Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question.
Required
2 points
2
Question 1
1.
After a dilation with center (0,0), the image of \overline{DB} is \overline{D'B'}. If DB = 4.5 and D'B' = 18, the scale factor of this dilation is:
Required
2 points
2
Question 2
2.
In the diagram below, \triangle ABC with sides of 13, 15, and 16, is mapped onto \triangle DEF after a clockwise rotation of 90° about point P.
If DE = 2x - 1, what is the value of x?
Required
2 points
2
Question 3
3.
On the set of axes below, \triangle ABC has vertices at A(-2,0), B(2,-4), C(4,2), and \triangle DEF has vertices at D(4,0), E(-4,8), F(-8,-4).
Which sequence of transformations will map △ABC onto △DEF?
Required
2 points
2
Question 4
4.
The figure below shows a rhombus with noncongruent diagonals.
Which transformation would not carry this rhombus onto itself?
Required
2 points
2
Question 5
5.
In the diagram below of circle O, points K, A, T, I, and E are on the circle, \triangle KAE and \triangle ITE are drawn, \overset{\frown}{KE}\cong\overset{\frown}{EI}, and \angle EKA \cong\angle EIT.
Which statement about \triangle KAE and \triangle ITE is always true?
Required
2 points
2
Question 6
6.
In right triangle ABC shown below, point D is on \overline{AB} and point E is on \overline{CB} such that \overline{AC} \parallel \overline{DE}.
If AB = 15, BC = 12, and EC = 7, what is the length of \overline{BD}?
Required
2 points
2
Question 7
7.
In rhombus VENU, diagonals \overline{VN} and \overline{EU} intersect at S. If VN = 12 and EU = 16, what is the perimeter of the rhombus?
Required
2 points
2
Question 8
8.
Given right triangle ABC with a right angle at C, m\angle B = 61^\circ.
Given right triangle RST with a right angle at T, m\angle R = 29^\circ.
Which proportion in relation to \triangle ABC and \triangle RST is not correct?
Required
2 points
2
Question 9
9.
A vendor is using an 8-ft by 8-ft tent for a craft fair. The legs of the tent are 9 ft tall and the top forms a square pyramid with a height of 3 ft.
What is the volume, in cubic feet, of space the tent occupies?
Required
2 points
2
Question 10
10.
In the diagram below of right triangle KMI, altitude \overline{IG} is drawn to hypotenuse \overline{KM}.
If KG = 9 and IG = 12, the length of \overline{IM} is
Required
2 points
2
Question 11
11.
Which three-dimensional figure will result when a rectangle 6 inches long and 5 inches wide is continuously rotated about the longer side?
Required
2 points
2
Question 12
12.
Which statement about parallelograms is always true?
Required
2 points
2
Question 13
13.
From a point on the ground one-half mile from the base of a historic monument, the angle of elevation to its top is 11.87°. To the nearest foot, what is the height of the monument?
Required
2 points
2
Question 14
14.
The area of a sector of a circle with a radius measuring 15 cm is 75\pi \, \text{cm}^2. What is the measure of the central angle that forms the sector?
Required
2 points
2
Question 15
15.
Point M divides \overline{AB} so that \text{AM:MB} = 1:2. If A has coordinates (-1, -3) and B has coordinates (8, 9), the coordinates of M are
Required
2 points
2
Question 16
16.
In the diagram below of triangle ABC, \overline{AC} is extended through point C to point D, and \overline{BE} is drawn to \overline{AC}.
Which equation is always true?
Required
2 points
2
Question 17
17.
In the diagram below of right triangle ABC, AC = 8, and AB = 17.
Which equation would determine the value of angle A?
Required
2 points
2
Question 18
18.
Francisco needs the three pieces of glass shown below to complete a stained glass window. The shapes, two triangles and a trapezoid, are measured in inches.
Glass can be purchased in rectangular sheets that are 12 inches wide. What is the minimum length of a sheet of glass, in inches, that Francisco must purchase in order to have enough to complete the window?
Required
2 points
2
Question 19
19.
