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AlgebraObjectiveSectionNote to SelfTo solve a system of linear equations using substitution or elimination1.8To solve quadratic equations by factoring.1.11QuadrilateralsObjectiveSectionNote to SelfTo find the midpoint between two points in the coordinate plane1.3To identify and use properties of perpendicular bisectors5.1To identify and use properties of angle bisectors5.1To identify and use medians5.2To identify and use altitudes5.2To use properties of parallelograms to solve problems6.2To use properties of diagonals of rectangles, rhombi, and squares6.4To determine whether a parallelogram is a rectangle, rhombus or square6.4To use properties of trapezoids and kites6.6ProofsObjectiveSectionNote to SelfTo recognize and use properties of equality and congruence2.6To prove statements using statements, postulates, and properties2.8TransformationsObjectiveSectionNote to SelfIdentify transformations as reflections, rotations, translations, or a composition4.7Reflect points over a line9.1Describe a reflection and find the line of reflection9.1Translate points if given vector notation or function notation9.2Describe a translation using vector notation or function notation9.2Rotate points (90, 180, or 270 degrees) around the origin9.3Describe a rotation9.3Transform points using a composition of transformation9.4Describe a composition of transformations9.4SimilarityObjectiveSectionNote to SelfTo write ratios7.1To write and solve proportions7.1To use proportions to identify similar polygons7.2To solve problems using the properties of similar polygons7.2To identify similar triangles7.3To solve problems using similar triangles7.3To use proportional parts within triangles7.4To use proportional parts with parallel lines7.4To use proportional relationships between angle bisectors, medians, and altitudes of similar triangles 7.5To use the Triangle Angle Bisector Theorem7.5To dilate a figure using a given scale factor and center of dilation9.6To predict and apply the relationship between the scale factor and side lengths9.6Right TrianglesObjectiveSectionNote to SelfFind the geometric mean between two numbers8.1Solve problems using similarity relationships in right triangles (geometric mean)8.1To use 45-45-90 right triangles to solve problems8.3To use 30-60-90 right triangles to solve problems8.3To use tangent, sine, and cosine ratios to determine side lengths of triangles8.4To use tangent, sine, and cosine ratios to determine angle measures in triangles8.4To use angles of elevation and depression to solve problems8.5AreaObjectiveSectionNote to SelfTo identify and use parts of circles10.1To find the circumference of a circle10.1To make constructions related to circles10.1To calculate the area of parallelograms and triangles11.1To calculate the area of trapezoids, kites, and rhombi11.2To find the area of circles11.3To find the area of sectors11.3To calculate the area of regular polygons11.4To calculate the area of composite figures11.4To find the ratio of perimeters and areas of similar figures11.5To use ratios to find the perimeter and area of similar figures11.53-D FiguresObjectiveSectionNote to SelfTo find the lateral area and surface area of a prism12.2To find the lateral area and surface area of a cylinder12.2To find the lateral area and surface area of a pyramid12.3To find the lateral area and surface area of a cone12.3To find the volume of a prism12.4To find the volume of a cylinder12.4To find the volume of a pyramid12.5To find the volume of a cone12.5To find the surface area of a sphere12.6To find the volume of a sphere12.6To find the volume and surface areas of similar solids12.8To Help You ReviewPractice problems are in this packet.Review past tests and quizzes to find areas where you need improvementRaise specific questions or ask to see specific problems during the reviewAs part of the review, we will go over problems that students request (as time permits).Review the attached study and test-taking tipsStudy TipsGet 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.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 plete 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.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.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.Make and study flashcards. Include:Subject of CardFrontBackVocabularyWordDefinition & pictureTheorems / PostulatesNameWording & picturePropertiesNameWording & exampleFormulaeFormulaWhat each variable representsNecessary units of measureProcessWhat the type of problem is called or what it looks likeSteps on how to solve it (put in your own words, if desired)StrategiesTopic of problemStrategies talked about in classCommon errorsTopic of problemThings to watch out forAvoid 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 TipsBring 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.Use a pencil and eraser. Crossing out mistakes leaves you with work that may be difficult for you to read.Write as neatly as possible. Many students misread their own writing. Also be sure you have correctly copied all the information from the problem.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.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.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.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.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.