Web viewDescribe a reflection and find the line of reflection. 9.1. ... To use tangent, ... what will be the volume of the water in the tank?

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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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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Duxbury Public Schools, 06/04/14,

Moved from right triangle unit to similarity

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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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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AlgebraSolve the equation for x.

1. x2 = (14−x)(x−5)2. 0 = 5x2 + 11x – 12

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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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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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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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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 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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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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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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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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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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Duxbury Public Schools, 06/04/14,

SR didn’t cover.


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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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69. Find the lateral area, surface area, and volume of the square pyramid on the right.



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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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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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Documents

Web viewDescribe a reflection and find the line of reflection. 9.1. ... To use tangent, ... what will be the volume of the water in the tank?