Example Items
Pre-Calculus
Pre-AP
Pre-Calculus 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 regarding Example Items.
(1) Download the Example Feedback Form and email it. The form is located
on the homepage of Assessment.dallasisd.org.
OR
(2) To submit directly, click “Example Feedback” after you login to the
Assessment website.
Second Semester
2016–2017
Code #: 1221
(Version 2: 5/17/17)
ACP Formulas
Pre-Calculus/Pre-Calculus PAP
2016–2017
Trigonometric Functions and Identities
Pythagorean Theorem:
a2 + b2 = c2
Special Right Triangles:
30° - 60° - 90°
x, x 3, 2x
45° - 45° - 90°
x, x, x 2
Law of Sines:
sin A sin B sin C
=
=
a
b
c
Heron’s Formula:
A=
Law of Cosines:
a2 = b2 + c2 – 2bc cos A
b2 = a2 + c2 – 2ac cos B
c2 = a2 + b2 – 2ab cos C
Linear Speed:
v =
Angular Speed:
ω
s
t
sin θ =
Reciprocal Identities:
1
csc θ
1
csc θ =
Pythagorean
Identities:
Sum & Difference
Identities:
Double-Angle
Identities:
cos θ =
sec θ =
sin θ
sin2 θ + cos2 θ = 1
1
s ( s − a) ( s − b ) ( s − c )
θ
=
t
tan θ =
sec θ
1
cot θ =
cos θ
1 + tan2 θ = sec2 θ
1
cot θ
1
tan θ
1 + cot2 θ = csc2 θ
cos( α + β ) = cos α cos β − sin α sin β
sin(α + β ) = sin α cos β + cos α sin β
cos(α − β ) = cos α cos β + sin α sin β
sin(α − β ) = sin α cos β − cos α sin β
sin2x = 2 sin x cos x
cos 2 x = cos2 x − sin2 x
cos 2x = 2 cos2 x − 1
cos 2x = 1 − 2 sin2 x
Projectile Motion
1 2
gt + (v0 sin θ )t + y0
2
Vertical Position:
y =−
Vertical Free-Fall
Motion:
s(t ) = −
1 2
gt + v0t + s0
2
Horizontal Distance:
x = (v0 cos θ )t
v(t ) = − gt + v0
g ≈ 32
ft
m
≈ 9.8
sec2
sec2
Conic Sections
Parabola:
(x - h)2 = 4p(y - k)
(y - k)2 = 4p(x - h)
Circle:
x2 + y2 = r2
(x – h)2 + (y - k)2 = r2
Ellipse:
( x − h)
Hyperbola:
( x − h)
2
a2
+
2
a2
−
(y − k )
2
(y − k )
b2
2
=1
b2
( x − h)
2
+
b2
(y − k )
2
=1
a2
−
(y − k )
2
=1
a2
( x − h)
b2
2
=1
ACP Formulas
Pre-Calculus/Pre-Calculus PAP
2016–2017
Exponential Functions
Simple Interest:
I = prt
Compound Interest:
r

A = P 1 + 
n


Exponential Growth or
Decay:
N = N0 (1 + r )
nt
t
Continuous Compound
Interest:
A = Pert
Continuous
Exponential Growth or
Decay:
N = N0ekt
Sequences and Series
The nth Term of an
Arithmetic Sequence:
an = a1 + (n − 1)d
Sum of a Finite
Arithmetic Series:
a
Sum of a Finite
Geometric Series:
a
Sum of an Infinite
Geometric Series:
a
Binomial Theorem:
(a + b)
Permutations:
n
n
k =1
k
k =1
k
∞
n =1
n
Pr =
an = a1r n−1
n
(a + an )
2 1
=
n
The nth Term of a
Geometric Sequence:
=
a1(1 − r n )
, r ≠1
1−r
=
a1
, r ≠1
1−r
n
Sn =
a1 − an r
, r ≠1
1−r
= n C 0 an b0 + n C1 an −1 b1 + n C2 an − 2 b2 + ⋅ ⋅ ⋅ + n C n a0 b n
n!
(n − r )!
Combinations:
n
Cr =
n!
(n − r )! r !
Coordinate Geometry
Distance Formula:
d = ( x2 − x1 )2 + (y2 − y1 )2
Slope of a Line:
m=
Midpoint Formula:
 x + x2
M= 1
,
2

Quadratic Equation:
ax2 + bx + c = 0
y2 − y1
x2 − x1
y1 + y2 

2

Quadratic Formula:
Slope-Intercept Form of a Line:
y = mx + b
Point-Slope Form of a Line:
y − y1 = m(x − x1 )
Standard Form of a Line:
Ax + By = C
x =
−b ± b2 − 4ac
2a
HIGH SCHOOL
Page 1 of 7
EXAMPLE ITEMS Pre-Calculus Pre-AP, Sem 2
1
2
Which graph represents the curve given by the equation x
t