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 InformationCheck weekly syllabus for date/time of final examBring 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 guideFinal Exam breakdown (45 questions): Non-Calculator:13 multiple choiceCalculator:21 multiple choice11 short answer/open responseYour Final Exam grade is 10% of your grade for the entire yearAlgebraSolve the equation for x.x2 = (14-x)(x-5)0 = 5x2 + 11x – 12QuadrilateralsFind the value of each variable in each parallelogram.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.If m∠MNQ = (3x + 3) ° and m∠QNP = (10x - 4)°, find m∠MQN.If MC = 4.5x - 2.5 and NC = 4x + 1.5, find QN.Quadrilateral ABCD is a rhombus. Find each value or measure.m∠DBCDCFind each measure.∠AMRProofsUse the first column to correctly order the given statements and corresponding reasons.Statement:Reason:1.m<U = 42°Given2.m<U + m<T = 180°Definition of Supplemental Angles3.<U and <T are supplementaryIf a quadrilateral is a? INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET , then consecutive? INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET INCLUDEPICTURE "" \* MERGEFORMATINET s are supplementary.4. STUVGiven5. 42?+?T = 180?Substitution Property of Equality6. m<T=138°Subtraction Property of Equality13. m<1 + m<3 = 180°Definition of Supplementary Angles<1 and <2 are supplementaryDefinition of Supplementary Anglesm<2 = m<3Vertical?s are = in measureline m || line nIf two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallelm<1 + m<2 = 180°Substitution Property of Equality<1 and <3 are supplementaryGivenTransformations14. 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.A(2, 2), B(4, –1), C(1, –2); M(–4, –1), N(–1, –2), P(–2, 2) 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.ΔABC with vertices A(–1, –4), B(–5, 3), and C(0, 5) in the line y = xquadrilateral WXYZ with vertices W(–3, –2), X(–4, 1), Y(1, 4), and Z(2, –2) in the y-axisGraph each figure and its image after the specified rotation about the origin.ΔPQR with vertices P(–1, –2), Q(–5, –4), and R(–3, –6)? 90°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.ΔDEF: D(–5, 1), E(–3, 5), F(0, 3) Translation: along <4, 3>A(–5, –4), B(–2, –3), C(–1, –6), D(–4, –8); k = 12 SimilarityThe 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.Each pair of polygons is similar. Find the value of x.Determine whether the triangles are similar. If so, write a similarity statement.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?Find x.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.Right TrianglesFind x.In ?TRN, R is a right angle. TN = 13 and RN = 5. Draw a diagram and find the following ratios: Cos TTan T Sin TSin NTan N Cos N?ABC is an isosceles right triangle and B is a right angle. Find the exact value of Tan 45°.Find x.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.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.The area of a circle is 201 square meters. Find the radius.Find the diameter of a circle with an area of 79 square feet.Find the area of the sector.Find the area of a regular hexagon that has an apothem of 63 cm and a side length of 12 cm.Find the area of the composite figure below.Find the area of the regular pentagon on the right.Find the area of the composite figure on the right.The pentagons are similar. Find the area of the small pentagon.The triangles are similar find x.3D FiguresFind the lateral area, surface area, and volume of the figure on the right.Find the lateral area, surface area, and volume of the figure on the right.Sarah has a fish tank with the dimensions shown.What is the surface area of the fish tank?If Sarah fills the tank to a depth of 17 inches, what will be the volume of the water in the tank?Find the lateral area, surface area, and volume of the figure on the right.Find the lateral area, surface area, and volume of the square pyramid on the right.Find the lateral area, surface area, and volume of the figure on the right.Find the lateral area, surface area, and volume of the figure on the right.Find the surface area and volume of the figure on the right.Find the surface area and volume of the figure on the right.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?This is the formula sheet that you will be given on the final exam.AreaLateral Area and Surface AreaVolumeSquare:Cube: Cube:Rectangle:Prism:Prism:Triangle:Cylinder:Cylinder:Trapezoid:Pyramid:Pyramid:Parallelogram: Cone:Cone:Circle:Sphere:Sphere:Regular polygon:Kite & Rhombus: CirclesC = 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 4/733. Not dilation; dimensions not scaled the same 34. x = 1135. x = 7336. x = 9337. x = 14238. x = 22.6°39. x = 13.340. 12/1341. 5/1242. 5/1343. 12/1344. 12/545. 5/1346. 147. x = 7348. x = 28.249. 22.6°50. x = 186.6 ft51. P = 43.8cm, A = 84cm252. P = 45.8in, A = 72in253. P = 60in, A = 195in254. b = 6m, h = 18m55. r = 8.0m56. d = 10ft57. A = 18.8cm258. A = 374.1cm259. A = 252.6cm260. A = 84.9m2 61. A = 238.1in262. A1=34.7ft263. x = 10cm64. LA= 180in2, SA=228in2, V=216in365. LA= 504m2, SA=720m2, V=2268m366. LA= 1512in2, SA=2088in267. V= 4896in368. LA= 37.7ft2, SA=51.8ft2, V=28.3ft369. LA =238.6mm2, SA=319.6mm2, V=378mm370. LA=60πin2=188.5in2, SA=301.6in2, V=301.6in371. LA=2704ft2, SA=3184ft2, V=9840ft372. SA=1661.9ft2, V=6370.6ft373. with r=19cm: SA=3402.3cm2, V=14365.5cm374. LA=23.6ft2 ................
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