Hilliard City Schools GAC 2

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Hilliard City SchoolsGAC 2Course Proficiency Study GuideI.Course Proficiency Purpose:The purpose of this study guide is to aid the students who wish to take theproficiency assessment for the credit flex option. Items that the student will berequired to know for proficiency will be administered in a multiple choice test.II.Description of the Assessment Format:This test is in a multiple choice format of 91 questions. You must use a # 2 pencilbecause it is scantron based. You must bring your own calculator but a formulasheet and scrap paper will be provided for you. Each question is worth 1 point andyour final grade will be based of number correct out of total questions.III.Proficiency Content must include:Equations Expressions & Inequalities:Solving EquationsSolving InequalitiesAbsolutely Value Equations and InequalitiesRadical Expressions & EquationsThe Pythagorean TheoremDistance and Midpoint FormulasSimplifying RadicalsOperations with Radical ExpressionsSolving Radical EquationsTrigonometric RatiosPolygons & QuadrilateralsThe Polygon Angle-Sum TheoremsProperties of ParallelogramsProving that a Quadrilateral is a ParallelogramProperties of Rhombuses, Rectangles & SquaresConditions for Rhombuses, Rectangles & SquaresTrapezoids & KitesPolygons in the Coordinate PlaneApplying Coordinate GeometryPage 1 of 3

Proofs using Coordinate GeometryRight Triangles & TrigonometryThe Pythagorean Theorem and Its ConverseSpecial Right TrianglesTrigonometryAngles of Elevation & DepressionAreaAreas of Parallelograms & TrianglesArea of Trapezoids, Rhombuses & KitesArea of Regular PolygonsPerimeters and Areas of Similar FiguresTrigonometry & AreaCircles & ArcsArea of Circles & SectorsFunctions Equations and GraphsRelations & FunctionsDirect VariationStandard FormParallel and Perpendicular LinesScatter Plots and Trend LinesSlope-Intercept FormLinear EquationsTwo-Variable InequalitiesLinear SystemsSolving Systems using Tables & GraphsSolving Systems AlgebraicallySystems of InequalitiesPolynomials & FactoringAdding & Subtracting PolynomialsMultiplying & FactoringMultiplying BinomialsMultiplying Special CasesFactoring x bx c2Factoring ax bx c2Factoring Special CasesFactoring by GroupingPage 2 of 3

Quadratic Functions & EquationsQuadratic GraphsQuadratic FunctionsSolving Quadratic EquationsFactoring to Solve Quadratic EquationsCompleting the SquareThe Quadratic Formula & the DiscriminantRational ExpressionsSimplifying Rational ExpressionsMultiplying & Dividing Rational ExpressionsDividing PolynomialsIV.Suggested Resources:Geometry and Algebra Connections 2 text bookReview Packet with answers (This review does not cover everything on the test.)Page 3 of 3

GAC 2NameCourse Proficiency Review j U240M1I1T 3KtuHtxaA cSeo4fBtPw8a4rDeP 9LiLRCd.y c YAIl4lu GrPixg3hdtLsp 9r4etsbesrqvaeQd5.sSolve each equation.1) p ( p)A) C) 2) n nB) D) A) C) B) D) Solve each inequality.3) m mA) m C) m 4) (r )B) m D) m A) r C) r B) r D) r Solve each compound inequality.5) b or b A) b or b C) b or b B) b D) b v and v 6)A) v C) v B) v D) v Solve each equation.7) n A)C) , , B)D) 8) k , ,A) q u2b0i1R1I QKHuetcaJ CSsoMfmt6wMa3rneX UL6LHCK.E Q QA4l8l7 0rUi3gIhGt2s0 Sr2eOsAeCrRvEexdC.j s bMua2ddeA GwMirtBhW QI4nxfbiOndiYtyeO 7Afl7g3eEbor1ae O2O.HC)-1- , B) D) , Worksheet by Kuta Software LLC

Sketch the graph of each line.10) x y A) 9) y x A) B) B) C) C) D) D) O U2g0A1Y16 3KvuhtjaP bSBolfPtYw9aarue0 ULnLjCd.Y v AA9lwlm Mr7iGgzh9txsZ hrAefsjeArTv9e5dU.A W 8MVaedreL 7wqiZt4hT MImnwfFi5nuiktyeX nAqlDgiewb3r9aJ x2e.f-2-Worksheet by Kuta Software LLC