 3t 2 with the parameter
y  2?
A
C
B
D
What is the rectangular form for the curve given by the parametric equations x
and y  t  1?
A
x  y 2  5y  3
B
x  y 2  5y  3
C
x  y 2  3y  5
D
x  y 2  3y  5
Dallas ISD - Example Items
 t 2  5t  1
Page 2 of 7
EXAMPLE ITEMS Pre-Calculus Pre-AP, Sem 2
3
A kicker in a football game attempts a field goal 50 yards from the goal post. The ball is on the
ground and is kicked with an initial velocity of 81 ft/sec at an angle of 66°. The height of the
crossbar on the goal post is 10 feet, as shown in the diagram.
For the field goal to be good, the ball must pass over the crossbar and between the uprights.
Assuming the kick is straight and passes between the uprights, which conclusion is true?
4
A
The ball hits the ground before reaching the goal post, so the field goal is no good.
B
The ball passes under the crossbar, so the field goal is no good.
C
The ball passes over the crossbar, so the field goal is good.
D
The ball hits the crossbar, so it cannot be determined if the field goal is good.
What are the polar coordinates of the point (2, –2)?
A
7 

 4 2, 4 


B
3 

 4 2, 4 


C
7 

 2 2, 4 


D
3 

 2 2, 4 


Dallas ISD - Example Items
Page 3 of 7
EXAMPLE ITEMS Pre-Calculus Pre-AP, Sem 2
5
6
7
Which polar equation produces a Spiral of Archimedes?
2π
3
A
 
B
r cos 
2
C
r sin 
 2
D
r
 2
If a plane intersects a double-napped cone parallel to the slant height of the cone, what type of
conic section is formed?
A
Parabola
B
Circle
C
Ellipse
D
Hyperbola
An ellipse centered at the origin has a vertical major axis of 12 units and an eccentricity of 0.5.
What is the equation of the ellipse?
A
x2
y2

36 144
B
x2
y2

108 144
C
x2
y2

9
36
1
D
x2
y2

27
36
1
1
1
Dallas ISD - Example Items
Page 4 of 7
EXAMPLE ITEMS Pre-Calculus Pre-AP, Sem 2
8
A hyperbola has vertices at (2, –5) and (2, 3). The slope of one asymptote is 
equation of the hyperbola?
9
A
(y  1)2
(x  2)2

16
64
1
B
(y  1)2
( x  2)2

16
64
1
C
( x  2)2
(y  1)2

16
8
1
D
( x  2)2
(y  1)2

16
8
1
 14π 
What is the exact value of tan  
 , if it exists?
3 

A
 3
B
3
3
C
3
D
10
Undefined
Which angle has a negative sine value and a negative cotangent value?
A
π
7
B
5π
8
C
4π
3
D
9π
5
Dallas ISD - Example Items
1
. What is the
2
Page 5 of 7
EXAMPLE ITEMS Pre-Calculus Pre-AP, Sem 2
11
12
If cos 

7
and tan 
25
A

25
24
B

24
25
C
24
25
D
25
24
 0, what is the value of csc  ?
In ABC, mA  32° , mC  110° and side c
nearest hundredth, of side a ?
Record the answer and fill in the bubbles on
the grid provided. Be sure to use the correct
place value.
Dallas ISD - Example Items
 750. What is the approximate length, to the
Page 6 of 7
EXAMPLE ITEMS Pre-Calculus Pre-AP, Sem 2
13
Owen’s house is 12 blocks from the library and 8 blocks from the school. The library is 9 blocks
from the school.
What is the approximate measure, to the nearest degree, of the angle between the path from
Owen’s house to the library and the path from Owen’s house to the school?
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 7 of 7
EXAMPLE ITEMS Pre-Calculus Pre-AP, Sem 2
14
15
16
An airplane flies east for 200 miles before turning 60º south and flying for 100 miles. What are
the magnitude and the direction of the airplane from its starting point?
A
Magnitude: 173.2 miles
Direction: E 19.1° S
B
Magnitude: 264.6 miles
Direction: E 19.1° S
C
Magnitude: 173.2 miles
Direction: E 30° S
D
Magnitude: 264.6 miles
Direction: E 30° S
If a = –6, 12, –9, b = 2, –16, 18, and c = 28, –14, 3, what is
A
51, 0, –24
B
57, –48, 30
C
24, –18, 12
D
20, 14, –24
Two forces act upon an object as shown.
What is the approximate magnitude of the resultant force?
A
22.2 pounds
B
24.8 pounds
C
30.9 pounds
D
48.2 pounds
Dallas ISD - Example Items
1
3
a  b  2c ?
3
2
EXAMPLE ITEMS Pre-Calculus Pre-AP, Sem 2
Answer
SE
Process Standards
1
D
P.3A
P.1B, P.1D, P.1E, P.1F
2
C
P.3B
P.1B, P.1D, P.1E, P.1F
3
B
P.3C
P.1A, P.1F, P.1G
4
C
P.3D
P.1B, P.1C, P.1D, P.1F
5
D
P.3E
P.1D, P.1F
6
A
P.3F
P.1F
7
D
P.3H
P.1B, P.1D, P.1E, P.1F
8
B
P.3I
P.1B, P.1D, P.1E, P.1F
9
C
P.4A
P.1C, P.1E, P.1F
10
D
P.4C
P.1B, P1.C, P1.F
11
A
P.4E
P.1B, P1.C, P1.F
12
422.95
P.4G
P.1B, P1.C, P1.F
13
49
P.4H
P.1A, P.1B, P.1C, P.1F
14
B
P.4I
P.1A, P.1B, P.1C, P.1E, P.1F
15
A
P.4J
P.1B, P.1C, P.1E, P.1F
16
B
P.4K
P.1A, P.1B, P.1C, P.1F
Dallas ISD - Example Items