Download Geometry Pre-AP

Example Items
Geometry
Pre-AP
Geometry 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 #: 1201
ACP Formulas
Geometry/Geometry PAP
2016–2017
Perimeter and Circumference
Square:
Circle:
P = 4s
C = 2r
C = d
Rectangle:
P = 2l + 2w
Arc Length:

x
 2 r
360
Triangle:
A
1
bh
2
Regular Polygon:
A
1
aP
2
Circle:
A = r
Sector of a Circle:
A
x

360
1
P
2
Area
Square:
Rectangle:
A = s2
A=lw
Parallelogram:
Rhombus:
A = bh
A = bh
A
1
d1d2 A = bh
2
A
Trapezoid:
2
 r2
1
(b1  b2 )h
2
Lateral Surface Area
Prism:
L = Ph
Pyramid:
L
Cylinder:
L = 2rh
Cone:
L = rl
Total Surface Area
Prism:
S = Ph + 2B
Cylinder:
S = 2rh + 2r
Sphere:
S = 4r2
2
1
P  B
2
Pyramid:
S 
Cone:
S = rl + r
Area of a Sector:
A
x

360
2
 r2
Volume
Rectangular Prism:
V = l wh
Cube:
V = s3
Prism:
V = Bh
Pyramid:
V 
Cylinder:
V = r 2h V = Bh
Sphere:
V 
Cone:
V 
1
Bh
3
1
Bh
3
4 3
r
3
Polygons
Interior Angle Sum:
S = 180(n – 2)
Measure of Exterior
Angle:
360
n
V 
1 2
r h
3
ACP Formulas
Geometry/Geometry PAP
2016–2017
Coordinate Geometry
Midpoint:
y  y2 
 x  x2
M  1
, 1

2
2 

Distance:
d  (x2  x1 )2  (y2  y1 )2
Slope of a Line:
m
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
Equation of a Circle:
(x – h)2 + (y – k)2 =r
y2  y1
x2  x1
2
Trigonometry
Pythagorean Theorem:
Trigonometric Ratios:
a2 + b2 = c2
sin A 
opposite leg
hypotenuse
cos A 
adjacent leg
hypotenuse
tan A 
opposite leg
adjacent leg
Special Right Triangles:
sin A sin B sin C


a
b
c
Law of Sines:
Law of Cosines:
45 - 45 - 90
30 - 60 - 90
a2  b2  c 2  2bc cos A
b2  a2  c 2  2ac cos B
c 2  a2  b2  2ab cos C
Probability
Permutations:
n
Pr 
n!
(n  r )!
Combinations:
n
Cr 
n!
(n  r )! r !
HIGH SCHOOL
Page 1 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
1
Lines r and s are graphed on a coordinate grid as shown.
Based on the information in the graph, which statement is true?
2
A
Lines r and s are parallel lines.
B
Lines r and s are perpendicular lines.
C
Lines r and s never intersect.
D
Lines r and s are neither parallel nor perpendicular.
Which equation describes a line that passes through (–5, –8) and is perpendicular to
5
y 
x  10 ?
4
A
y
 0.8 x  12
B
y
 1.25x  14.25
C
y
 1.25x  1.75
D
y
 0.8 x  3
Dallas ISD - Example Items
Page 2 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
3
Mr. Castro asked his Geometry class to consider the conditional statement shown.
If a figure is a rectangle, then it has four sides.
Which statement represents the contrapositive of the conditional?
4
A
If a figure has four sides, then it is a rectangle.
B
If a figure does not have four sides, then it is not a rectangle.
C
If a figure is not a rectangle, then it has four sides.
D
If a figure is not a rectangle, then it does not have four sides.
A geometry student concluded the statement shown.
Supplementary angles form a linear pair.
Which diagram can be used as a counterexample to this student’s conclusion?
A
1
2
m1 = 12°
B
m2 = 168°
3
4
m3 = 30°
m4 = 150°
6
C
5
7
m5 = 90°
m6 = 40°
m7 = 50°
D
The statement is true, therefore there is no counterexample.
Dallas ISD - Example Items
Page 3 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
5
6
Euclid’s Fifth Postulate (Parallel Postulate) states “If there is a line and a point not on the line,
then there exists exactly one line through the point that is parallel to the given line.” Is this also
true in Spherical geometry?
A
Yes, all postulates and facts are the same for Spherical and plane geometry.
B
Yes, there is exactly one line through the point that is parallel to the given line.
C
No, there are many lines that pass through the point that is parallel to the given line.
D
No, there are no parallel lines in Spherical geometry.
In the figure shown, octagon FGHJKLMN and pentagon AEIOU are both regular polygons,
m  ZAU = 41°, and GO is a straight line.
F
G
A
H
N
M
E
41°
Z
J
L
K
U
I
O
What is m  HJZ ?
A
72°
B
69.5°
C
68°
D
45°
Dallas ISD - Example Items
Page 4 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
7
The diagram shows the arcs used to construct
, given
ABC.
A
D
C
B
If mABC = 84° and mCBD = x2 + 6, what is the value of x ?
8
A
6
B
18
C
36
D
42
In
ABC, AC = 11 and BC = 24.
A
24
11
C
Which inequality describes all possible lengths of AB ?
A
13
 x  35
B
13
 x  35
C
11
 x  24
D
11
 x  24
Dallas ISD - Example Items
B
x
Page 5 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
9
Read the proof and answer the question.
t
Given: l  m
1
Prove:  1
3
 8
2
4
5 6
7 8
Statements
1. l  m
l
m
Reasons
1. Given
2.  1
 4
2. Vertical Angles are Congruent
3.  4
 8
3.
4.  1
 8
4. Transitive Property of Congruence
Which completes reason 3 of this proof?
A
Substitution Property of Equality
B
Symmetric Property of Equality
C
Alternate Interior Angles are congruent
D
Corresponding Angles are Congruent
Dallas ISD - Example Items
?
Page 6 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
10
The lines and rays in the figure are coplanar. Line p is parallel to line q.
s
148°
p
1
q
63°
t
Based on the information in the diagram, what is m1?
11
A
64°
B
85°
C
95°
D
211°
In the figure, M is the midpoint of AD and BC .
A
B
M
D
C
Based on this information, which triangle congruence relationship proves
A
ASA (Angle–Side–Angle)
B
SAS (Side–Angle–Side)
C
SSA (Side–Side–Angle)
D
SSS (Side–Side–Side)
Dallas ISD - Example Items
ABM

