Sample Questions for GEE 21
1)
Multiple Choice
The Venn diagram below represents the relationship between
trapezoids, rectangles, squares, rhombuses, and quadrilaterals.
Quadrilaterals
Rhombuses
Squares
Trapezoids
Rectangles
According to the diagram, which statement is not correct?
A.
B.
C.
D.
Every rhombus is a square.
Every square is a rectangle.
No trapezoid is a rhombus.
No rectangle is a trapezoid.
Massachusetts, Fall 2002
2)
Aaron used the Pythagorean theorem to find the height of a tree. He
calculated that the tree was 625 feet tall. Which of the following should
be used to write the height of the tree?
A. ± 25 feet
B. 25 feet
C. – 25 feet
D. 25 2 feet
Arizona, 2003
Focused Learning Lessons for Mathematics
65
Geometry
3) Which of these equations represents a line passing through (5,3) and (-5,-3)?
3
x
5
5
B. y = x
3
A. y =
C. y = 5
D. y = 3
Arizona, 2003
4)Suppose that VABC is reflected over the x -axis. What are the coordinates of
the image of point C? Use the graph below to answer the question.
A. (2,5)
B. (2, -5)
C. (-2,5)
D. (-2,-5)
Massachusetts, Spring 2001
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66
Geometry
5) Triangle ACD shown below is similar to triangle ABE.
The measure of EB = 6
The measure of DC = 8
The measure of AD = 12
What is the measure of AE?
A.
B.
C.
D.
16
9
3
8
Massachusetts, Fall 2002
6) Ricardo drew a rectangle. Which statement must be true?
A.
B.
C.
D.
Ricardo’s
Ricardo’s
Ricardo’s
Ricardo’s
figure
figure
figure
figure
is a parallelogram.
is a regular polygon.
is a square.
is a rhombus.
Massachusetts, Spring 2001
Focused Learning Lessons for Mathematics
67
Geometry
7) What is the length x of the altitude of the triangle shown below?
A.
B.
C.
D.
20cm
25cm
30cm
40cm
Massachusetts, Spring 2001
8) Which of the following linear equations is derived from the table of values
below?
x
-3
0
3
y
8
4
0
3
A. y = − x + 3
4
3
B. y = − x − 3
4
4
C. y = − x + 4
3
4
D. y = − x − 4
3
Arizona, 2003
Focused Learning Lessons for Mathematics
68
Geometry
9) If Figure ABCD is translated so that the image of A is A’ at (-3,2), then the
coordinates of the image of point B will be? Use the graph below to answer
the question.
A.
B.
C.
D.
(0,0)
(-1,4)
(-2,-1)
(-3,1)
Massachusetts, Spring 2001
10)
A tree casts a 20 foot shadow. When Jenna measures a pole that has be
inserted vertically into the ground, she finds that it is 5 feet tall and casts
a 4 foot shadow the same time of the day. How tall is the tree?
A.
B.
C.
D.
100 feet
25 feet
20 feet
16 feet
Arizona, 2003
Focused Learning Lessons for Mathematics
69
Geometry
11) A rhombus is graphed on a coordinate plane. It has vertices located at
(7,7), (7,2), and (10,6). What are the coordinates of the fourth vertex? You
may use the grid below.
A.
B.
C.
D.
(10,-1)
(10,3)
(10, 7)
(10,11)
Louisiana, 2003
12)
Sam gave the following description of a three-dimensional figure.
The solid has 6 faces
The solid has 8 vertices.
The solid has 12 edges.
Which of the following figures matches Sam’s description?
Arizona, 2003
Focused Learning Lessons for Mathematics
70
Geometry
13)
In order to stabilize a tightrope at a circus, a wire that has a length of 30
feet is attached from the top of the vertical support at point A to point B
on the ground. Point B is 10 feet from the base of the vertical support as
shown in the figure below. Based on this information, which of the
following is closest to the value of h, the height of the vertical support?
A.
B.
C.
D.
16
20
28
32
feet
feet
feet
feet
Massachusetts, Fall 2002
14)
On the coordinate plane, what is the distance between the points (3,4)
and (11,10)?
