HONORS GEOMETRY BSemester Exam Review MCPS Page 1 20142015 Honors Geometry B Exam Review 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 oftor 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 thetkey on your calculator.Do not use 3.14 fort . On the next two pages you will find the formulas that will be available to you in the exam booklet.FIGURES ARE NOT DRAWN TO SCALE!!!!! HONORS GEOMETRY BSemester Exam Review MCPS Page 2 Area/Circumference Triangle:12A bh = Rectangle: A bh = Trapezoid: ( )1 212A b b h = +Parallelogram: A bh = Regular Polygon:1apothem perimeter2A = Circle Area:2A r t =Circle Circumference: 2 C r d t t = = VolumePrism/Cylinder: area of base height V Bh = = Pyramid/Cone: 1 1area of base height3 3V Bh = = Sphere: 343V r t =Density Formula Density = Mass Volume Coordinate Geometry Slope:2 12 1y yx x Midpoint:1 2 1 2,2 2x x y y + + | | |\ . Distance: ( ) ( )2 22 1 2 1x x y y + Conic Sections Circle and Parabola Equation of a circle with center at( ) , h kand radius r: ( ) ( )2 22x h y k r + =Equations of a parabola with vertex at( ) , h k with p the distance from vertex to focus and vertex to directrix : ( ) ( ) ( )2 2 14 or4x h p y k y k x hp = = ; opens up if0 p > , opens down if0 p < . ( ) ( ) ( )2 2 14 or4y k p x h x h y kp = = ;opens right if0 p > , opens left if0 p < . HONORS GEOMETRY BSemester Exam Review MCPS Page 3 Conic Sections Ellipse and Hyperbola Equations of an ellipse with center at( ) , h k ,a b > :Major axis horizontal:( ) ( )2 22 21x h y ka b + =Major axis vertical:( ) ( )2 22 21x h y kb a + = Equations of a hyperbola with center at( ) , h k :Transverse axis horizontal:( ) ( )2 22 21x h y ka b =Transverse axis vertical:( ) ( )2 22 21y k x ha b = Circles Arc Length (degrees): ( ) 2360xS r t = Arc Length (radians): S ru = Sector Area (degrees):( )2360xA r t = Sector Area (radians):( )22A rutt= Angle and Arc Formulas 12m A mBC Z= ( )12m GDE mGE mFH Z = + ( )12m J mMN mLK Z= 1801 radian = degreest 1 degree = radians180t

BACEDFGHLJKMNHONORS GEOMETRY BSemester Exam Review MCPS Page 4 Unit 31.Which pairs of figures have the same volume? a.b. c. For items 2 through 4, find the volume if each figure is revolved about the dashed line. 2.3.4. 5.Name the cross section that is formed in each case. a.A cone, cut by a plane parallel to the base, not through the apex (top). b.A cone, cut by a plane perpendicular to the base, through the apex (top). c.A rectangular pyramid, cut by a plane parallel to the base, not through the apex(top). d.A square pyramid, cut by a plane perpendicular to the base, not through the apex(top), through one side only. e.A cylinder, cut by a plane parallel to the base. f.A cylinder, cut by a plane perpendicular to the base. 4 r = 5555Cross sections equidistant from the bases are congruent and the heights of the solids are equal. 53 74 362 Bases are squares HONORS GEOMETRY BSemester Exam Review MCPS Page 5 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 ofthe popcorn in the box? c.When popcorn is popped, it is stored in a cube that is 45 centimeters on eachside.How many boxes of popcorn can be filled from this container? HONORS GEOMETRY BSemester Exam Review MCPS Page 6 11.The three figures below have the same volume.Find the missing height in each case. a.b. h = ______h = ________ For items 12 through 14, find the volume of each solid described. 12.A sphere with radius 6 cm. 13.A cone with radius 5 cm and height 9 cm. 14.A square pyramid with base of side 8 cm and height 3 cm. 12 3 6 h 3 3 2 24 h HONORS GEOMETRY BSemester Exam Review MCPS Page 7 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 termsoftor to the nearest cubic millimeter. b.What is the volume of the tin used in the part?You may give your answer interms oftor to the nearest cubic millimeter. c.What is the volume of copper used in the part?You may give your answer interms oftor to the nearest cubic millimeter. 5 mm 6 mm 4 mm 3 mm Copper Tin HONORS GEOMETRY BSemester Exam Review MCPS Page 8 Unit 4 Use the word bank to complete the following definitions.Words may be used more than once. Word bank:centerfocusdirectrixsumdifferenceradius 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 thedistances 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. 20. 2 24 x y + = 21.( ) ( )2 22 1 9 x y + + = x y Ox y OHONORS GEOMETRY BSemester Exam Review MCPS Page 9 For 22 and 23, write equations for the following circles and state the circumference and area of each circle. 22.23. Equation: _________________________Equation: _______________________ Circumference: _____________Circumference: ____________ Area : _______________Area:_____________ 24.Write the equation of a circle whose center is at the point( ) 1, 5 with the point( ) 7, 20on the circle. 25.Is the point( ) 5, 3on the circle whose equation is( ) ( )2 23 2 65 x y + + = ?Show how you determined your answer. xy Oxy OHONORS GEOMETRY BSemester Exam Review MCPS Page 10 For each equation of a circle, complete the square to put it in the form( ) ( )2 22x h y k r + =, then give the center and the radius. 26. 2 26 27 x y y + = 27. 2 22 16 35 0 x x y y + + + = For items 28 through 30, sketch graphs of the following parabolas.For each graph, also graph the focus and directrix. 28. 26 x y = 29. 28 y x =30.( ) ( )22 4 1 x y = x y Oxy Oxy OHONORS GEOMETRY BSemester Exam Review MCPS Page 11 For items 31 and 32, write the equation for the parabola.

