Transcription
Name:Class:Date:ID: AALGEBRA 2 FINAL EXAM REVIEWMultiple ChoiceIdentify the choice that best completes the statement or answers the question.1. Classify –6x5 4x3 3x2 11 by degree.a. quinticb. cubicc.d.quarticquadratic2. Classify 8x4 7x3 5x2 8 by number of terms.a. trinomialc. polynomial of 5 termsb. binomiald. polynomial of 4 termsConsider the leading term of each polynomial function. What is the end behavior of thegraph?8763. 5x ! 2x ! 8x 1a. The leading termdown and up.b. The leading termdown.c. The leading termup and up.d. The leading termand down.548is 5x . Since n is even and a is positive, the end behavior is8is 5x . Since n is even and a is positive, the end behavior is up and8is 5x . Since n is even and a is positive, the end behavior is8is 5x . Since n is even and a is positive, the end behavior is down34. !3x 9x 5x 3a. The leading termup.b. The leading termdown and down.c. The leading termup and down.d. The leading termand up.5is !3x . Since n is odd and a is negative, the end behavior is up and5is !3x . Since n is odd and a is negative, the end behavior is5is !3x . Since n is odd and a is negative, the end behavior is5is !3x . Since n is odd and a is negative, the end behavior is downWrite the polynomial in factored form.5. x3 9x2 18xa. 6x(x 1)(x 3)b. 3x(x 6)(x 1)c.d.1x(x 6)(x – 3)x(x 3)(x 6)
Name:ID: AWhat are the zeros of the function? Graph the function.6. y x(x ! 2)(x 5)a. 2, –5b.0, –2, 57. Divide 4x 3 2x 2 3x 4 by x 4.a. 4x 2 ! 14x 59b. 4x 2 18x ! 53, R 240c.0, 2, –5d.2, –5, –2c.d.4x 2 ! 14x 59, R –2324x 2 18x ! 53c.d.!6x 30x ! 19, R –2026x ! 30x 19, R 20Divide using synthetic division.328. Divide !6x 18x ! 7x ! 10 by (x ! 2).a.b.2!6x 6x 526x ! 6x ! 522
Name:ID: A9. Use the Rational Root Theorem to list all possible rational roots of the polynomial equationx 3 ! 6x 2 4x 9 0. Do not find the actual roots.a. –9, –1, 1, 9c. –9, –3, –1, 1, 3, 9b. 1, 3, 9d. no rootsUse Pascal’s Triangle to expand the binomial.10. (d ! 2) 6a. d 6 12d 5 60d 4 160d 3b. d 6 ! 6d 5 15d 4 ! 20d 3 c. d 6 ! 12d 5 60d 4 ! 160d 3d. d 6 6d 5 15d 4 20d 3 240d 2 192d 6415d 2 ! 6d 1 240d 2 ! 192d 6415d 2 6d 111. Find all the real square roots of 0.0004.a. 0.00632 and –0.00632b. 0.06325 and –0.06325c.d.0.0002 and –0.00020.02 and –0.02c.!c.11c.x7 !xd.!42xFind the real-number y and simplify if possible.13.4a.14.a.b.11 "433b.Ê7x ÁÁÁÁËx !77x7 ! 49x7x ! 49x1143d. ˆ 49What is the simplest form of the expression?15.3a.b.108a 16 b 93a 5 b 34a 5 b 33334ac.3a 5 b3ad.none of these3a433
Name:ID: AWhat is the simplest form of the product?716.750x y "46a.2x yb.10x y46xy44675yc.5x y3yd.30x y54125yWhat is the simplest form of the quotient?317.1623a.2333b.3162c.333d.3What is the simplest form of the radical expression?18. 32a ! 6a.!6b.92a2a2ac.!32ad.not possible to simplifyWhat is the simplest form of the expression?19.20 45 !5a.45c.13b.65d.555What is the product of the radical expression?Ê20. ÁÁÁÁ 7 !Ë21.2 ˆ ÁÊÁ 8 ÁÁ Ëa.54 56b.54 !2 ˆ 22ÊÁˆÊÁÁ 5 ! 2 ÁÁÁ 5 ÁË ÁËa. 23b. 20c.13 152d.58 562c.d.2718ˆ2 43
Name:ID: AHow can you write the expression with rationalized denominator?22.3 !63 6!1 ! 2a.183!3 ! 2b.189c.!3 22d.9 !21823.2 33362a.36 9318c.62b.336 332d.6236 93462336 3346Simplify.124. 313"9a.25. 16a.b.39b.33c.3d.3121642c.d.16216326. Write the exponential expression 3x 8 in radical form.a.38x3b.83x 3c.333x8d.38What is the solution of the equation?27.2x 8 ! 6 !4a. 4b.–2c.12d.–3b.2c.26d.38328. ( x 6 )a. 145 858x3
