72 Choice is B
EL
33.0 units
R
28
A
A cylinder is 20 inches long and has a diameter of 10 inches. What is the
approximate volume of the cylinder?
A
200 cubic inches
B
630 cubic inches
C
1,570 cubic inches
D
6,280 cubic inches
D= 2r
R=5
V= BH ---> B is the area of the base pie r^2
V= 5^2(20)(3.14)= 1570 Choice is C
22
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GRADE 8 MATHEMATICS—RELEASED FORM
The table below displays the number of DVDs sold and rented at a store for
5 weeks.
Week
1
DVDs Sold
25
DVDs Rented
y=1.2x
50
2
45
79
3
40
70
4
22
48
5
5
28
no association
B
weak association
C
negative association
D
positive association
stat edit stat clacl
y=1.2x+20.49
Positive slope dvd rented goes up as dvd sold goes up
same directions positive slope
r^2 = .999 strong relationship
Statistics and probability
EA
A
SE
D
Which describes the association between the number of DVDs sold and the
number of DVDs rented?
EL
Choice is D
R
29
23
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GRADE 8 MATHEMATICS—RELEASED FORM
What is the area of the triangle shown below?
3m
6 square meters
C
12 square meters
D
15 square meters
Geometry
1) Pythagorean Theorem find the base
2) A= 1/2bh
25-9=16 sq root = 4
A=1/24(3)
=6
Choice is B
D
B
SE
4 square meters
EL
EA
A
5m
R
30
24
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GRADE 8 MATHEMATICS—RELEASED FORM
The table shows the air temperatures at different elevations.
Line of best fit - statistics and Probability
Temperature (°F)
0
75°
100
70°
200
67°
300
64°
400
59°
500
55°
600
50°
D
Elevation (feet)
y =
B
y = 1 x − 75
C
y = 1 x + 75
D
y =
25
EL
25
y= -.04x+74.96
1/25=.04
Choice is A
EA
−1
x + 75
25
A
SE
stat edit stat calc
Which line best fits this set of data?
−1
x − 75
25
R
31
25
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Statistics and probability
line of best fit
GRADE 8 MATHEMATICS—RELEASED FORM
Mary collected data each day on how many commercials she saw and how long
she watched TV. She displayed her data in a scatterplot.
Television Commercials
20
Choose 5 points strategically
18
(55,17)
16
14
D
(50,15)
SE
12
10
(25,9)
8
EA
Total Number of Commercials
6
(20,6)
(15,5)
Y=.3x+.25
Y= .292(90)+.74
=27.02 Choice is B
EL
4
2
0
10
R
32
20
30
40
50
60
70
80
90
Time (in minutes)
According to the trend line shown in the scatterplot, about how many
commercials will Mary see if she watches TV for 1 1 hours?
2
A
19
B
27
C
39
D
90
26
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GRADE 8 MATHEMATICS—RELEASED FORM
Alicia and Melissa did jumping jacks. The table below shows the number of
jumping jacks that Alicia had done in different amounts of time.
Alicia
Time (minutes)
1 2 3
4
5
6
7
8
Jumping Jacks 30 60 90 120 150 180 210 240
Stat Edit Stat Calc
m = 30
The graph below shows the number of jumping jacks Melissa had done in different
amounts of time.
Compare slopes
D
y
160
SE
140
120
100
80
EA
60
40
20
0
1 2 3 4 5 6 7 8
Time (minutes)
x
EL
Number of Jumping Jacks
Melissa
m = about 25
Compare all points
5 and 6 are very close!!
150/6 =25
100/4=25 exact
Choice is D
30-25=5
Expressions and
Equations
Which choice best describes the difference between the rates at which the girls
did jumping jacks?
R
33
A
Melissa did 6 more jumping jacks per minute than Alicia.
B
Alicia did 6 more jumping jacks per minute than Melissa.
C
Melissa did 5 more jumping jacks per minute than Alicia.