Write the slope-intercept form of the equation of each line given the slope and y-intercept. 11) Slope , y-intercept A) y x B) y x C) y x D) y x Write the slope-intercept form of the equation of each line.12) x y A) y x C) y x B) y x D) y x 13) y ( x ) A) y x B) y x C) y x D) y x Write the slope-intercept form of the equation of the line through the given point with the given slope.14) through: ( , ), slope A)B)C)D)y x y x y x y x 15) through: ( , ), slope A) y x C) y x B) y x D) y x Write the slope-intercept form of the equation of the line through the given points.16) through: ( , ) and ( , )A)B)C)D)y x y x y x y x N 926001L1e pKXuJtOaI ESholfrtswAaSruem pLyLqCk.h G DAKlzlb Crbi9g7hFtCs1 cr4eWsaeXrbvzeSd1.G 9 6M0aGdsea dwLiitjhr vIgn9f6isnhiyteej 1AplJgYeqbUrAaC r2I.o17) through: ( , ) and ( , ) A) y x B) y x C) y x D) y x -3-Worksheet by Kuta Software LLC

Write the slope-intercept form of the equation of the line described.18) through: ( , ), parallel to y x A) y x C) y x 19) through: ( , ), parallel to y x B) y x D) y x A) y x C) y x 21) through: ( , ), perp. to y x 20) through: ( , ), perp. to y x A) y x C) y x B) y x D) y x A) y x C) y x B) y x D) y x B) y x D) y x Write the standard form of the equation of each line.22) y xA)B)C)D) x y x y x y x y L s2a0U1N1l mK9uHtJaW VSWorf9tmwuaSr9eM jLvLgCZ.u W iALlol7 trHicgkhstAs3 yr2eKsDeErjv8eZd9.E e AMzafdpeg NwSiatyhT SIsnOfqidnei7txer oArl7gfeAb1rLaT Y2D.g23)A)B)C)D)-4- y x x y x y x y x y Worksheet by Kuta Software LLC

Sketch the graph of each linear inequality.25) x y A) 24) y x A) B) B) C) C) D) D) K E270f1m1b FKeuwtaa8 SSVovfXtJw1a0rfey ILCLlC5.r P UA4lKlf Ar5itg9h7t1sH 4rJe5sRetrPvieodD.e q SMBaRdae5 RwXiutzhP qIRncf7isn3iOtneE iAIlUg5eHbzrLaj i2X.0-5-Worksheet by Kuta Software LLC

Simplify.26) b 28) b b A) b bC) 30)A)B)C)D)B) D) ( n ) n 29) v v A) v C) B) D) 31) ( x ) n n n n n32) ( )( )A) C) 27)B) D) 34) A)B)C)D)33)( x x x x x x x x x x )( )A) C) B) D) 35) Solve each equation. Remember to check for extraneous solutions.36) x A) C) 38)B) D) n A) C) B) D) , S m2K0M1j1S CKGugtYaw 5Sfo9fjtbw8a1raeI nLKLyCq.G U MAPlMlN trziZgrhytssz vr2evs8eArAvbeadL.J R SMWaXd4ew iw0ietJh2 1I7n3fZiwniiXtCeD 8A9l7ghe9bfrXaB m21.e37)m m A) C) 39) x xA) , C) -6-B) D) , B) , D) , Worksheet by Kuta Software LLC

Solve each system by graphing.41) y x y x 40) y x y x A) ( , )C) ( , )A) ( , )C) ( , )B) ( , )D) ( , )B) ( , )D) ( , )Solve each system algebraically.42) y x y A) ( , )C) No solution43) x y x y B) ( , )D) ( , )44) x y x y A)B)C)D)( , )( , )Infinite number of solutions( , ) X 22e0I1w15 oKDu8tmal 0SQobfytjwTaYrweP PLvL9C1.X k 4Adlil4 KrViygth5tNs8 urneIsbecrWvaebdL.e t xMLaddvep nwIiPtsh8 XIYnRfkiQnUintLeb EA3lagXeibAr4aK r2Y.HA) ( , )C) ( , )B) ( , )D) ( , )45) x y x y A)B)C)D)-7-( , )Infinite number of solutions( , )No solutionWorksheet by Kuta Software LLC