In the diagram of quadrilateral NAVY below, m \angle YNA = 30^\circ, m \angle YAN = 38^\circ, m \angle AVY = 94^\circ, and m \angle VAY = 46^\circ.
Which segment has the shortest length?
Required
2 points
2
Question 20
20.
What is an equation of a circle whose center is (1,4) and diameter is 10?
Required
2 points
2
Question 21
21.
On the set of axes below, \triangle ABC, altitude \overline{CG}, and median \overline{CM} are drawn.
Which expression represents the area of \triangle ABC?
Required
2 points
2
Question 22
22.
In right triangle ABC, m\angle C = 90^\circ and AC \neq BC. Which trigonometric ratio is equivalent to \sin B?
Required
2 points
2
Question 23
23.
As shown in the diagram below, the radius of a cone is 2.5 cm and its slant height is 6.5 cm.
How many cubic centimeters are in the volume of the cone?
Required
2 points
2
Question 24
24.
What is an equation of the image of the line y = \frac{3}{2}x - 4 after a dilation of a scale factor of \frac{3}{4} centered at the origin?
PART II
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.
Required
2 points
2
Question 25
25.
Write an equation of the line that is parallel to the line whose equation is 3y + 7 = 2x and passes through the point (2,6).
Required
2 points
2
Question 26
26.
Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and \overline{FC} intersects \overline{AGD } at H.
If m\angle B = 118^\circ and m\angle AHC = 138^\circ, determine and state m\angle GFH.
Required
2 points
2
Question 27
27.
As shown in the diagram below, secants \overrightarrow{PWR} and \overrightarrow{PTS} are drawn to circle O from external point P.
If m\angle RPS = 35^\circ and m\overset{\frown} {RS} = 121^\circ, determine and state m\overset{\frown}{WT}.
Required
2 points
2
Question 28
28.
On the set of axes below, \triangle ABC is graphed with coordinates A(-2,-1), B(3,-1), and C(-2,-4). Triangle QRS, the image of \triangle ABC, is graphed with coordinates Q(-5,2), R(-5,7), and S(-8,2).
Describe a sequence of transformations that would map △ABC onto △QRS.
Required
2 points
2
Question 29
29.
Given points A, B, and C, use a compass and straightedge to construct point D so that ABCD is a parallelogram.
[Leave all construction marks.]
Required
2 points
2
Question 30
30.
On the set of axes below, \triangle DEF has vertices at the coordinates D(1,-1), E(3,4), and F(4,2), and point G has coordinates (3,1). Owen claims the median from point E must pass through point G.
Is Owen correct? Explain why.
Required
2 points
2
Question 31
31.
A walking path at a local park is modeled on the grid below, where the length of each grid square is 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state, to the nearest square foot, the area of the walking path.
PART III
Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit.
Required
4 points
4
Question 32
32.
A triangle has vertices A(-2, 4), B(6, 2), and C(1, -1).
Prove that \triangle ABC is an isosceles right triangle.
[The use of the set of axes below is optional.]
Required
4 points
4
Question 33
33.
Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool using city water at a rate of $3.95 per 100 gallons of water.
Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with a water delivery service at a rate of $200 per 6000 gallons.
If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and state who paid more to fill her pool. [1 ft3 water = 7.48 gallons]
Required
4 points
4
Question 34
34.
As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginning of the top step. Each step is 6 inches tall and 8 inches deep.
If the angle of elevation of the ramp is 4.76^\circ, determine and state the length of the ramp, to the nearest tenth of a foot.
Length of the ramp: _______ feet
Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom of the stairs to the bottom of the ramp.
Horizontal distance: _______ feet
PART IV
Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for the question to determine your answer. Note that diagrams are not necessarily drawn to scale. For the question in this part, a correct numerical answer with no work shown will receive only 1 credit.
Required
6 points
6
Question 35
35.
In the diagram of quadrilateral ABCD with diagonal \overline{AC} shown below, segments GH and EF are drawn, \overline{AE} \cong \overline{CG}, \overline{BE}\cong\overline{DG}, \overline{AH} \cong\overline{CF}, and \overline{AD}\cong\overline{CB}.