D
Alicia did 5 more jumping jacks per minute than Melissa.
27
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GRADE 8 MATHEMATICS—RELEASED FORM
A town’s buildings were graphed on a coordinate grid.
y
+10
Fire Station
+9
+8
Post Office+
7
Town Hall
+6
+5
Library
+4
+3
D
+2
+1
–8 –7 –6 –5 –4 –3 –2 –1 0
–1
+1 +2 +3 +4 +5 +6 +7 +8 +9 +10
x
SE
–10 –9
–2
–3
–4
EA
–5
–6
–7
–8
EL
–9
–10
Which equation would represent a line drawn to connect the Town Hall and Post
Office?
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34
−2
x + 28
A
y =
B
y =
C
y = 3x + 9
5
D
y = 1 x + 59
3
−1
8
8
3
x + 53
Ordered (5,6); (-3,7)
Pairs
m= (7-6)/(-3-5)
-1/8
8
Choice B
Expression and Equation
3
28
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GRADE 8 MATHEMATICS—RELEASED FORM
Rain is flowing into two containers at different rates. The figure below shows the
volume of water in each container at different times.
y
Container 1
Grpah
Minutes Gallons
8
5
2
5
10
4
15
6
20
8
25
10
6
5
4
5
5
2
2
2
2
2
2
m = y/x
2/5
SE
x
5 10 15 20 25
Minutes
4/20=1/5
D
5
0
Table
Container 2
10
Gallons
What is the difference in the rate of change between the two containers?
1
gallon per minute
5
B
3
gallon per minute
5
C
5
gallons per minute
2
D
15
gallons per minute
2
EL
EA
A
2/5-1/5= 1/5
Expressions and Equations
R
35
29
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GRADE 8 MATHEMATICS—RELEASED FORM
A system of equations is shown below.
2x + 4y = 0
y = 1x −3
2
What is the x-value in the solution to the system of equations?
Ax+By= C ; y=mx+b
–
3
A
Expressions and Equations
–
1.5
B
D
3
You may use
Substitution
Elimination
Graphing
or Matrices
2
4= 0
-1/2 1 = -3
2nd matrix edit enter A 2 x 2; 2nd matrix edit B 2 x1
2nd quit
2nd matrix enter A inverse
2nd matrix enter B
(3, -1.5)
Choice is D
D
1.5
EL
EA
SE
C
R
36
30
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GRADE 8 MATHEMATICS—RELEASED FORM
In which table is y a function of x?
x
y
–
3
6
2
B
x
y
–
1
0
5
5
2
3
2
7
3
2
3
5
4
D
A
Functions from a table
5 repeats
SE
2 repeats
C
D
3
4
5
–
1
0
EA
2
y
EL
x
–
5
7
x
y
0
6
–
1
3
2
4
–
1
5
- 1 repeats
R
37
Concept = x value does not repeat
Concept vertical line test
31
= Choice is C
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GRADE 8 MATHEMATICS—RELEASED FORM
38
Which function has a greater rate of change than the function that passes through
the points given in the table below?
x
y
4
2
6
3
8
4
10
5
12
6
C
y = 1+ 1x
1/2
y = −1 + 1 x
4
EL
1/4
slope of the given table
stat edit stat clac = 1/2
Compare numbers
3/5; 3/7; 1/2; 1/4
.6; .42; .5; .25
Choice is A
R
D
2
Concept = writing a linear equation in different forms
slope =(-A/B) or the coefficient of x when the equation is
solved for y
y-intercept = (C/B) or B , the constant when the equationn
is solved for y
x-intercept = (C/A), or substitute y=0, and solve for y
Concept = greater slope = steeper slope (Larger absolute
value)
SE
B
3x − 5y = 25
-3 /-5 = 3/5
7y − 3x = 14
-(-3)/-7 = -3/7
EA
A
D
Linear Function
32
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GRADE 8 MATHEMATICS—RELEASED FORM
Larry started riding his bike at a rapid pace. He got tired and stopped to rest.
