Transcript Algebra I Released Items

Algebra I Released Items
2000
A.2
The student will represent verbal
quantitative situations algebraically and
evaluate these expressions for given
replacement values of the variables.
Students will choose an appropriate
computational technique, such as
mental mathematics, calculator, or
paper and pencil.
Which expression correctly represents
the area of the rectangle above?
3
4
5
+
x2
2)
(x
+
2
(x
1
2
6)
+
2)
+
6(
x
8x
A. 8x
B. 6(x + 2)
C. (x + 2)(x + 6)
D. x2 + 2
25% 25% 25% 25%
What is the value of 2a2 + b5ab – 4
if a = 4 and b = 5?
2
3
4
5
25%
56
25%
3
-2
6
1
25%
4
25%
-1
4
-264
-144
3
56
4
A.
B.
C.
D.
if a = 10
1
2
3
4
5
4
5/
25%
25%
25
6
5/6
5/4
5
25
25%
5/
A.
B.
C.
D.
25%
5
What is the value of
and b = 15?
A.10
The student will apply the laws of
exponents to perform operations on
expressions with integral exponents,
using scientific notation when
appropriate.
1
2
3
4
5
25%
25%
25%
2
25%
0
-½
1
0
2
-½
A.
B.
C.
D.
1
If a ≠ 0,
2
2
(a )(a )=
The sun is about 1.5 x 108 kilometers from
Earth. If light travels about 3 x 105 kilometers
per second, about how many seconds does it
take light from the sun to reach Earth?
2
3
4
5
25%
0
0
25%
5,
00
1
25%
50
25%
50
5
50
500
5,000
5
A.
B.
C.
D.
A.11
The student will add, subtract, and
multiply polynomials and divide
polynomials with monomial divisors,
using concrete objects, pictorial
representations, and algebraic
manipulations.
The area of a rectangle is given by
A = 6x2y + 4y2x and the width of the
rectangle is w = 2xy. What is the length,
l, of the rectangle if l = A/w?
3
4
5
2y
+
3x
+
l=
+
y
6x
2
l=
2
4x
4y
2x
..
2y
2x
+
2y
3x
=
l
1
l=
l = 3x2y + 2y2x
l = 6x2y + 4y2x + 2xy
l = 4x + 2 y
l = 3x + 2 y
A.
B.
C.
D.
2y
25% 25% 25% 25%
Which expression is equivalent to
2
3
4
5
+
5/
3
-3
2x
-x
2
2x
1
+
+
2
2x
x
+
5
5x
x+5
2x2 + 5x
2x2 - x + 5/3
2x - 3 + 5/3
A.
B.
C.
D.
5/
3
25% 25% 25% 25%
Which expression is equivalent to
(3a + b)(2a - 4b)?
5a - 3 b
6a2 - 4b2
5a2 - 10ab + 5ab2
6a2 - 10ab - 4b2
3
4
5
b2
0a
b
6a
2
-1
0a
-1
2
5a
2
b
+
2
6a
1
-4
5a
b2
-4
-3
5a
b2
25% 25% 25% 25%
b
A.
B.
C.
D.
A.12
The student will factor completely firstand second-degree binomials and
trinomials in one or two variables. The
graphing calculator will be used as both
a primary tool for factoring and for
confirming an algebraic factorization.
Which is the complete factorization
of the trinomial x2 – x - 12?
1
2
3
4
5
)
)
-1
-2
+
(x
(x
+
12
)(x
6)
(x
+
)(x
-3
(x
(x
+
3)
(x
-4
)
+ 3)(x - 4)
- 3)(x + 4)
+ 6)(x - 2)
+ 12)(x - 1)
4)
(x
(x
(x
(x
A.
B.
C.
D.
25% 25% 25% 25%
Which is the complete factorization
of the trinomial 3x2 + 10x - 8?
1
2
3
4
5
4)
-2
x
(3
(x
-2
)(3
x
)(x
+
4)
+
-4
2)
(3
x
+
(x
(3
x
+
2)
(x
-4
)
4)
4)
4)
4)
)
(3x + 2)(x (x + 2)(3x (x - 2)(3x +
(3x - 2)(x +
A.
B.
C.
D.