Sketch the solution to each system of inequalities.46) y x y x A) 47) y x y x A) B) B) C) C) D) D) D Z2E0h1r17 4KJuDtoah 3S2orfWtiwVazrter 3LfLtC9.9 Q ZA6lkle Ar1iTgyh7ttsU Fr0eDseeQrGvuekdg.9 l DMxa4dreB zw3iCtBhD LIWn6fsiRnPiHtJew HAalCgPePbVryaE F27.C -8-Worksheet by Kuta Software LLC

Sketch the graph of each function.48) y x x A) 49) y x x A) B) B) C) C) D) D) x R2d0c1A14 vKDuTtnau bSVovfMt6w4aVrReg aLILzC0.E d bAdlOlh 2rJi6gZhvtdsb ZrOess3emrCvheLdF.V 6 sMfaddde2 awQimt0hh CIen1foi5nPijtteS 1AIlOgoezbxr9aP u2I.G -9-Worksheet by Kuta Software LLC

Factor each completely.50) n n n A)B)C)D)51) n n n (n )(n ) n (n )(n ) n (n )(n )Not factorableA)B)C)D)52) k kA)B)C)D)(n )(n )(n )(n )Not factorable(n )(n )53) x x k(k ) k(k ) (k )(k ) k(k )B) x( x )D) x( x )A) x( x )C) x( x )54) k 55) n n A) (k ) A) (n ) B) ( n )( n )C) (n )(n )B) ( k ) C) ( k )( k )D) Not factorableD) (n ) Solve each equation by taking square roots.56) x A)C) , , B) D) , 57) p A) , C), D) , B) Solve each equation by factoring.58) n nA) , C) 59) m mB) D) , 60) r r A) , C) , A) , C) , B) , D) , 61) x xB) , D) , p r2c0Q1c1n lKAuYteam dSOoMfltVwwa7r5ec QLNLeCw.V y kA0lylB XraiVgBhWtosl mrXeosReFrEvNe2dl.2 I 0MUaMdEeV 0wsiZtqhs kIhnjfJiknFiztEeM hALlXg0eqbFrgaj t2A.6A) , C) , -10-B) , D) , Worksheet by Kuta Software LLC

Find the value that completes the square and then rewrite as a perfect square. 62) x x 63) m m 64) p p 65) r r Solve each equation by completing the square.66) a a A)B)C)D)67) x x , , , , A)B)C)D) , , , , Solve each equation with the quadratic formula.68) k k A) , C) , 69) p p B) , D) , A) , C) B) , D) , Find the discriminant of each quadratic equation then state the number and type of solutions.70) n n A)B)C)D) ; two real solutions ; two real solutions ; two real solutions ; one real solution71) x x A)B)C)D) ; one real solution ; two imaginary solutions ; two imaginary solutions ; two real solutionsName each polynomial by degree and number of terms.72) m A)B)C)D)fourth degree trinomiallinear monomialquadratic monomiallinear binomial 6 v2t0U1J1x gKoumtXae lSqoZfctJwVa5r9e1 gLXLzCj.i Q oAAl8ll jrzi9gThGtVsd DrBeos6eAr3vQeVdM.m c 1Mgaodlem 4w4iLtjhM UIgntfCidn0i7tReN KAqlUgbeibzrpaR 52C.X73) n n A)B)C)D)-11-quadratic monomialquadratic trinomialfifth degree binomialcubic binomialWorksheet by Kuta Software LLC

Simplify each expression.74) ( m m ) ( m m )A)B)C)D) m m m m m m m m 75) ( a a a ) (a a a )A)B)C)D) a a aa a a a a a aa a a aFind each product.76) ( k )( k )77) (a )( a )78) ( x ) 79) ( x )( x )Factor each completely.80) k k k 81) n n n Divide.82) ( p p p ) ( p ) p B) p p p C) p p p D) p p p A) p p 5 x2z0S1O17 4Kmu5tYaN HSkoqfxt8wiaSr1el cLJLzCq.q D MAmlwl9 drriFgnhft1sf srieLsZePr9vZebdb.4 r bMwacdCeG 9whirtehF 2IgnEfJiqniivtaeY GAolUgmeObNr1a0 U2j.e83) ( x x x ) ( x ) x B) x x x C) x x x D) x x x A) x x -12-Worksheet by Kuta Software LLC