When he started again, he was going at a slower rate. Which graph best shows
Larry’s trip?
B
SE
D
Total Distance
Total Distance
A
Time
Time
Time
Total Distance
EL
EA
Rapid = steep slope = m2
stopped = zero slope = horizontal line
slower rate = less steep than m1
D
Choice A is the best choice relating to the steepness of a line and horizontal
line with a zero slope
R
C
Total Distance
39
Time
Linear Function
33
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GRADE 8 MATHEMATICS—RELEASED FORM
Alice compared the graphs of two functions.
•
The first function was y = 3x + 4.
•
The second function fits the values in the table below.
Linear Function
x
y
2
17
5
32
8
47
D
11 62
B
2
C
3
D
4
Find the equation of the line
stat Edit
Stat Clac
y = 5x+7
The distance = 7-4= 3
Choice C
EA
1
EL
A
SE
What is the distance between the y-intercepts of the two functions?
R
40
34
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GRADE 8 MATHEMATICS—RELEASED FORM
Rectangle WXYZ will be dilated by a scale factor of 1 , creating rectangle W′X′Y′Z′.
2
y
Geometry
+6
+5
+4
+3
+2
+1
–6 –5 –4 –3 –2 –1 0
–1
Z
–2
X
+1 +2 +3 +4 +5 +6
Y
SE
–3
x
D
W
–4
–5
EA
–6
What will be the perimeter of rectangle W′X′Y′Z′?
4 units
B
6 units
C
12 units
D
24 units
EL
A
R
41
Concept = Dilation = shrink = reduce divide by a number less than 1
= Enlarge by a number greater than one
Pre-image--> before dilation
Image ---> after dilation
Scale factor shrink or enlarge divide or multiply
W ----> W' - read w prime is a dilated point
Concept = dilate
Concept = Perimeter
w'=(.5, -1.5); x' = (.5,.5) , y'= (.5,-.5), z'= (-1.5,-.5)
Concept = Sketch the graph
Concept = Calculate the distance
P= 2+1+2+1 = 6 Choice B
35
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GRADE 8 MATHEMATICS—RELEASED FORM
42
Lines l and m are parallel to one another and cut by transversals s and t.
Geometry
x
l
40°
m
D
60°
SE
s
80°
C
120°
D
140°
EL
B
R
40°
EA
What is the value of x?
A
Concept two line cut by a transversal form the following
angels
t
1) Corresponding angles are congruent = equal
2) Alternate interior angles = equal
3) Alternate exterior angles = equal
4) Consecutive interior angles are supplementary =180
(same side interior angles)
Consecutive exterior are supplementary = 180
5) Vertical angles are congruent = equal
6) Linear Pair are supplementary = 180 degrees
60+y+40= straight angle = 180 degrees
180-100= 80 degrees
+40+80 = x = 120
Choice C
36
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GRADE 8 MATHEMATICS—RELEASED FORM
43
Molly wants to put a fence around an area. The fence will follow the diagram of the
triangle shown below.
10 ft
Geometry
SE
D
18 ft
B
38 ft
C
43 ft
D
49 ft
EL
28 ft
Concept = Perimeter = Thge distance around the shape =
add all sides
Concept = Pythagorean theorem =
10^2+ b^2 = 18^2
b^2= (18^2-10^2)=224= square root of 224 =14.97
P = 10+18+14.97 =42.96 = 43 feet
Choice C
R
44
A
EA
About how much fencing does Molly need?
The points (–3, –1) and (–3, 5) are adjacent vertices of a rectangle. Two of the
sides of the rectangle have a length of 8 units. What is the length of a diagonal of
the rectangle?
