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Geo H - Final Exam - Study Guide & Review Packet
AlgebraObjective Section Note to Self
1. To solve a system of linear equations using substitution or elimination
1.8
2. To solve quadratic equations by factoring. 1.11
QuadrilateralsObjective Section Note to Self
3. To find the midpoint between two points in the coordinate plane 1.3
4. To identify and use properties of perpendicular bisectors 5.1
5. To identify and use properties of angle bisectors 5.1
6. To identify and use medians 5.27. To identify and use altitudes 5.28. To use properties of parallelograms to
solve problems 6.29. To use properties of diagonals of
rectangles, rhombi, and squares 6.410. To determine whether a parallelogram
is a rectangle, rhombus or square 6.4
11. To use properties of trapezoids and kites 6.6
ProofsObjective Section Note to Self
12. To recognize and use properties of equality and congruence 2.6
13. To prove statements using statements, postulates, and properties
2.8
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Geo H - Final Exam - Study Guide & Review Packet
TransformationsObjective Section Note to Self
1. Identify transformations as reflections, rotations, translations, or a composition
4.7
2. Reflect points over a line 9.13. Describe a reflection and find the line
of reflection 9.14. Translate points if given vector
notation or function notation 9.25. Describe a translation using vector
notation or function notation 9.26. Rotate points (90, 180, or 270
degrees) around the origin 9.37. Describe a rotation 9.38. Transform points using a composition
of transformation 9.49. Describe a composition of
transformations 9.4
SimilarityObjective Section Note to Self
1. To write ratios 7.12. To write and solve proportions 7.13. To use proportions to identify similar
polygons 7.24. To solve problems using the
properties of similar polygons 7.25. To identify similar triangles 7.36. To solve problems using similar
triangles 7.37. To use proportional parts within
triangles 7.48. To use proportional parts with parallel
lines 7.49. To use proportional relationships
between angle bisectors, medians, and altitudes of similar triangles
7.5
10. To use the Triangle Angle Bisector Theorem 7.5
11. To dilate a figure using a given scale factor and center of dilation 9.6
12. To predict and apply the relationship between the scale factor and side
9.6
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Geo H - Final Exam - Study Guide & Review Packetlengths
Right TrianglesObjective Section Note to Self
1. Find the geometric mean between two numbers 8.1
2. Solve problems using similarity relationships in right triangles (geometric mean)
8.1
3. To use 45-45-90 right triangles to solve problems 8.3
4. To use 30-60-90 right triangles to solve problems 8.3
5. To use tangent, sine, and cosine ratios to determine side lengths of triangles 8.4
6. To use tangent, sine, and cosine ratios to determine angle measures in triangles
8.4
7. To use angles of elevation and depression to solve problems 8.5
AreaObjective Section Note to Self
1. To identify and use parts of circles 10.12. To find the circumference of a circle 10.13. To make constructions related to
circles 10.14. To calculate the area of
parallelograms and triangles 11.15. To calculate the area of trapezoids,
kites, and rhombi 11.26. To find the area of circles 11.37. To find the area of sectors 11.38. To calculate the area of regular
polygons 11.49. To calculate the area of composite
figures 11.410. To find the ratio of perimeters and
areas of similar figures 11.511. To use ratios to find the perimeter and
area of similar figures 11.5
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Geo H - Final Exam - Study Guide & Review Packet
3-D FiguresObjective Section Note to Self
1. To find the lateral area and surface area of a prism 12.2
2. To find the lateral area and surface area of a cylinder 12.2
3. To find the lateral area and surface area of a pyramid 12.3
4. To find the lateral area and surface area of a cone 12.3
5. To find the volume of a prism 12.46. To find the volume of a cylinder 12.47. To find the volume of a pyramid 12.58. To find the volume of a cone 12.59. To find the surface area of a sphere 12.610. To find the volume of a sphere 12.611. To find the volume and surface areas
of similar solids 12.8
To Help You Review Practice problems are in this packet. Review past tests and quizzes to find areas where you need improvement Raise specific questions or ask to see specific problems during the review As part of the review, we will go over problems that students request (as time permits). Review the attached study and test-taking tips
Study Tips1. Get help ASAP. Do not wait until the day before an assessment to see the
teacher for extra help. If you show up with questions regarding 12 different topics, and there are several other students seeking help, you might not be able to get all your questions cleared up.