Simplify each and state the excluded values.84) m m m85) m ; B) ; C) ; D); , m A) n n n A) ; B); , n n C); n D) n ; Simplify each expression.86) x x x x xx x C)x A) xx x D) B) d 9240s151m lKTu8tMaE XShoQfgtZwTaMrBe3 NLJLfCB.6 b 3AYlbl7 krci5gyhJt0sS Dr5eisbeZrgvkeddG.9 4 aMca0dve1 VwEiEthhI rInnGfaiJnLiKt4ev JAulpgaefbprGai m2c.i87)A)r r r r r C) r -13-r r r D)(r )(r )B)Worksheet by Kuta Software LLC

Answers to Course Proficiency Review1) A5) C9) D13) C17) A21) A25) B29) A33) C37) C41) C45) D49) D53) D57) D61) C65)69)73)77)81)85) ; (r ) AB a a ( n )( n )B2) C6) C10) B14) C18) B22) B26) b b30) B34) 38) B42) A46) C50) B54) C58) B 62); x 66) C70) D74) D78) x x 82) B86) B( ) Z G2j0z1m1H CKrugtHa8 nSDoHfLt0wQaHrJeN PLvLtC0.9 E KAblrln Or2iegyhPt1sn ErieOs4eTrivMeWdb.l Y LMaaudUeI VwaiGtXho 6IonAfwiRnciGtoeF lAQl5gWerbUrTaV 92f.O3) C7) D11) B15) A19) D23) D27) n n31) D35) 39) C43) C47) A51) A55) D59) C63) ; (m ) 67)71)75)79)83)87)-14-ADB x DB4) A8) A12) B16) C20) B24) A28) A32) D36) C40) D44) C48) D52) A56) C60) A 64); p 68) D72) D76) k k 80) ( k )( k )84) D()Worksheet by Kuta Software LLC

GAC 2NameCourse Proficiency Review X 22T02171H iKJu3teaB PSNowfbtoweaNrzeB aLxL2CY.5 j xAwlQlF rrBiGgIhatRsn ErHeMsleDrcvXe3dY.HSolve for x.1)Z2)WF x C x EY XA) C) DB) D) A) C) B) D) Solve for x. Each figure is a parallelogram.3)4)B MLE x JKA) C) x CDA) C) B) D) B) D) 5) CN NE x DE6) QS GS xQGNCA) C) 7) x A) C) PA) C) 8) WBB) D) ZR XB) D) E 42u0J1x1Z sKhuDt8aA bSZoAf8tlw8aHrkeR cL8L7Ch.o W PAUlqlg Sr1ihg9hotXsC krfe0sSe3rEvfeNdb.h 0 IMwaIdueP Xw9iKt0h3 AI3nvf3iUnZiWt5eO YGheYobmJeFt6rvyk.sB) D) GYSH xFA) C) -1-EB) D) Worksheet by Kuta Software LLC

Solve for x. Each figure is a trapezoid.9) DM xC XUN x TSF A) C) 10)EB) D) WA) C) VB) D) Find the area of each.11)12) yd m m yd yd13)14) mi in mi15) in in in inFind the measure of one interior angle in each polygon. Round your answer to the nearest tenth ifnecessary.16) S y2i0r1h1n BKIuwtTa6 wS3oxfUtswGaar5ez 1LtLcCw.H Q wAvl2l2 4rti5gkhbtXsA 4rEews3eDr0v3eXdg.G E XMEaTd2eS mw7ipt3ht 7IdnOfFiDnKiXtleH 5GIeioamRewt3rUyz.w17)-2-Worksheet by Kuta Software LLC

Find the area of each regular polygon. Round your answer to the nearest tenth if necessary.18)19) A) C) B) D) 20)A) C) B) D) 21) A) C) B) D) A) C) B) D) Find the missing side of each triangle. Leave your answers in simplest radical form.22)23) mix km km mixFind the area of each triangle. Round intermediate values to the nearest tenth. Use the rounded values tocalculate the next value. Round your final answer to the nearest tenth.24)25) P 52e031u1l 5KVuKtXau GSjowfwtywFaBr6eJ qLsLXCU.p e vAJlol9 8ryiPgxhItUs0 4rqeIsAeqrHvkekdL.o G ZMfazd2eV DwQi1tvhF 6IMnrfxi2nui8t4e6 KG2eHoUmme6tUrqyv.4 -3-Worksheet by Kuta Software LLC