Geoemtry
Concept = Distance formula
A
9 units
Concept property of a rectangle = opposite sides are
B
10 units
congruent
Concept = Sketch a graph = from -1 to 5 = 6 units
C
12 units
Concept = Pythagorean theorem
D
14 units
a^+b^= C^2
6^2+8^2= 36+64= 100
Take the square root of 100 = 10
Choice B
37
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GRADE 8 MATHEMATICS—RELEASED FORM
45
What is the approximate volume of the cone below?
Geometry
7 cm
183 cm3
C
549 cm3
D
733 cm3
Volume of Cone = 1/3 Bh ( B = area of the base = (pi) (r^2)
Diameter = 2r
10 = 2r
r=5
(1/3)(5^2)(3.14)(7) = 183.16
Choice B
SE
B
EA
70 cm3
A
85°
B
130°
C
145°
D
150°
EL
The measures of the angles of a triangle are 50°, 35°, and 95°. What is the
measure of the largest exterior angle of the triangle?
R
46
A
D
10 cm
Geometry
1) Concept = The sum of the angle in a triangle =
180 degrees
2) Concept = The sum of two remote angles = the
sum of exterior angle
3) Concept = Linear pair = 180 degrees
The smallest interior = 35
The largest exterior = 180-35=145 degrees
Choice C
( Draw a picture , label each angle and apply the
concepts and theorems )
38
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GRADE 8 MATHEMATICS—RELEASED FORM
Which scenario would most likely show a negative association between the
variables?
Statistics
the height of a tree, x, and the amount of time it takes to climb to the top of
the tree, y
B
the number of people in the mall, x, and the number of cars in the parking
lot, y
C
miles traveled in a car, x, and the amount of gasoline used, y
D
time spent reading a book, x, and the number of pages left to read, y
D
A
EL
EA
SE
A) up, up or +,+ ---> y increases as x increases
B) up, up
C)up , up
D) up, down ---> more time, less pages left to read
Choice D
Concept --> interpret independent x and dependent Y ( Verbs --used left) pay
attention to each statement, then if both are going in the same direction +,+ or
-,- then it's (a positive relationship, positive correlation, positive association ,
positive slope); on the other hand, +,- or -,+, then it's a negative assciation.
R
47
39
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GRADE 8 MATHEMATICS—RELEASED FORM
Statistics
James is fitting the linear equation y = 1 x to a data set. Which scatterplot shows
2
the data set that the linear equation would fit best?
A
B
2
1
1
1
D
2
2
1
EA
SE
Slope = Y /x = Vertical Change / Horizontal Change
2/1 = 2
C
1
1
EL
2
2
2/2=1
D
2
1
2
-1/2= -1/2
1
2
1/2= 1/2 Choice D
Concepts line of best fit
slope; y-intercept
R
48
40
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GRADE 8 MATHEMATICS—RELEASED FORM
Students were surveyed about book bags. The results are shown below.
Statistics
Carry a
Book Bag
Do Not Carry
a Book Bag
Male
Female
47
57
63
48
D
A student concluded that, for those in the survey, females are more likely to carry
a book bag than males. Which explanation best supports the student’s conclusion?
For females, 54% carry a book bag, while for males, 43% carry a book bag.
B
For females, 27% carry a book bag, while for males, 22% carry a book bag.
C
For females, 57 carry a book bag, while for males, 47 carry a book bag.
D
For females, 48 do not carry a book bag, while for males, 63 do not.
