2015-2016 Honors Geometry B Review - Montgomery …€¦ · · 2016-03-21HONORS GEOMETRY B Semester ... Notes to the student: This review prepares you for the semester B Honors
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Notes to the student: This review prepares you for the semester B Honors Geometry Exam. The exam will cover units 3, 4, and 5 of the Honors Geometry curriculum.
The exam consists of two parts. Part 1 is 15 selected response items each worth 2 points. The second part is 15 extended response items worth varying numbers of points for a total of 70 points.
A calculator may be used on both parts of the exam.
Many answers will be in terms of or in radical form. You may leave answers in that form or approximate as a decimal to two places past the decimal point. For most accurate approximations use the key on your calculator. Do not use 3.14 for . On the next two pages you will find the formulas that will be available to you in the exam booklet.
6. What is the relationship between the volumes of a cone and a cylinder if the cone and cylinder have the same radii and heights?
7. What is the relationship between the volumes of a pyramid and a prism, if the pyramid and prism have the same base areas and heights?
8. A scoop of ice cream is in the shape of a sphere with radius 3 cm is placed in a cone that has a radius of 2 cm and a height of 9 cm. If the ice cream melts into the cone, will the ice cream overflow the cone? Show how you determined your answer.
9. The scoop of ice cream in item 8 has a mass of 124 grams. What is the density (in g/cm3 ) of the ice cream?
10. A movie theater sells popcorn in pyramid-shaped boxes whose base is a square of side 15 centimeters and a height of 25 centimeters.
a. What is the volume of the popcorn box?
b. The density of popcorn is 0.03 grams per cubic centimeter. What is the mass of the popcorn in the box?
c. When popcorn is popped, it is stored in a cube that is 45 centimeters on each side. How many boxes of popcorn can be filled from this container?
15. A company is producing a special part for a machine. The part consists of a cylinder of tin (white) that is inside of another cylinder made of copper (shaded). The part is shown below.
a. What is the total volume of the entire part? You may give your answer in terms of or to the nearest cubic millimeter.
b. What is the volume of the tin used in the part? You may give your answer in terms of or to the nearest cubic millimeter.
c. What is the volume of copper used in the part? You may give your answer in terms of or to the nearest cubic millimeter.
Use the word bank to complete the following definitions. Words may be used more than once.
Word bank: center focus directrix sum
difference radius equidistant foci
16. A circle is the set of points in the plane that are _________________ from a given point, called the _______________. The distance from the given point to every point on the circle is called the ____________.
17. A parabola is a set of points in the plane that are ___________ from a given point, called the _________, and a given line, called the ____________.
18. An ellipse is a set of points in the plane such that the ___________ of the distances from each point on the ellipse to two fixed points, called the ___________, is the same.
19. A hyperbola is a set of points in the plane such that the __________ of the distances from each point on the hyperbola, to two fixed points, called the ________, is the same.
For items 20 and 21, sketch graphs of the following circles.
Items 49 through 52 (this item continues on the next page) uses the quadrilateral below.
Kelly thinks that the figure might be a square. Remembering her geometry she does the following.
49. Kelly first needs to know if the figure is a parallelogram. Show that the figure is a parallelogram by showing that the slopes of opposite sides are equal.
50. Kelly now wants to determine if the figure is a rectangle. There are two ways to do this.
a. Show, by using slopes, that one of the angles is a right angle, and therefore there are four right angles and the figure is a rectangle.
b. Show that the diagonals of the parallelogram are congruent, and the figure is a rectangle.
51. Now that Kelly knows the figure is a rectangle. If she can show that it is a rhombus then it must be a square. Again there are two ways to do this.
a. Show that all four sides are the same length, and therefore the figure is a rhombus.
b. Show, by using slope computations that the diagonals are perpendicular, and therefore the figure is a rhombus.
52. Kelly also remembers a property of parallelograms that the diagonals bisect each other. Show that this true by determining the midpoint of each diagonal and showing that each midpoint has the same coordinates.
85. A piece of jewelry is a segment of a circle with radius 10 mm, as shown in the shaded region below.
What is the area, in square mm, of the shaded region? Your answer may be in terms of or rounded to two decimal places. If you use in a calculation, use the calculator’s key.