Find the missing side lengths. Leave your answers as radicals in simplest form.26)27)ua 45 b45 v28)29)aba60 b30 Find the measure of the indicated angle to the nearest degree.30)31)?19?224127Find the missing side. Round to the nearest tenth.32)33)x53 1012x65 Find the area of each triangle. Round intermediate values to the nearest tenth. Use the rounded values tocalculate the next value. Round your final answer to the nearest tenth.34)20 42 q R2E0o1q1x NKFuNtCaZ rSZoefCttwjaBrjel ULdLGCr.I t 5Akl5lp yrAiXgDhutSsi PrKexsrekrgvleqdm.x P aMna9dnez MwEiztbhe FIZnKfOiHnsiMtxej cG8ezotmoe3tHrXy8.q-4-Worksheet by Kuta Software LLC

Find the area of each figure. Round your answer to the nearest tenth.35)36)6 mi6 kmIf an angle is given, name the arc it makes. If an arc is given, name its central angle.37) BC38) CDBCCE411 24 3B3 2DEDA) 1C) 4A) 4C) 2B) 2D) 3B) 1D) 3Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters areactual diameters.39) mIF40) mIKMEFIJ K IGL H A) C) B) D) M 72O0M1Z1C mKHuXtmal ySYoZfatWwGaUrJeN 2LlLpCY.S U 9ABlZle Yr6iLgLhftKsg trdeEsJeTrFvHe3dt.7 o pMyawdPeM kwiixtdhf dIrnefhignMiqtMe2 DGCe0oCmwe2tErWyw.3MA) C) -5-B) D) Worksheet by Kuta Software LLC

41) m IGK42) mZWY IHV W LZ GJX KA) C) B) D) YA) C) B) D) Find the circumference of each circle. Use your calculator's value of . Round your answer to the nearesttenth.43)44)7.7 mi8 miA) miC) miB) miD) miA) miC) miB) miD) miFind the length of each arc.46)45) 14 cm16 mi mi miC) A)B) miD) mi 9 U220l1i1W FK0u7tWaK oS5o1fptYwWaerueL fLuLXCE.9 y 4A8lTlB PrBi6gohvtGsE 8r4e6sFeardvGeOdv.P Z AMQa1dIe1 wwHiytkhH hILn8f7iSnwi1tFeD wGqedoIm8eYt5rNye.EA) cm C) cm-6- cm cmD) B)Worksheet by Kuta Software LLC

Find the area of each sector.47)48)10 ft 12 miA) mi²C) mi² B) mi² D) mi² 8 U2a0c1O1g xKVuxtfac CSyoPfXtNwraTrMea yLuLlCh.Q K KA6lxl1 3r9iTgnh1tOsC nrWeYsWevrAvDeSd7.c 4 4Mzaudneb kw3idtJhM MIgnbfBi2nGiJtnee yG3efoumzeatNrmy5.8 ft² C)ft² A)-7-B) ft² D) ft²Worksheet by Kuta Software LLC

Answers to Course Proficiency Review1) C5) D9) A13) 13.5 mi²17) 21) D25) 29) a , b 33) 10.937) A41) B45) A2) C6) B10) B14) 78.28 in²18) B22) km26) u , v 30) 41 34) 38) C42) C46) D I m2Z0Z111m 2Kuu4toaw 1Smocfatnw0axrWeH wL5LCC6.m 8 XAGlUlj erFiqgIhstesk irFeAsSezrQvXe0d6.8 j RMdawdieR ywLi5t3hM GIpnyfPiYntietQea iGweioNmqeCt4rEye.b3) B7) A11) 72 m²15) 17.64 in²19) B23) mi27) a , b 31) 33 35) mi²39) B43) D47) D-8-4) A8) A12) 58.5 yd²16) 20) A24) 28)32)36)40)44)48)a , b 13.3 km²BCAWorksheet by Kuta Software LLC

Adding & Subtracting Polynomials Multiplying & Factoring Multiplying Binomials Multiplying Special Cases Factoring x2 bx c Factoring ax2 bx c Factoring Special Cases Factoring by Grouping . Page 3 of 3 Quadratic Functions & Equati

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