31.32. 33.Look at the parabola below. Show that the point( ) 8, 8 Psatisfies the definition of the parabola by showing that the distance between the focus and the point( ) 8, 8 Pis equal to the distance from the point( ) 8, 8 Pto the directrix.xy O xy O6123456xyO1098765432 112345678910109875432178910F( ) 0, 2 F ( ) 2.5, 0 F HONORS GEOMETRY BSemester Exam Review MCPS Page 12 For items 34 and 35, sketch graphs of the following ellipses. 34. 2 2125 16x y+ = 35. ( ) ( )2 21 319 4y x ++ = For items 36 and 37, write equations for the ellipses below. 36.37. 38.Determine whether the point( ) 2,1is on the ellipse whose equation is 2 219 4x y+ =. x y Ox y Oxy Ox y OHONORS GEOMETRY BSemester Exam Review MCPS Page 13 For items 39 and 40, sketch the following hyperbolas. 39. ( )22214 1yx = 40. 2 219 9y x = For items 41 and 42, write equations for the hyperbolas below. 41.42. x y Ox y Ox y Ox y OHONORS GEOMETRY BSemester Exam Review MCPS Page 14 43.How many points of intersection do the graphs of the circle 2 216 x y + =and the parabola 2y x =have?You may use the grid below to help you. 44.How many points of intersection do the graphs of the circles( )222 4 x y + =and ( )222 4 x y + + =have?You may use the grid below to help you. xy Oxy OHONORS GEOMETRY BSemester Exam Review MCPS Page 15 Look at the graph of lineABon the coordinate plane below. 45.What is the length ofAB ? 46.Point C is between points A and B and has coordinates( ) 2, 2 . What is the ratio : AC CB ? 47.Determine the coordinates of point D so that the ratio: 1: 4 AD DB = . 6123456xyO10987 6 5 4 3 2 112345678910109875432178910( ) 10, 7 A ( ) 10, 8 B HONORS GEOMETRY BSemester Exam Review MCPS Page 16 48.Look at line k whose equation is3 2 y x = on the coordinate plane below. Write equations for the following lines. a.Parallel to line k, passing through the point( ) 0, 2 . b.Perpendicular to line k, passing through( ) 0, 5 . xy Ok HONORS GEOMETRY BSemester Exam Review MCPS Page 17 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 thereare four right angles and the figure is a rectangle. b.Show that the diagonals of the parallelogram are congruent, and the figure is arectangle. xy O ( ) 1, 4 A ( ) 2, 0 D ( ) 5,1 B ( ) 2, 3 C HONORS GEOMETRY BSemester Exam Review MCPS Page 18 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, andtherefore 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. HONORS GEOMETRY BSemester Exam Review MCPS Page 19 For items 53 and 54, determine the area and perimeter of each shaded figure below.Each grid line represents 10 meters.53.54. Area: ____________________Area: _____________________ Perimeter: ________________Perimeter: _________________ Unit 5 For items 55 through 63, find the value of x in each figure below. 55.56.57.C is the center xo xo xo C 50o 70o 160o xyxy 0 102030 40506070 8090100 0 102030 40506070 8090100 10 20 60 80 10 20 80 50 HONORS GEOMETRY BSemester Exam Review MCPS Page 20 58.59.60. ABis a diameter 61.62.63. 64.Quadrilateral ABCD is inscribed in the circle below. a.________ m A m C Z + Z= .Explain your reasoning. b.IfAC is a diameter, what is andm D m B Z Z ? Explain your reasoning. xo xo AB 28o 60o 60o 85o xo xo xo xo 50o 20o 290o 70o 35o 40o A D C B HONORS GEOMETRY BSemester Exam Review MCPS Page 21 Look at the circle O below. Determine the following: 65. mAB_______66. mEF_______ 67. mBC_______68.m AFB Z_______ 69.m FDB Z______70.m FEA Z_______ D 60oA B C E F 140o 20o42oO HONORS GEOMETRY BSemester Exam Review MCPS Page 22 Look at circle P below. Line m is tangent to the circle at point R. 8, 10, PR PS UW TZ = = Complete the following. 71.m PRS Z = ________72.SR =________ 73.TU is congruent to which segment? _______________ 74.WTU Zis congruent to what angle? _______________ 75. TWis congruent to which arc? ____________ 76.SX =_________ 77.What part of the circumference of a circle is represented by arc whose measure istradians? 78.What part of the circumference of a circle is represented by an arc whose measure is 3t radians? P R S T U W Z m X HONORS GEOMETRY BSemester Exam Review MCPS Page 23 Jerald is creating a new target game.The game involves concentric circles (circles with the same center P) and sectors as shown below.The radius of the smaller circle is 6 inches, while the radius of the larger circle is 9 inches. The length of DEis 12 inches. The measure ofAPC Zis 40o.The measure ofJPH Z is 90o. 79.What is the length of AB? _______ 80.What is the radian measure ofAPB Z? __________ 81.What is the area of sector EPD ? __________ 82.What is the length of AC? _________ 83.What is the area of sectorEPH? _____________ 84.What is the measure of the circle segment bounded byJHand JH? ____________ B D P C E H J A HONORS GEOMETRY BSemester Exam Review MCPS Page 24 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 t or rounded to two decimal places.If you uset in a calculation, use the calculatorstkey. 10 mm 10 mm 90o