2. Do not wait until the night before to start studying. If you wait, you might not be able to ask your teacher for help if you have trouble. The more prepared you are, the less stress you should feel during the assessment.
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Geo H - Final Exam - Study Guide & Review Packet3. Complete any practice tests. These are found in most textbooks. If no
practice test is available, try a few problems from each relevant section/topic. Try them under test conditions (no notes, quiet environment, set amount of time). Check your answers with the back of the book. Bring SPECIFIC questions to your teacher.
4. Try the teacher’s examples on your own. Check and compare your work to the teacher’s solutions from the notes. Bring SPECIFIC questions to your teacher.
5. Review notes for all sections and topics. Be sure you understand the definitions, rules, formulae, processes, strategies, and examples. Bring SPECIFIC questions to your teacher.
6. Make and study flashcards. Include:
Subject of Card Front BackVocabulary Word Definition & pictureTheorems / Postulates Name Wording & pictureProperties Name Wording & exampleFormulae Formula What each variable
representsNecessary units of measure
Process What the type of problem is called or what it looks like
Steps on how to solve it (put in your own words, if desired)
Strategies Topic of problem Strategies talked about in class
Common errors Topic of problem Things to watch out for
7. Avoid some stress: On the day of the assessment, do not talk to other students about it unless you think they can clarify a problem you are having.
Test-Taking Tips1. Bring a calculator with which you are familiar. While dividing decimals by
hand is noble, it eats up your time and takes your focus away from the test material.
2. Use a pencil and eraser. Crossing out mistakes leaves you with work that may be difficult for you to read.
3. Write as neatly as possible. Many students misread their own writing. Also be sure you have correctly copied all the information from the problem.
4. Write information down as soon as you get the test. Write formulae, rules, etc. somewhere on the test so you do not forget them later.
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Geo H - Final Exam - Study Guide & Review Packet5. Read the instructions carefully. Be sure you are answering the question
being asked, and that you are answering all parts. You are not always just solving for X.
6. Do the easy problems first. This lets you spend more time on difficult problems. If you are prepared, some of the problems (vocabulary, fill-ins, etc.) should be very quick to complete. Do problems in this order: easy problems, problems with the highest point value, then do the remaining problems.
7. Do not spend too much time on one problem. Go back if you get stuck. Something that comes up later in the test may help you.
8. Remember the questions the teacher asks the class when solving similar problems. It’s easy to “get it” in class because the teacher leads you to the solution with these questions. Lead yourself with these same questions.
9. Check your work and your answers when you finished the test. Plug answers back into equations. Check to make sure your answers are reasonable and/or realistic: Could the length of a ladder really be -0.5ft?
Final Exam Information Check weekly syllabus for date/time of final exam Bring a #2 pencil, calculator, and something to read (in case you finish early) You will be given a copy of the formula sheet that is attached at the end of this guide Final Exam breakdown (45 questions):
Non-Calculator: 13 multiple choiceCalculator: 21 multiple choice
11 short answer/open response Your Final Exam grade is 10% of your grade for the entire year
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Geo H - Final Exam - Study Guide & Review Packet
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Geo H - Final Exam - Study Guide & Review Packet
AlgebraSolve the equation for x.
1. x2 = (14−x)(x−5)2. 0 = 5x2 + 11x – 12
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Geo H - Final Exam - Study Guide & Review Packet
QuadrilateralsFind the value of each variable in each parallelogram.
3. 4.
5. Determine whether WXYZ with vertices W(–2, 0), X(1, 1), Y(2, –2), Z(–1, –3) is a rhombus, a rectangle, or a square. List all that apply.
Quadrilateral MNPQ is a rectangle.6. If m∠MNQ = (3x + 3) ° and m∠QNP = (10x - 4)°,
find m∠MQN.
7. If MC = 4.5x - 2.5 and NC = 4x + 1.5, find QN.
Quadrilateral ABCD is a rhombus. Find each value or measure.
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Geo H - Final Exam - Study Guide & Review Packet
8. m∠DBC
9. DC
Find each measure.10. ∠A 11. MR
ProofsUse the first column to correctly order the given statements and corresponding reasons.
12.
