Example Items
Algebra II
Pre-AP
Algebra II Pre-AP Example Items are a representative
set of items for the ACP. Teachers may use this set of items along with the
test blueprint as guides to prepare students for the ACP. On the last page,
the correct answer and content SE is listed. The specific part of an SE that an
Example Item measures is not necessarily the only part of the SE that is
assessed on the ACP. None of these Example Items will appear on the ACP.
Teachers may provide feedback with the form available on the Assessment
website: assessment.dallasisd.org.
First Semester
2016–2017
Code #: 1211
ACP Formulas
Algebra II/Algebra II PAP
2016–2017
Coordinate Geometry
Midpoint:
y  y2 
 x  x2
M  1
, 1

2 
 2
Distance:
d  (x2  x1 )2  (y2  y1 )2
m
Slope:
y2  y1
x2  x1
Logarithms
Product
Property:
logx ab  logx a  logx b
Quotient
Property:
logx
a
 logx a  logx b, b  0
b
Power
Property:
logb m p  p logb m
Change of
Base:
loga n 
logb n
logb a
Properties of Exponents
Product of Powers:
am an  a(m n)
Power of a Power:
(am )n  a mn
Quotient of Powers:
am
 a(m  n)
n
a
Rational Exponent:
an 
Negative Exponents:
an 
m
n
am
1
an
Quadratic Equations
Standard Form:
f (x)  ax 2  bx  c
Quadratic Formula:
b  b2  4ac
x 
2a
Axis of Symmetry:
x
f (x)  a( x  h)2  k
Vertex Form:
Parabolas:
(x  h)2  4py(y  k )
(y  k )2  4py(x  h)
b
2a
Polynomials
Perfect Square
Trinomials:
a2 + 2ab + b2 = (a + b)2
a2 – 2ab + b2 = (a – b)2
Difference of Squares:
a2 – b2 = (a – b)(a + b)
Sum of Cubes:
a3 + b3 = (a + b)(a2 – ab + b2)
Difference of Cubes:
a3 – b3 = (a – b)(a2 + ab + b2)
Square of a Sum:
(a  b)2  (a  b)(a  b)  a2  2ab  b2
Square of a Difference:
(a  b)2  (a  b)(a  b)  a2  2ab  b2
Product of a Sum and a Difference:
(a  b)(a  b)  a2  b2
ACP Formulas
Algebra II/Algebra II PAP
2016–2017
Matrices
Adding:
a b e f   a  e b  f 




 c d   g h  c  g d  h 
Subtracting:
a b  e f   a  e b  f 




 c d   g h  c  g d  h 
Multiplying by a Scalar:
 a b  ka kb 
k


c d  kc kd 
Multiplying:
a b
 e f   ae  bg af  bh

  


c
d


 g h  ce  dg cf  dh 
HIGH SCHOOL
Page 1 of 12
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
1
2
Given f ( x )  2 x  4  1 and g(x )  x  4  1 , which statement is true?
A
The functions f ( x ) and g( x ) have the same domain and the same range.
B
The functions f ( x ) and g( x ) have different domains and different ranges.
C
The functions f ( x ) and g( x ) have the same domain and different ranges.
D
The functions f ( x ) and g( x ) have different domains and the same range.
What is the restricted domain of f ( x )
 ( x  4)2  8 such that f 1( x) is a function?
  x  12 and is a function.
A
If the domain of f ( x ) is restricted to (– , –4], then f 1( x )
B
If the domain of f ( x ) is restricted to [–4,
), then f 1( x )
  x  12 and is a function.
C
If the domain of f ( x ) is restricted to [–4,
), then f 1( x )
  x  8  4 and is
a function.
D
If the domain of f ( x ) is restricted to (– , –4], then f 1( x )
a function.
Dallas ISD - Example Items
  x  8  4 and is
Page 2 of 12
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
3
Which graph represents the functions f ( x ) and f 1 (x ) ?
A
C
B
D
Dallas ISD - Example Items
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
4
The graph of a system of equations is shown.
Which system of equations is represented by this graph?
A
B
3
x 1
2
1
y  ( x  5)2  7
8
y 
y 
y
C
D

3
x 1
2
1
( x  5)2  7
8
2
x 1
3
1
y  ( x  5)2  7
8
y

2
x 1
3
1
y  ( x  5)2  7
8
y

Dallas ISD - Example Items
Page 4 of 12
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
5
Horatio has 57 coins consisting of nickels, dimes, and quarters. He has twice as many dimes as
nickels. If the coins are worth a total of $7.25, which system of equations is used to determine
how many of each coin Horatio has?
A
n  d  q  57
n  2d
5n  10d  25q  7.25
B
n  d  q  57
n  2d
0.05n  0.10d  0.25q  7.25
C
n  d  q  57
d  2n
5n  10d  25q  7.25
D
n  d  q  57
d  2n
0.05n  0.10d  0.25q  7.25
6
A system of equations is shown.
 3
7
3x  y  2 z  6
x  2y  3z
2 x  3y  z
What is the solution to this system of equations?
A
(–2, –1, 1)
B
(–2, 1, –1)
C
(1, –1, –2)
D
(1, –2, –1)
Dallas ISD - Example Items
Page 5 of 12
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
7
A system of inequalities is shown.
 0
y  0.2 x
x
2
x 2
3
2y  3x  16
y