25% 25% 25% 25%
A.13
The student will estimate square
roots to the nearest tenth and use
a calculator to compute decimal
approximations of radicals.
In kilometers, the approximate distance to the
earth’s horizon from a point h meters above the
surface can be determined by evaluating the
expression √12h. About how far is the apparent
horizon to a person looking out to sea from the
top of a cliff 350 meters above sea level?
21 km
65 km
130 km
225 km
km
5
km
22
5
0
4
13
3
65
2
21
1
km
25% 25% 25% 25%
km
A.
B.
C.
D.
Enter question text...
1
2
3
4
5
25%
2.
6
25%
1.
7
25%
1.
3
0.8
1.3
1.7
2.6
0.
8
A.
B.
C.
D.
25%
A.5
The student will analyze a given set of
data for the existence of a pattern,
represent the pattern algebraically and
graphically, if possible, and determine if
the relation is a function.
Which of the following tables represents
a function?
3
4
5
25%
25%
25%
25%
D
D.
C
C.
B
2
B.
A
1
A.
Which table most likely matches this
graph?
B.
A.
C.
D.
25%
25%
5
D
4
25%
C
3
B
2
A
1
25%
(0, -3), (2, -2), (4, -1), (6, 0), . . .
These ordered pairs follow a pattern. If
(10, y) is in this pattern, what is the
value of y?
4
5
25%
4
3
25%
3
2
25%
2
1
1
2
3
4
1
A.
B.
C.
D.
25%
Using the same relationship between x
and y as the table, what is the value of
y when x is 8?
25%
25%
4
5
5
3
3
2
2
1
25%
-1
2
3
5
-1
A.
B.
C.
D.
25%
A.15
The student will determine the domain
and range of a relation given a graph or
a set of ordered pairs and will identify
the relations that are functions.
What is the domain of the set of
ordered pairs
{(-5, -4), (-4, 4), (2, 3), (4, 5)}?
-4, 2, 4}
3, 4, 5}
-4, 4, 5}
2, 3, 4}
3,
4
5}
2,
4,
4,
5
-4
,
{5,
5
{5,
4
{4,
3
3,
2,
-4
,
2
{5,
1
}
25% 25% 25% 25%
}
{-5,
{-4,
{-5,
{-5,
4}
A.
B.
C.
D.
What is the domain of the function
shown below?
5
nu
ho
le
at
ur
al
ll
w
A
4
ll
n
3
A
2
nu
m
be
nu
ea
l
A
ll
r
A
1
m
be
rs
rs
s
integers
real numbers
natural numbers
whole numbers
nt
eg
er
All
All
All
All
ll
i
A.
B.
C.
D.
m
be
rs
25% 25% 25% 25%
Which of the following is not a graph
of a function?
A.
B.
25%
25%
4
5
D
3
C
2
B
1
25%
D.
A
C.
25%
A.16
The student will, given a rule, find the
values of a function for elements in its
domain and locate the zeros of the
function both algebraically and with a
graphing calculator. The value of f(x)
will be related to the ordinate on the
graph.
What is the range of the function
ƒ(x) = 5 - 8x when the domain is
{-2, 2, 4}?
A.
25%
B.
25%
25%
25%
C.
D.
5
21
22
23
24
25
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
D
4
C
3
B
2
A
1
Using the function machine in the
diagram, what is the output when 12 is
input?
25% 25% 25% 25%
7
8.5
19
29
4
5
21
22
23
24
25
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
29
3
19
2
8.
5
1
7
A.
B.
C.
D.
Enter question text...
2
3
4
5
21
22
23
24
25
6
7
8
9
10
11
12
2
1
13
25%
14
15
25%
16
17
25%
18
19
27
25%
14
2
8
14
27
8
A.
B.
C.
D.
20
A.19
The student will analyze a relation to
determine whether a direct or inverse
variation exists and represent it algebraically
and graphically, if possible.
a varies directly as b and a = 12
when b = 4. What is the constant of
variation?
A.
B.
C.
D.
-8
⅓
3
8
1
2
3
4
5
21
22
23
24
25
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
a varies directly as b and the
constant of variation is ¼. Which
equation represents the relationship?
