Download Geometry - Dallas ISD

Example Items
Geometry
Geometry 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 #: 1101
(Version 2 : 12/02/16)
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 13
EXAMPLE ITEMS Geometry, Sem 1
1
CT has a midpoint at (–1, 0).
If C is located at (–7, –3), what is the location of point T ?
A
(–13, –6)
B
(–4, –1.5)
C
(2, 1.5)
D
(5, 3)
Dallas ISD - Example Items
Page 2 of 13
EXAMPLE ITEMS Geometry, Sem 1
2
The graph of AB is shown.
Which equation represents a line parallel to AB that passes through the point (0, 4)?
3
4
x4
3
A
y 
B
y

3
x4
4
C
y

3
x4
4
D
y 
4
x4
3
During Geometry class, Clarence and Alicia wrote the conditional statement shown.
If two angles are acute, then they are congruent.
Which statement represents the inverse of the conditional?
A
If two angles are not acute, then they are not congruent.
B
If two angles are congruent, then they are acute.
C
If two angles are not congruent, then they are acute.
D
If two angles are not congruent, then they are not acute.
Dallas ISD - Example Items
Page 3 of 13
EXAMPLE ITEMS Geometry, Sem 1
4
A geometry student concluded the statement shown.
Supplementary angles form a linear pair
Which diagram represents a counterexample to this student’s conclusion?
A
1
2
1 = 12°
B
2 = 168°
3
4
3 = 25°
4 = 155°
6
C
5
7
5 = 90°
6 = 40°
7 = 50°
D
5
The statement is true, therefore there is no counterexample.
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
No, there are no parallel lines in Spherical geometry.
B
No, there are many lines that pass through the point that are parallel to the given line.
C
Yes, there is exactly one line through the point that is parallel to the given line.
D
Yes, all postulates and facts are the same for Spherical and plane geometry.
Dallas ISD - Example Items
Page 4 of 13
EXAMPLE ITEMS Geometry, Sem 1
6
The figures shown are regular polygons.
120°
90°
72°
60°
There is a pattern formed by the number of sides in the polygon and the measure of each
exterior angle of the polygon. If this pattern continues, what is the measure of each exterior
angle, in degrees, of a regular polygon with 40 sides?
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 5 of 13
EXAMPLE ITEMS Geometry, Sem 1
7
The diagram shows the arcs and segments used to construct SR, given
Based on this construction, which term describes SR ?
8
A
Median
B
Altitude
C
Angle bisector
D
Perpendicular bisector
In
ABC, AC
= 13 and BC = 18 as shown.
Which inequality describes all possible lengths of AB ?
A
13
 x  18
B
13
 x  18
C
5
 x  31
D
5
 x  31
Dallas ISD - Example Items
PQR.
Page 6 of 13
EXAMPLE ITEMS Geometry, Sem 1
9
In the diagram, a
 b.
Based on the information in the diagram, what is m1?
A
48°
B
75°
C
153°
D
201°
Dallas ISD - Example Items
Page 7 of 13
EXAMPLE ITEMS Geometry, Sem 1
10
Line l, line m, line p, line q, and ray t are coplanar.
Given: m1 = 7x + 3.5
m2 = 2x + 10
What value of x makes the information in this diagram true?
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 8 of 13
EXAMPLE ITEMS Geometry, Sem 1
11
In the figure, RA
 NA and R  N .
R
N
A
E
Which triangle congruence theorem is used to prove
12
A
AAS (Angle–Angle–Side)
B
ASA (Angle–Side–Angle)
C
SAS (Side–Angle–Side)
D
SSA (Side–Side–Angle)
In the diagram,
PQR

G
RAE 
NAG ?
YWX.
Based on the information in the diagram, what is the length of XY ?
A
2
B
5
C
7
D
13
Dallas ISD - Example Items
Page 9 of 13
EXAMPLE ITEMS Geometry, Sem 1
13
In
JKL, C is the centroid and QC
 4.
What is the length of QL ?
A
6
B
8
C
12
D
32
Dallas ISD - Example Items
Page 10 of 13
EXAMPLE ITEMS Geometry, Sem 1
14
Isosceles triangle PLM is shown.
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 11 of 13
EXAMPLE ITEMS Geometry, Sem 1
15
In the figures, pentagon ABCDE and pentagon LMNOP are drawn with the dimensions shown.
B
20
C
M
18
(4y – 2)
(2x – 1)
A
D
E
If pentagon ABCDE is similar to pentagon LMNOP, what is the value of x ?
5.83
B
6.25
C
7.25
D
15.5
Dallas ISD - Example Items
O
L
16
A
N
12
P
Page 12 of 13
EXAMPLE ITEMS Geometry, Sem 1
16
Triangle ABC is shown.
Based on the information in the diagram, what is the length of BM ?
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 13 of 13
EXAMPLE ITEMS Geometry, Sem 1
17
Triangle FGH is shown.
Based on the information in the diagram, what is the area 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
FGH ?
EXAMPLE ITEMS Geometry, Sem 1
Answer
SE
Process Standards
1
D
G.2B
G.1B, G.1C, G.1D, G.1E
2
D
G.2C
G.1B, G.1C, G.1D
3
A
G.4B
G.1B, G.1D, G.1F, G.1G
4
A
G.4C
G.1B, G.1C, G.1D, G.1F, G.1G
5
A
G.4D
G.1C, G.1D, G.1F, G.1G
6
9
G.5A
G.1B, G.1C, G.1D
7
A
G.5C
G.1B, G.1C, G.1D, G.1F
8
C
G.5D
G.1B, G.1C, G.1D
9
B
G.6A
G.1B, G.1C
10
8.5
G.6A
G.1B, G.1C, G.1D, G.1F
11
B
G.6B
G.1B, G.1C, G.1D, G.1E, G.1F
12
D
G.6C
G.1B, G.1C, G.1F
13
C
G.6D
G.1B, G.1C, G.1D
14
2.75
G.6D
G.1B, G.1C, G.1D, G.1F
15
C
G.7A
G.1B, G.1C, G.1D, G.1F
16
7
G.8A
G.1B, G.1C, G.1D, G.1E
17
150
G.8B
G.1B, G.1C, G.1D, G.1E
Dallas ISD - Example Items