EA
SE
A
EL
Total male + female carry book bag = 47+57 =104
female = (57/104)*100 = 54 %
male = (47/104)*100 = 45%
Choice A
Concept ---> Percentage - Population Surveyed --> 100%
R
49
41
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GRADE 8 MATHEMATICS—RELEASED FORM
Statistics
Which equation best fits the data shown in the scatterplot below?
y
+5.0
+4.5
+4.0
+3.5
+3.0
+2.5
D
+2.0
+1.5
SE
+1.0
+0.5
–10
–9
–8 –7
–6
–5 –4 –3 –2 –1 0
–0.5
+1 +2 +3 +4 +5 +6 +7 +8 +9 +10
x
EA
–1.0
–1.5
–2.0
EL
–2.5
R
50
A
y = 1x −1
B
y = 1x − 1
C
y = 3x −2
D
y = x − 3
4
2
4
2
–3.0
–3.5
–4.0
–4.5
–5.0
1) Stat Edit
L1
L2
x
y
9
5
7
3.75
3
0
1
-1
.7875 Enter math 1 frac enter enter
Answer Choice C
42
Concepts Use TI-84 - Line of best fit
2) Stat Calc
#4 Linear Regression
Enter
Enter
Y=ax+b
a=.7875
b=-2
r^2= .990
r=.995
y=.7875x-2
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GRADE 8 MATHEMATICS—RELEASED FORM
Directions:
This is the end of the mathematics test.
1. Put all of your papers inside your test book and close your test book.
2. Place your calculator on top of the test book.
R
EL
EA
SE
D
3. Stay quietly in your seat until your teacher tells you that testing is
finished.
43
GRADE 8 MATH—RELEASED FORM
Grade 8 Math
RELEASED Form
2012–2013
Answer Key
Type
Key
S1
MC
C
S2
GR
-7
S3
GR
3/4 or .75
Domain
D
Item Number
SE
Calculator Inactive
Type
Key
1
MC
D
EE — Expressions and Equations
2
MC
B
EE — Expressions and Equations
3
MC
4
MC
5
MC
7
EE — Expressions and Equations
C
F — Functions
D
F — Functions
MC
C
SP — Statistics and Probability
GR
2
NS — The Number System
GR
26
NS — The Number System
NS — The Number System
R
8
A
EL
6
Domain
EA
Item Number
9
GR
29
10
GR
.3125
EE — Expressions and Equations
11
GR
8
EE — Expressions and Equations
12
GR
12
EE — Expressions and Equations
13
GR
1800
F — Functions
14
GR
17
F — Functions
15
GR
35.5
F — Functions
GRADE 8 MATH—RELEASED FORM
Calculator Active
Type
Key
16
MC
A
EE — Expressions and Equations
17
MC
C
EE — Expressions and Equations
18
MC
D
EE — Expressions and Equations
19
MC
A
EE — Expressions and Equations
20
MC
D
EE — Expressions and Equations
21
MC
B
F — Functions
22
MC
A
F — Functions
23
MC
A
F — Functions
24
MC
B
G — Geometry
25
MC
C
EE — Expressions and Equations
26
MC
C
G — Geometry
27
MC
B
G — Geometry
28
MC
C
G — Geometry
29
MC
D
SP — Statistics and Probability
MC
B
G — Geometry
MC
A
SP — Statistics and Probability
MC
B
SP — Statistics and Probability
33
MC
D
EE — Expressions and Equations
34
MC
B
EE — Expressions and Equations
35
MC
A
EE — Expressions and Equations
36
MC
D
EE — Expressions and Equations
37
MC
C
F — Functions
31
R
32
SE
EA
EL
30
Domain
D
Item Number
GRADE 8 MATH—RELEASED FORM
Type
Key
38
MC
A
F — Functions
39
MC
A
F — Functions
40
MC
C
F — Functions
41
MC
B
G — Geometry
42
MC
C
G — Geometry
43
MC
C
G — Geometry
44
MC
B
G — Geometry
45
MC
B
G — Geometry
46
MC
C
G — Geometry
47
MC
D
SP — Statistics and Probability
48
MC
D
SP — Statistics and Probability
49
MC
A
SP — Statistics and Probability
50
MC
C
SP — Statistics and Probability
SE
EA
EL
Item Types:
MC = multiple choice
GR = gridded response
Domain
D
Item Number
R
Links to instructions for the gridded-response items can be found on the main
accountability page.