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Geo H - Final Exam - Study Guide & Review Packet
Statement: Reason:1.m<U = 42° Given2.m<U + m<T = 180° Definition of Supplemental Angles3.<U and <T are supplementary If a quadrilateral is a , then
consecutive s are supplementary.4. STUV Given5. 42 + T = 180 Substitution Property of Equality6. m<T=138° Subtraction Property of Equality
13.
m<1 + m<3 = 180° Definition of Supplementary Angles<1 and <2 are supplementary Definition of Supplementary Anglesm<2 = m<3 Vertical s are = in measureline m || line n If two lines are cut by a transversal
and same-side interior angles are supplementary, then the lines are parallel
m<1 + m<2 = 180° Substitution Property of Equality<1 and <3 are supplementary Given
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Geo H - Final Exam - Study Guide & Review Packet
Transformations14. Identify the type of congruence transformation shown as a either a reflection, translation, or rotation.
Graph each pair of triangles with the given vertices. Then, identify the transformation.
13. A(2, 2), B(4, –1), C(1, –2);M(–4, –1), N(–1, –2), P(–2, 2)
14. A(–1, –1), B(–1, –4), C(2, –4);
M(–1, 1), N(–4, 1), P(–4, 4)
Graph each figure and its image under the given reflection.15. ΔABC with vertices
A(–1, –4), B(–5, 3), and C(0, 5)in the line y = x
16. quadrilateral WXYZ with vertices
W(–3, –2), X(–4, 1), Y(1, 4), and Z(2, –2)in the y-axis
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Geo H - Final Exam - Study Guide & Review Packet
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Geo H - Final Exam - Study Guide & Review PacketGraph each figure and its image after the specified rotation about the origin.
17. ΔPQR with vertices P(–1, –2), Q(–5, –4), and R(–3, –6); 90°
18. parallelogram WXYZ with vertices W(–3, 3), X(–2, 7), Y(4, 5) and Z(3, 1); 180°
Graph each figure with the given vertices and its image after the indicated translation.
Find the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor.
19. ΔDEF: D(–5, 1), E(–3, 5), F(0, 3)
Translation: along <4, 3>
20. A(–5, –4), B(–2, –3), C(–1, –6), D(–4, –8); k = 12
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Geo H - Final Exam - Study Guide & Review Packet
Similarity21.The ratios of the measures of the three angles in a triangle are 4 : 5 : 11.
Find the measure of each angle.
Determine whether each pair of figures is similar. If so, write the similarity statement and scale factor. If not, explain your reasoning.
22. 23.
Each pair of polygons is similar. Find the value of x.24. 25.
Determine whether the triangles are similar. If so, write a similarity statement.26. 27.
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Geo H - Final Exam - Study Guide & Review Packet28.When Rachel stands next to her cousin, Rachel’s shadow is 2 feet long and
her cousin’s shadow is 1 foot long. If Rachel is 5 feet 6 inches tall, how tall is her cousin?
29.
30.
31.
32. Find x.
33.Jason wants to determine if his foosball table is a dilation of his school’s soccer field. The dimensions of the table are 30 inches by 55.5 inches, and the dimensions of the field are 60 yards by 110 yards. Is the table a dilation? Explain.
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Geo H - Final Exam - Study Guide & Review Packet
Right TrianglesFind x.
34. 35. 36.
37. 38. 39.
In ∆TRN, R is a right angle. TN = 13 and RN = 5. Draw a diagram and find the following ratios:
40. Cos T
41. Tan T
42. Sin T
43. Sin N
44. Tan N
45. Cos N
46.∆ABC is an isosceles right triangle and B is a right angle. Find the exact value of Tan 45°.
Find x.47. 48. 49.
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Geo H - Final Exam - Study Guide & Review Packet
50.Kara is standing about 50 feet from the base of her apartment building, looking up at it with an angle of elevation of 75°. What is the approximate height of Kara’s building?
AreaFind the perimeter and area of each figure. Round to the nearest tenth if necessary.
51. 52. 53.
54.The height of a parallelogram is three times its base. If the area of the parallelogram is 108 square meters, find its base and height.
Find the indicated measure. Round to the nearest tenth.55. 56. 57.
The area of a circle is 201 square meters. Find
Find the diameter of a circle with an area of 79
Find the area of the sector.
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Geo H - Final Exam - Study Guide & Review Packet
the radius. square feet.
58. 59.Find the area of a regular hexagon that has an apothem of 6√3 cm and a side length of 12 cm.
Find the area of the composite figure below.