DCM ?
Page 7 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
12
In the diagram, quadrilateral WXYZ is rotated to create quadrilateral W'X'Y'Z'.
Based on the information in the diagram, what is the length of WZ ?
A
3
B
5
C
30
D
40
Dallas ISD - Example Items
Page 8 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
13
PLM is an isosceles triangle with LP
 LM .
L
(7x – 9)
P
(3x – 2)
(5x – 6)
What is the length of PM to the nearest hundredth?
Record the answer and fill in the bubbles on
the grid provided. Be sure to use the correct
place value.
Dallas ISD - Example Items
M
Page 9 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
14
Two triangles are shown.
Based on the information in the diagram, which statement is true?
A
ABC

LKJ, therefore AB
 LK and AC  L J .
B
ABC

JKL, therefore AB
 LK and AC  L J .
C
ABC 
JLK, therefore AB
 JL and AC  JK .
D
ABC

LJK, therefore AB
 AC and LK  L J .
Dallas ISD - Example Items
Page 10 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
15
Triangle ABC is shown.
Based on the information in the diagram, what value of x will make JK
Record the answer and fill in the bubbles on
the grid provided. Be sure to use the correct
place value.
Dallas ISD - Example Items
 AC ?
Page 11 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
16
Triangle ACE is shown.
Based on the information in the diagram, what is the perimeter of
Record the answer and fill in the bubbles on
the grid provided. Be sure to use the correct
place value.
Dallas ISD - Example Items
ACE?
Page 12 of 12
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
17
Triangle MNP is shown.
Based on the information in the diagram, what is the area of
A
75
B
100
C
105
D
125
Dallas ISD - Example Items
MNP ?
EXAMPLE ITEMS Geometry Pre-AP, Sem 1
Answer
SE
Process Standards
1
D
G.2B
G.1B, G.1C, G.1F
2
A
G.2C
G.1B, G.1C, G.1D, G.1E, G.1F
3
B
G.4B
G.1A, G.1B, G.1F
4
A
G.4C
G.1B, G.1C, G.1D, G.1F, G.1G
5
D
G.4D
G.1C, G.1F, G.1G
6
C
G.5A
G.1B, G.1C, G.1F
7
A
G.5C
G.1B, G.1C, G.1F
8
B
G.5D
G.1B, G.1C, G.1D, G.1F
9
D
G.6A
G.1B, G.1C, G.1F, G.1G
10
C
G.6A
G.1B, G.1C, G.1F
11
B
G.6B
G.1B, G.1D, G.1F
12
C
G.6C
G.1B, G.1C, G.1F
13
2.75
G.6D
G.1B, G.1C, G.1F
14
A
G.7A
G.1B, G.1D, G.1F, G.1G
15
4
G.8A
G.1B, G.1C, G.1E, G.1F
16
224
G.8A
G.1B, G.1C, G.1E, G.1F
17
D
G.8B
G.1B, G.1C, G.1E, G.1F
Dallas ISD - Example Items