13
14
16
17
¼
¼
4b
15
18
–
12
19
b
11
=
25
10
a
24
9
+
23
8
b
22
7
a
21
6
=
5
a
4
¼
b
3
=
2
a
1
25% 25% 25%
=
a = ¼b
a = 4b
a=b+¼
a=b–¼
A.
B.
C.
D.
25%
20
A.1
The student will solve linear equations
and inequalities in one variable, solve
literal equations (formulas) for a given
variable, and apply these skills to solve
practical problems. Graphing calculators
will be used to confirm algebraic
solutions.
Using the distance formula, d = rt,
what is the value of t when d = 3,520
and r = 550?
4
5
21
22
23
24
25
6
7
8
9
10
11
12
13
14
16
17
0
0
0
15
25%
18
6,
00
3
25%
19
1,
93
2
25%
2,
97
1
25%
4,
07
6.4
2,970
4,070
1,936,000
6.
4
A.
B.
C.
D.
20
23
24
25
8
9
10
11
12
13
14
15
16
17
1
18
19
>
22
7
25%
x
21
6
10
5
25%
x
4
25%
<
3
x
2
x
1
<
1
25%
<
x<1
x<5
x < 10
x>1
A.
B.
C.
D.
5
What is the solution to 2x – 4 < 6?
20
A rectangle has a perimeter of 60
inches and length of 22 inches. What
is the width of the rectangle?
23
24
25
8
9
10
11
12
13
14
17
15
16
17
18
19
in
.
22
7
25%
8
21
6
in
.
5
25%
14
4
4
3
25%
16
2
6
1
25%
in
.
176 in.
164 in.
14 in.
8 in.
in
.
A.
B.
C.
D.
20
A.3
The student will justify steps used in
simplifying expressions and solving
equations and inequalities.
Justifications will include the use of
concrete objects, pictorial
representations, and the properties of
real numbers.
The statement
“If 2(3a - 4) = 12, then 6a – 8 = 12”
is justified by the —
A. Associative property of
multiplication
B. Multiplication property of
equals
C. Addition property of equals
D. Distributive property
12
13
14
16
17
rib
u
tiv
e
pr
op
er
ty
of
...
rt
y
pr
op
e
n
at
io
15
is
t
11
D
25
10
iti
on
24
9
dd
23
8
A
22
7
ul
tip
lic
21
6
M
5
pr
op
er
t..
rt
y
pr
op
e
tiv
e
4
oc
ia
3
ss
2
A
1
.
..
25% 25% 25% 25%
18
19
20
If A < B, which of the following
statements cannot be true?
22
23
24
25
7
8
9
10
11
12
13
15
-B
C
16
17
<
-A
<
B
<
14
-C
21
6
A
5
B
C
+
B
<
4
C
3
+
2
A
1
AC
A+C<B+C
A-C<B-C
AC < BC
-A < -B
A.
B.
C.
D.
-C
25% 25% 25% 25%
18
19
20
A.6
The student will select, justify, and
apply an appropriate technique to graph
a linear function in two variables.
Techniques will include slope-intercept,
x- and y-intercepts, graphing by
transformation, and the use of the
graphing calculator.
Which equation is represented by
this line?
25% 25% 25% 25%
24
25
9
10
11
12
13
14
15
16
17
2
2
18
19
+
23
8
20
2x
22
7
y=
21
6
x+
5
y=
4
x/2
3
y=
2
y=
1
x-
2
+2
y=x-2
y = x/2 + 2
y=x+2
y = 2x + 2
A.
B.
C.
D.
Which line on the graph below has
y-intercept 3 and x-intercept -2?
B.
A.
25%
25%
25%
25%
D.
4
5
21
22
23
24
25
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
D
3
C
2
B
1
A
C.
A.7
The student will determine the slope of a line
when given an equation of the line, the graph
of the line, or two points on the line. Slope
will be described as rate of change and will be
positive, negative, zero, or undefined. The
graphing calculator will be used to investigate
the effect ofchanges in the slope on the graph
of the line.
What is the slope of the line
represented by 2x - 3y = 4?
21
22
23
24
25
6
7
8
9
10
11
12
13
14
15
16
17
25%
18
19
-2
5
/3
4
25%
-2
3
3
2
2
1
25%
2/
3/2
2/3
-2/3
-2
3/
A.
