End of Semester Test: Geometry B Plato/Edmentum

A circle is defined by the equation given below. �2 + �2 − � − 2⁢� − 114 = 0 What are the coordinates for the center of the circle and the length of the radius?

(/2, 1) 2 units

Which equation represents circle N?

(x + 7)2 + (y − 6)2 = 50

What is the number of possible permutations of 8 objects taken 4 at a time?

1,680

Circle O has radius of 24 units. Arc XY located on the circle has a central angle of 75∘. What is the area of the associated sector, in square units?

120pi

Zoe is shopping for a new car and has to make some decisions. The model she's chosen comes in two versions, hybrid and electric. For the exterior, she can choose red, blue, or green. For the interior, she can choose fabric, leather, or vinyl.

1/9 1/3

Rounded to the nearest tenth, what is the perimeter of the triangle? (30,60,90 hypotenuse = 5cm)

11.8 centimeters

Jim's sock drawer has two pairs of black socks, three pairs of white, one pair of green, and two pairs of gray. One evening he randomly picks three socks assuming that he will get a matched pair, but instead turns up with 1 black, 1 white, and 1 gray sock. Without putting back the socks he picked, he picks another sock randomly. What is the probability that he will have a complete pair?

11/13

A developer buys an empty lot to build a small house. What is the area of the lot?

193 yd

A cylinder has a height of 4 meters and a radius of 1.5 meters. What is the approximate radius of a sphere that has the same surface area as the cylinder?

2.0 m

To make cream ice pops, Nina uses conical molds that each have a height of 15 cm and a radius of 2 cm. How much ice pop mixture can each mold hold when full?

20pi cubic cm

What is the value of x in the triangle?

3

On a football field, the left and right tackles are lined up on the same yard line. A linebacker is 15 yards away from that yard line. The angles of the lines of sight of the tackles to the linebacker that are made with the yard line are shown in the diagram. Approximately how far apart are the left and right tackles?

39.3 yards

The shape of a township with a population of 12,620 people is shown.

4.4

An airplane departs airport A at a heading of 300∘ (N 60∘W). After traveling 320 miles, the airplane adjusts its course to 350∘ (N 10∘W) and flies an additional 112 miles to reach airport B.

401 miles

A student club has 15 members. How many ways can a committee of 6 members be chosen?

5,005

The length of an arc of a circle is 7.34 units, and the measure of the corresponding central angle is 81°. What is the approximate length of the radius of the circle?

5.19 units

A composite figure is shown. What is the surface area for each part of the figure? What is the total surface area of the figure?

60 480 180 720

In the diagram, point M is the center of the circle. If m∠PMN = 134°, what is m∠PON?

67

What is the equation of the parabola shown with its focus on this graph?

y = -1/12x^2 + 1

In her notebook, Pia wrote these steps to construct a square inscribed in a circle: Use a compass and a straightedge to find chord LM, which is the perpendicular bisector of JK. Then, use a straightedge to draw the four chords that make up the square: JL, LK, KM, and MJ. Which instruction is Pia missing?

Draw any diameter on a circle and label it JK.

A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers. Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder. The figure shows both designs.

The heights of both designs must be the same, the base areas of both designs must be the same, and each cross-section taken at the same height on both designs must have the same area.

What is the missing term in the table? If there were two doors instead of three doors, what would the sample size be?

The missing term is A-2. The sample size would be 6.

Jenna attempted to construct equilateral triangle EFG inscribed in circle C. First, she used a compass to draw circle C and labeled its center. Next, she used a straightedge to draw a diameter of the circle. She labeled the endpoints of the diameter D and E. Then, keeping the compass set equal to the radius of circle C, she drew an arc centered at point E, which intersected the circle at two points that she labeled F and G. Finally, she used a straightedge to draw three chords connecting points E, F, and G. What was the first error Jenna made in her construction?

When Jenna drew the arc that intersected circle C, she should have used point D as the center of the arc.

What is the probability that a person who is above 35 years old has a hemoglobin level of 9 or above?

[X] 0.432

In the given figure, what is the measure of angle CPE?

[X] 68

A quadrilateral is inscribed in circle O. The angle measures of the quadrilateral, in degrees, are given by the expressions shown in the figure.

[X] 75

In ABC, the angle bisectors meet at point D. Point E is on , and is perpendicular to . Point F is the location where the perpendicular bisectors of the sides of the triangle meet. What is the radius of the largest circle that can fit inside ABC?

[X] AD

A new company uses cylindrical gas tanks to deliver propane gas. As their orders increase, they switch to new gas tanks with triple the height and triple the radius of the original tanks. What will be the effect of the scaled dimensions on the volume of the tanks?

[X] The volume of the new tanks will be 3 times the volume of the original tanks.

Consider the two cylinders.

[X] The volumes of these two cylinders are not equal If another cross section is taken at a different height, the areas of the cross sections will always be equal.

Triangle XYZ has an altitude as shown. Eric and Maggie are both trying to prove the law of sines.

correctly started by both Eric and Maggie set the right side of the equation equal transitive property of equality

The perimeter of base DHGC is 30 inches, and the perimeter of base SWVR is 20 inches. Complete the table with the ratios of the heights, surface areas, and volumes of these two similar rectangular prisms. Assume the ratios are written in the form figure 1 : figure 2.

height 3/2 SA 9/4 27/8

You pick a card from a shuffled pack and draw a king. You put it back in the pack, shuffle, and then pick another card. This time you draw a queen. How are the two events of picking a king and picking a queen related?

independent

The table shows the results of a survey of 200 randomly selected people about where they live and whether they hike regularly.

independent equal not regularly hiking

An image of a castle is shown. The height of the tower on the right is 80 ft. The diameter of this tower is 20 ft. The building attached to the tower has a length of 200 feet, width of 40 feet, and height of 60 feet. First, determine which shapes best model these two sections of the castle. Then, determine the approximate surface area of the stone part of the castle given the provided dimensions.

left = rectangular prism right = cylinder [X] surface area = 5027 ft

An instrument maker creates a triangle in the shape of an isosceles triangle by bending a metal rod. The rod is 13 inches long, and the bottom of the triangle is longer than the two sides. What is the length of the longest side?

longest side is 5 inches other two sides will each be 4 inches

First, drag a value to represent the missing angle in the triangle. Then, complete the trigonometry equality statements.

missing angle = 90 - theta sin 28 = cos 62 cos 33 = sin 57 cos 31 = sin 59 cosine 90 - theta = sin(theta)

How can the surface area of the onion be approximated?

modeled by a sphere 38.5 inches

The circle is rotated around the horizontal dashed line. Which type of geometrical figure will be generated?

sphere

If the given figure is sliced through points J, K, and L, which best describes the shape of the resulting cross-section?

trapezoid

Given the focus and directrix shown on the graph, what is the vertex form of the equation of the parabola?

x = 1/10(y-3)^2 - 3/2