60. Find the area of the regular pentagon on the right.
61. Find the area of the composite figure on the right.
62. The pentagons are similar. Find the area of the small pentagon.
63. The triangles are similar find x.
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Geo H - Final Exam - Study Guide & Review Packet
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Geo H - Final Exam - Study Guide & Review Packet
3D Figures64. Find the lateral area, surface area, and volume
of the figure on the right.
65. Find the lateral area, surface area, and volume of the figure on the right.
Sarah has a fish tank with the dimensions shown.
66. What is the surface area of the fish tank?
67. If Sarah fills the tank to a depth of 17 inches, what will be the volume of the water in the tank?
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Geo H - Final Exam - Study Guide & Review Packet
68. Find the lateral area, surface area, and volume of the figure on the right.
69. Find the lateral area, surface area, and volume of the square pyramid on the right.
70. Find the lateral area, surface area, and volume of the figure on the right.
71. Find the lateral area, surface area, and volume of the figure on the right.
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Geo H - Final Exam - Study Guide & Review Packet
72. Find the surface area and volume of the figure on the right.
73. Find the surface area and volume of the figure on the right.
74.An office has recycling barrels that are cylindrical with cardboard sides and plastic lids and bases. Each barrel is 3 feet tall with a diameter of 30 inches. How many square feet of cardboard are used to make each barrel?
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Geo H - Final Exam - Study Guide & Review PacketThis is the formula sheet that you will be given on the final exam.
Area Lateral Area and Surface Area
Volume
Square:Cube: Cube:
Rectangle:Prism: Prism:
Triangle:
Cylinder: Cylinder:
Trapezoid:
Pyramid: Pyramid:
Parallelogram: Cone:
Cone:
Circle: Sphere:Sphere:
Regular polygon:
Kite & Rhombus:
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Geo H - Final Exam - Study Guide & Review Packet
Circles
C =
C = Sector area: Arc length:
1. x = -4, 72. Change to: 0 = 5x2 + 11x – 12 x= 5/4 , -33. x = 4, y = 94. x = 2, y = 35. slopes are opp. recip.,sides ≅. WXYZ is square.6. m<MQN = 66°7. QN = 678. m<DBC = 53°9. DC = 1510. m<A = 123°11. MR = 1212. 270°rotation about the origin13. reflection across the “x” axis14. translation <-3, 5>15. (x, y) → (y, x)16. (x, y) → (-x, y)17. (x, y) → (-y, x)18. (x, y) → (-x, -y)19. (x, y) → (x+4, y+3)20. (x, y) → (0.5x, 0.5y)21. 36° ,45°, 99°22. not similar. only 1 ≅,sides not proportional23. Similar. MNPQ XWZY. K = 2/324. x = 525. x = 8.826. not similar27. Similar. ∆ NMP ∆ ZYX28. x = 2’9”29. x = 5/430. x = 6.7531. x = 51°32. x = 60/7 = 8 4/7
33. Not dilation; dimensions not scaled the same 34. x = 1135. x = 7√336. x = 9√337. x = 14√238. x = 22.6°39. x = 13.340. 12/1341. 5/1242. 5/1343. 12/1344. 12/545. 5/1346. 147. x = 7√348. x = 28.249. 22.6°50. x = 186.6 ft51. P = 43.8cm, A = 84cm2
52. P = 45.8in, A = 72in2
53. P = 60in, A = 195in2
54. b = 6m, h = 18m55. r = 8.0m56. d = 10ft57. A = 18.8cm2
58. A = 374.1cm2
59. A = 252.6cm2
60. A = 84.9m2 61. A = 238.1in2
62. A1=34.7ft2
63. x = 10cm64. LA= 180in2, SA=228in2, V=216in3
65. LA= 504m2, SA=720m2, V=2268m3
66. LA= 1512in2, SA=2088in2
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Geo H - Final Exam - Study Guide & Review Packet67. V= 4896in3
68. LA= 37.7ft2, SA=51.8ft2, V=28.3ft3
69. LA =238.6mm2, SA=319.6mm2, V=378mm3
70. LA=60πin2=188.5in2, SA=301.6in2, V=301.6in3
71. LA=2704ft2, SA=3184ft2, V=9840ft3
72. SA=1661.9ft2, V=6370.6ft3
73. with r=19cm: SA=3402.3cm2, V=14365.5cm3
74. LA=23.6ft2
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