B.
C.
D.
25%
20
Which describes the slope of the
line that passes through (-7, 3) and
(8, 5)?
Positive
Negative
Zero
Undefined
24
25
9
10
11
12
13
14
15
16
ed
ro
17
18
ef
in
23
8
19
nd
22
7
U
21
6
Ze
5
eg
4
N
3
si
tiv
2
Po
1
at
iv
e
25% 25% 25% 25%
e
A.
B.
C.
D.
20
Which line on the graph has
undefined slope?
3
4
5
21
22
23
24
25
6
7
8
9
10
11
12
13
14
15
16
17
25%
18
25%
19
20
D
2
A
1
25%
C
25%
B
A
B
C
D
A.
B.
C.
D.
A.8
The student will write an equation
of a line when given the graph of
the line, two points on the line, or
the slope and a point on the line.
Which is an equation of a line that
has a slope of -½ and contains
the point (2, 3)?
y = 2x – ½
y = -x/2 +4
y = x/2 + 3
y = 3x + 2
13
14
y
16
3
17
+
+
+4
15
18
3x
12
19
=
11
y
25
10
x/
2
24
9
=
23
8
y
22
7
-x
/
21
6
=
5
y
4
2
–
3
2x
2
=
1
2
25% 25% 25% 25%
½
A.
B.
C.
D.
20
Which is most likely an equation for
the line shown?
25% 25% 25% 25%
14
15
16
4
17
18
19
-2
13
2x
12
=
11
y
25
10
+
24
9
-x
23
8
=
22
7
y
21
6
-2
5
x
4
=
3
y
2
=
1
-x
y = -x
y=x-2
y = -x + 4
y = 2x - 2
y
A.
B.
C.
D.
20
Which is an equation for the line that
passes through (0, 2) and (-2, 0)?
25
10
11
12
13
14
15
16
17
-2
18
x
24
9
19
=
23
8
25%
y
22
7
-x
21
6
=
5
=
4
y
3
x
+
-x
=
2
y
1
25%
-2
25%
2
25%
y
y = -x
y=x+2
y = -x - 2
y=x-2
A.
B.
C.
D.
20
A.9
The student will solve systems of two
linear equations in two variables, both
algebraically and graphically, and apply
these techniques to solve practical
problems. Graphing calculators will be
used as both a primary tool of solution
and to confirm an algebraic solution.
One competitor in a 100-mile bicycle race took a total
of 5 hours to complete the course. His average speed
in the morning was 23 miles per hour. His average
speed in the afternoon was 13 miles per hour. How
many hours did he ride in the morning, and how
many hours did he ride in the afternoon?
25% 25% 25% 25%
25
10
11
12
13
14
15
17
af
...
ho
ur
s,
ur
s,
ho
-4
.5
-3
16
or
ni
ng
24
9
or
ni
ng
23
8
M
22
7
or
ni
ng
21
6
af
...
ho
ur
s,
ur
s,
ho
.5
5
M
4
-2
3
or
ni
ng
2
M
1
a.
..
2.5 hours
hours
1.5 hours
hour
18
M
2.5 hours, afternoon 3 hours, afternoon - 2
3.5 hours, afternoon 4 hours, afternoon - 1
-3
Morning Morning Morning Morning -
a.
..
A.
B.
C.
D.
19
20
What is the solution to this system
of equations?
x = -2, y = -3
x = 0, y = -3
x = 1, y = -2
x = 2, y = -1
x
17
18
-1
19
y
16
=
-2
=
15
2,
14
=
13
x
12
y
11
1,
25
10
=
24
9
x
23
8
0,
22
7
=
21
6
x
5
y
=
4
y
3
-2
,
2
=
1
=
-3
25% 25% 25% 25%
-3
A.
B.
C.
D.
20
The length of a rectangle is 2
centimeters longer than its width. The
perimeter is 16 centimeters. What are the
length and width of the rectangle?
cm
cm
cm
cm
22
23
24
25
7
8
9
10
11
12
13
14
15
16
18
cm
cm
17
19
cm
,2
21
6
4
5
cm
,4
4
6
3
cm
,5
2
7
1
cm
,3
5
4
3
2
5
cm,
cm,
cm,
cm,
cm
7
6
5
4
cm
A.
