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.
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(1) Download the Example Feedback Form and email it. The form is located
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Second Semester
2016–2017
Code #: 1101
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 2
1
Quadrilateral MATH is shown on the coordinate grid.
If quadrilateral MATH is rotated 90° clockwise about the origin, then translated using the rule
 x, y    x  2, y  9 , what will be the coordinates of T '' ?
A
(–7, 3)
B
(–3, 15)
C
(4, 14)
D
(–8, 14)
Dallas ISD - Example Items
Page 2 of 13
EXAMPLE ITEMS Geometry, Sem 2
2
Which figure does not model the Pythagorean Theorem correctly?
A
C
B
D
Dallas ISD - Example Items
Page 3 of 13
EXAMPLE ITEMS Geometry, Sem 2
3
Tamika is making a flag design in the shape of a parallelogram.
Which x- and y-values must she use in order to guarantee that the flag is in the shape of
a parallelogram?
A
x
y
 3
 2
B
x
y
3
 3
C
x
 3
y

1
2
x

y

1
2
3
D
Dallas ISD - Example Items
Page 4 of 13
EXAMPLE ITEMS Geometry, Sem 2
4
Michelle built a triangular garden in her yard as shown in the diagram. The fence that runs from
the greens section to the onions section is 40 feet long and forms a 37° angle with the fence
connecting the tomatoes and onions.
About how long is the tomatoes-onions fence?
5
A
24 feet
B
30 feet
C
32 feet
D
50 feet
A rectangular television screen has a diagonal measurement of 32 inches.
Based on the information in the diagram, what are the approximate length, x, and width, y, of
the television?
A
x = 27.7 inches
y = 16.0 inches
B
x = 22.6 inches
y = 16.0 inches
C
x = 18.5 inches
y = 4.9 inches
D
x = 15.1 inches
y = 10.7 inches
Dallas ISD - Example Items
Page 5 of 13
EXAMPLE ITEMS Geometry, Sem 2
6
7
A plane intersects a three-dimensional figure and is perpendicular to its base. If the intersection
is a rectangle, which three-dimensional figure is intersected by the plane?
A
Cone
B
Cylinder
C
Sphere
D
Square pyramid
A rectangular prism is shown.
If the prism is dilated by a scale factor of
1
, which statement is true?
4
A
The surface area of the new prism is
1
the surface area of the original prism.
64
B
The surface area of the new prism is
1
the surface area of the original prism.
16
C
The surface area of the new prism is
1
the surface area of the original prism.
8
D
The surface area of the new prism is
1
the surface area of the original prism.
4
Dallas ISD - Example Items
Page 6 of 13
EXAMPLE ITEMS Geometry, Sem 2
8
Jaxon drew a regular hexagon as shown.
Based on the information in the diagram, what is the approximate area of Jaxon’s hexagon?
9
A
7.8 cm2
B
15.6 cm2
C
54.0 cm2
D
93.5 cm2
A composite figure is shown on the coordinate grid.
What is the total area of this composite figure?
A
36 square units
B
84 square units
C
120 square units
D
204 square units
Dallas ISD - Example Items
Page 7 of 13
EXAMPLE ITEMS Geometry, Sem 2
10
A regular hexagonal pyramid is shown.
Based on the information in the diagram, what is the total surface area of the pyramid to the
nearest hundredth of a square inch?
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 2
11
The composite figure is create by combining a rectangular prism with a semi-cylinder.
Based on the information in the diagram, what is the volume of this composite figure to the
nearest cubic centimeter?
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 9 of 13
EXAMPLE ITEMS Geometry, Sem 2
12
KM and JL are chords of circle P.
Based on the information in the diagram, what is the length of JL ?
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 13
EXAMPLE ITEMS Geometry, Sem 2
13
In circle O, mAOB  22°.
Based on this information, what is the length of 
AB , in terms of ?
A
26 units
B
1859
 units
180
C
13
 units
22
D
143
 units
90
Dallas ISD - Example Items
Page 11 of 13
EXAMPLE ITEMS Geometry, Sem 2
14
A pizza was cut into 8 equal slices as shown. Leslie ate 5 slices.
45°
If the diameter of the pizza was 16 inches, what was the area of the pizza that Leslie ate?
A
25.1 square inches
B
78.5 square inches
C
125.7 square inches
D
201.1 square inches
Dallas ISD - Example Items
Page 12 of 13
EXAMPLE ITEMS Geometry, Sem 2
15
Circle M is shown on the coordinate grid.
Which equation represents circle M ?
A
(x  4)2  (y  3)2  25
B
(x  4)2  (y  3)2
 25
C
(x  3)2  (y  4)2
 25
D
(x  3)2  (y  4)2
 25
Dallas ISD - Example Items
Page 13 of 13
EXAMPLE ITEMS Geometry, Sem 2
16
In rectangle ABCD, BC , CF , FD , and AD are congruent.
What is the probability that a point chosen at random lies the shaded region?
17
A
1
8
B
1
4
C
1
3
D
1
2
Matt has a standard deck of 52 playing cards. What is the probability that Matt draws two face
cards without replacement?
A
3
13
B
9
169
C
11
221
D
33
676
Dallas ISD - Example Items
EXAMPLE ITEMS Geometry, Sem 2
Answer
SE
Process Standards
1
A
G.3A
G.1B, G.1E, G.1F
2
B
G.6D
G.1B, G.1C, G.1E, G.1F
3
D
G.6E
G.1A, G.1B, G.1C, G.1F
4
C
G.9A
G.1A, G.1B, G.1C, G.1F
5
A
G.9B
G.1A, G.1B, G.1C, G.1F
6
B
G.10A
G.1B, G.1F
7
B
G.10B
G.1B, G.1F, G.1G
8
D
G.11A
G.1B, G.1C, G.1F
9
C
G.11B
G.1B, G.1C, G.1F
10
219.53
G.11C
G.1B, G.1C
11
193
G.11D
G.1B, G.1C, G.1F
12
14
G.12A
G.1B, G.1C, G.1F
13
D
G.12B
G.1B, G.1C, G.1F
14
C
G.12C
G.1A, G.1B, G.1C, G.1F
15
A
G.12E
G.1B, G.1E, G.1F
16
B
G.13B
G.1B, G.1C, G.1F
17
C
G.13C
G.1A, G.1B, G.1C, G.1F
Dallas ISD - Example Items