Which graph represents the solution to this system?
A
C
B
D
Dallas ISD - Example Items
Page 6 of 12
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
8
The graph of a parabola is shown.
Which equation represents this parabola?
1
3
  (x  2)2  3
A
y
B
y  
C
y
D
y  
1
(x  2)2  3
3
1
3
  (x  2)2  3
1
(x  2)2  3
3
Dallas ISD - Example Items
Page 7 of 12
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
9
A parabola is used to model the path of a basketball as shown in the diagram.
Which equation represents the path of the basketball?
1
8
  ( x  12)2  18
A
y
B
y  
C
y
D
y  
1
( x  12)2  18
8
1
3
  ( x  18)2  12
1
( x  18)2  12
3
Dallas ISD - Example Items
Page 8 of 12
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
10
Mr. Allen asks his Algebra II students to convert the equation y  2 x 2  16 x  37 to vertex form.
The steps Raymond uses are shown:
Step 1:
y  (2 x 2  16 x)  37
Step 2:
y  2(x 2  8 x)  37
Step 3:
y  2(x 2  8 x  16)  37  16
Step 4:
y  2(x  4)2  21
In which step does Raymond make his first mistake?
A
Step 1
B
Step 2
C
Step 3
D
Step 4
Dallas ISD - Example Items
Page 9 of 12
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
11
Brianna has planted a rectangular shape garden that has an area of 72 square feet. She wants to
create a walkway of uniform width around the garden.
If the outside dimensions of the walkway are 12 feet by 18 feet, how wide is the walkway,
in feet?
Record the answer and fill in the bubbles on
the grid provided. Be sure to use the correct
place value.
Dallas ISD - Example Items
Page 10 of 12
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
12
13
What is the solution to the inequality 2 x 2  5x  21  8 x 2  15 ?
A

3
2
x   x  
2
3

B

2
3
x   x  
3
2


C

3
or x
x x  
2

D

2
3
or x  
x x  
3
2



2

3
If the function f ( x)  x is changed to g(x ) 
1
f (x  12)  10, how is the graph of the function
4
transformed?
A
The graph of f ( x) is compressed vertically by a factor of
1
, and translated 12 units to the
4
right and 10 units down to create the graph of g(x ).
B
The graph of f ( x) is compressed vertically by a factor of
1
, and translated 12 units to the
4
left and 10 units up to create the graph of g(x ).
C
The graph of f ( x) is stretched vertically by a factor of
1
, and translated 12 units to the
4
right and 10 units down to create the graph of g(x ).
D
The graph of f ( x) is stretched vertically by a factor of
right and 10 units up to create the graph of g( x ).
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1
, and translated 12 units to the
4
Page 11 of 12
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
14
What value of q makes the equation 3q  27  6q  9 true?
Record the answer and fill in the bubbles on
the grid provided. Be sure to use the correct
place value.
15
Which is not a factor of 9 x 3  18 x 2  16 x  32 ?
A
x 2
B
x 2
C
3x  4
D
3x  4
Dallas ISD - Example Items
Page 12 of 12
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
16
The graph of a function is shown.
What are the domain and range of this function?
A
Domain: (–7, )
Range: (–9, )
B
Domain: (–9, )
Range: (–7, )
C
Domain: [–7, )
Range: [–9, )
D
Domain: [–9, )
Range: [–7, )
Dallas ISD - Example Items
EXAMPLE ITEMS Algebra II Pre-AP, Sem 1
Answer
SE
Process Standards
1
A
2A.2A
2A.1B, 2A.1F
2
D
2A.2C
2A.1E, 2A.1F, 2A.1G
3
A
2A.2C
2A.1E, 2A.1F, 2A.1G
4
D
2A.3A
2A.1B, 2A.1D, 2A.1E, 2A.1F
5
D
2A.3A
2A.1A, 2A.1B, 2A.1D, 2A.1E, 2A.1F
6
C
2A.3B
2A.1B, 2A.1C
7
B
2A.3F
2A.1B, 2A.1C, 2A.1D, 2A.1E, 2A.1F
8
D
2A.4B
2A.1B, 2A.1C, 2A.1D, 2A.1E, 2A.1F
9
B
2A.4B
2A.1A, 2A.1B, 2A.1C, 2A.1D, 2A.1E, 2A.1F
10
C
2A.4D
2A.1B, 2A.1C, 2A.1D, 2A.1E, 2A.1F
11
3
2A.4F
2A.1A, 2A.1B, 2A.1C, 2A.1F
12
B
2A.4H
2A.1B, 2A.1D, 2A.1E, 2A.1F
13
A
2A.6C
2A.1B, 2A.1D, 2A.1F, 2A.1G
14
11
2A.6E
2A.1B, 2A.1C
15
B
2A.7E
2A.1B, 2A.1C, 2A.1D, 2A.1E, 2A.1F
16
C
2A.7I
2A.1D, 2A.1E, 2A.1F
Dallas ISD - Example Items