B.
C.
D.
25% 25% 25% 25%
20
A.14
The student will solve quadratic
equations in one variable both
algebraically and graphically. Graphing
calculators will be used both as a
primary tool in solving problems and to
verify algebraic solutions.
The number of seconds to complete a chemical
reaction was determined to be given by the
equation s = 250 - 5T -T2 where s is the number
of seconds and T is the temperature in degrees
Celsius at which the reaction occurred. If a
chemical reaction was complete in 200 seconds,
what was the temperature at which the reaction
25% 25% 25% 25%
occurred?
5° C
7° C
10° C
12° C
23
24
25
8
9
10
11
12
13
14
15
16
17
18
19
°C
22
7
12
21
6
°C
5
10
4
C
3
7°
2
C
1
5°
A.
B.
C.
D.
20
x2 – x – 6 = 0
Which is the solution set for the
equation above?
21
22
23
24
25
6
7
8
9
10
11
12
13
14
15
16
17
18
19
6}
5
25%
{5,
4
5}
3
25%
{6,
2
25%
{2,
1
25%
3}
2}
3}
5}
6}
2}
{-3,
{-2,
{-6,
{-5,
{3,
A.
B.
C.
D.
20
A.4
The student will use matrices to
organize and manipulate data, including
matrix addition, subtraction, and scalar
multiplication. Data will arise from
business, industrial, and consumer
situations.
0.5[A] = ?
A.
B.
25%
25%
25%
D.
4
5
21
22
23
24
25
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
D
3
C
2
B
1
A
C.
25%
A.17
The student will, given a set of data
points, write an equation for a line of
best fit, using the median fit method,
and use the equation to make
predictions.
Using the median fit method, which scatterplot
most likely has a line of best fit represented by
y
=
x
+5?
A.
B.
25%
25%
25%
D.
4
5
21
22
23
24
25
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
D
3
C
2
B
1
A
C.
25%
Which equation best represents the
data shown on the scatterplot?
25% 25% 25% 25%
18
-5
17
19
2x
16
=
15
y
14
-3
13
x
12
=
11
y
25
10
3
24
9
–
23
8
½
x
22
7
=
21
6
y
5
–
4
x/
2
3
=
2
y
1
1
y = x/2 – 1
y = ½x – 3
y=x-3
y = 2x - 5
A.
B.
C.
D.
20
A.18
The student will compare multiple onevariable data sets, using statistical
techniques that include measures of
central tendency, range, stem-and-leaf
plots, and box-and-whisker graphs.
23
24
25
8
9
10
11
12
13
14
15
16
17
18
19
0
22
7
18
21
6
4
5
17
4
4
3
16
2
15
1
0
Mari and Marc are bowling a 3-game match to
determine the top bowler for their league. Marc
averaged 163 for his three games. Mari bowled
171 and 145 for her first two games. What is
the least she must bowl for her third game if
she is to win the championship?
25% 25% 25% 25%
A. 150
B. 164
C. 174
D. 180
20
This is a stem-and-leaf plot of a group of
test scores. What is the median score?
4
5
21
22
23
24
25
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
.5
3
25%
77
2
25%
77
1
25%
76
73
76
77
77.5
73
A.
B.
C.
D.
25%
In which data set is the median
value equal to the mean value?
23
24
25
8
9
10
11
12
13
}
,5
2,
46
0,
18
2,
15
59
7}
,2
11
0,
,1
14
16
17
3,
4
22
7
18
{3
21
6
,1
5
,9
4
{7
3
4,
2
6}
,1
,1
,9
,7
,4
2
{2
1
{6
{2, 4, 7, 9, 11}
{7, 9, 10, 11, 16}
{6, 12, 18, 24, 27}
{33, 40, 46, 52, 59}
1}
A.
B.
C.
D.
25% 25% 25% 25%
19
20
This is a box-and-whisker plot of a set
of scores.
In which quartile would a score of 76
fit in this set?
25% 25% 25% 25%
22
23
24
25
7
8
9
10
11
12
13
14
15
16
17
18
19
h
21
6
4t
5
3r
4
d
3
2n
2
t
1
d
1st
2nd
3rd
4th
1s
A.
B.
C.
D.
20