A.
B.
C.
D.
15)
10
7
5
14
Which of these arguments is valid?
A. Figure ABCD is a rectangle, or figure ABCD is not a rectangle.
Therefore, figure ABCD is a trapezoid.
B. All freshmen take Algebra 1. John is taking Algebra 1. Therefore,
John is a freshman.
C. All rectangles are parallelograms. Figure ABCD is a parallelogram.
Therefore, figure ABCD is a rectangle.
D. The teacher said students could not receive an A in the class, unless
they got an A on the final exam. Ashley received an A in the class.
Therefore, Ashley got an A on the final exam.
Arizona, 2003
Focused Learning Lessons for Mathematics
71
Geometry
16)
The following figure is to be rotated 90 o clockwise. What will the figure
look like after the rotation?
Massachusetts, Spring 2000
17)
A boat traveled 4 miles due east away from a dock. Then it turned and
traveled 5 miles due north. Finally, it turned again and traveled back to
the dock as shown in the figure below. Which of the following is closest
to the total distance the boat traveled?
A.
B.
C.
D.
12
13
15
18
miles
miles
miles
miles
Massachusetts, Fall 2002
Focused Learning Lessons for Mathematics
72
Geometry
18)
VABC and VDEF are shown on the grid below.
transformations will map VABC onto VDEF?
A.
B.
C.
D.
Reflect VABC
Reflect VABC
Reflect VABC
Reflect VABC
spaces.
over
over
over
over
the
the
the
the
Which of the following
y-axis and shift up 6 spaces.
x-axis and shift up 6 spaces.
y-axis and shift down 6 spaces.
y-axis, reflect over the x-axis, and shift down 4
Massachusetts, Spring 2002
19) Use the statements below to answer the question that follows.
Wrestling burns more calories than swimming or skating.
Skating burns more calories than running.
Running burns more calories than swimming or cycling.
Cycling burns more calories than dancing.
Which of the following is true?
A.
B.
C.
D.
Swimming burns more calories than skating.
Dancing burns more calories than wrestling.
Skating burns more calories than dancing.
Running burns more calories than wrestling.
Louisiana, 2003
Focused Learning Lessons for Mathematics
73
Geometry
20) Which statement best describes the slope of the line graphed below?
A. –6
B. −
2
3
C.
3
2
D. 4
Arizona, 2003
21)
Which of the following best represents the equation of the line shown on
the graph below?
3
x−2
2
3
2
C. y = − x −
2
3
2
x−2
3
2
D. y = − x − 2
3
A. y =
Focused Learning Lessons for Mathematics
B. y =
74
Massachusetts, Fall 2002
Geometry
Problems 22 and 23 are free response questions. Show steps and explain
in words how you arrived at your answer.
22)
John tells David that his flowerbed is not only a parallelogram, but also a
rhombus and a rectangle. What is the shape of the flowerbed and why is
it all three figures?
Massachusetts, Spring 2002
23)
A developer is looking at the drawings of two proportional parcels of
land shown below. One of the dimensions of parcel B is not readable.
How many square feet are in parcel B?
Florida, Spring 2001
Focused Learning Lessons for Mathematics
75
Geometry
Sample Questions
1) A
2) B
3) A
4) D 5) B
Answer Key
6) A
7) C
8) C
9) A
10) B 11) D
12) B 13) C 14) A 15) D 16) D 17)C 18) A 19) C 20) C 21) A
22)
The flowerbed is in the shape of a square. The flowerbed is a
parallelogram because it is a quadrilateral with opposite sides parallel.
The flowerbed is a rhombus because it is a quadrilateral with opposite
sides parallel and all four sides equal. The flowerbed is a rectangle
because it is a quadrilateral with opposite sides equal and parallel as well
as 4 right angles.
23)
Since A and B are proportional each pair of corresponding sides has the
same ratio. A proportion can be set up to find the missing side x.
200 350
=
300
x
200x = 105000
x = 525
525 feet is the length of the side of parcel B. To find the area of parcel B
multiply the length 300 by the width 525 and get 157,500 square feet.
Focused Learning Lessons for Mathematics
76
Geometry