Name:ID: A29. Let f(x) 4x ! 5 and g(x) 6x ! 3. Find f(x) ! g(x).a. 10x – 8b. 10x – 2c. –2x – 8d.–2x – 2d.–1030. Let f(x) 3x 2 and g(x) 7x 6. Find f " g and its domain.2a. 6x 2 4x 42; all real numbers except x !3b. 6x 2 4x 42; all real numbersc. 21x 2 32x 12; all real numbers6d. 21x 2 32x 12; all real numbers except x !731. Let f(x) x 2 ! 16 and g(x) x 4. Finda.b.c.d.x 4;x 4;x ! 4;x ! snumbersexceptexceptexceptexceptfgand its domain.x#4x # !4x#4x # !432. Let f(x) x 2 and g(x) x 2 . Find ÊÁË g û f ˆ ( !5 ) .a. 9b. –3c. 49What is the inverse of the given relation?33. y 7x 2 ! 3.a.y b.x x 37y 3734. y 3x 91a. y x 33b.y 3x ! 3x!37c.y2 d.y c.y 3x 3d.y 6x!371x!33
Name:ID: AGraph the exponential function.35. y 4 xa.b.c.d.36. Suppose you invest 1600 at an annual interest rate of 4.6% compounded continuously. How much willyou have in the account after 4 years?a. 800.26b. 6,701.28c. 10,138.07d. 1,923.2337. How much money invested at 5% compounded continuously for 3 years will yield 820?a. 952.70b. 818.84c. 780.01d. 705.78Write the equation in logarithmic form.38. 2 5 32a. log 32 5 " 2b. log 2 32 5c.d.7log 32 5log 5 32 2
Name:ID: AEvaluate the logarithm.39. log . log 3 243a.541. log 0.01a. –10Write the expression as a single logarithm.42. 3 log b q 6 log b va.b.log b (q 3 v 6 )Ê 3 6 ˆ log b ÁÁÁÁ qv Ëc.d.( 3 6 ) log b ÊÁË q v ˆ Ê 36ˆlog b ÁÁÁÁ q v Ë 43. log 3 4 ! log 3 2a.log 3 2b.log 3 2c.log 2d.Expand the logarithmic expression.44. log 3d12log 3 da.log 3 d ! log 3 12c.b.!d log 3 12d.log 3 12 ! log 3 dlog 3 1245. log 3 11 p 3a.log 3 11 " 3 log 3 pc.log 3 11 3 log 3 pb.log 3 11 ! 3 log 3 pd.11 log 3 p46. Use the Change of Base Formula to evaluate log 7 28.a.b.1.7123.332c.d.81.7121.4473log 2
Name:ID: ASolve the exponential equation.47.1 64 4x ! 3161a.1248. 4b.14c.712d.1112b.83c.38d.24x 83a.4Solve the logarithmic equation.49. 3 log 2x 4a. 10.7722b.5Round to the nearest ten-thousandth if necessary.c.2.7826d.0.6309650. Find the horizontal asymptote of the graph of y !4x 6x 36.a.y 1c.8x 9x 3y 0b.1y !2d.no horizontal asymptoteSimplify the rational expression. State any restrictions on the variable.251.p ! 4p ! 32p 4!p 8; p # !4p ! 8; p # !4a.b.c.d.!p ! 8; p # 4p 8; p # 4252.q 11q 242q ! 5q ! 24q 8a.; q # !3, q # !8q !8!(q 8)b.;q # 8q !8c.d.9q 8; q # !3, q # 8q !8!(q 8); q # !3, q # 8q !8
Name:ID: AWhat is the product in simplest form? State any restrictions on the variable.53.4a57b4a."2b22a44a97b64ab.7b2, a # 0, b # 0c., a # 0, b # 0d.7b4a2, a # 0, b # 04 9 6a b , a # 0, b # 07What is the quotient in simplified form? State any restrictions on the variable.54.x 2 x 42x!1x 4x ! 5(x 2)(x 5)a., x # ! 5, ! 4x 4(x 2)(x 4)b., x # 1, ! 52(x ! 1) (x 5)c.d.(x 2)(x 4), x # 1, ! 5, ! 42(x ! 1) (x 5)(x 2)(x 5), x # 1, ! 4x 4Simplify the sum.55.7 a 8a.72a ! 647a ! 49(a ! 8)(a 8)14b.2a a ! 56c.14(a ! 8)(a 8)d.7a 63(a ! 8)(a 8)Simplify the difference.256.b ! 2b ! 82b b !2a.!6b !1b ! 10c.2b.b ! 2b ! 142b b !2d.10b !4b !1b ! 10b !1
Name:ID: ASimplify the complex fraction.257.5t12t! a.33t12t3!5b.!4c.!53d.!14d.!113d.6458.x 31 3x12x 4a.2x 3x4xb.3x 9c.4x23x 10x 3d.not herec.!c.–9 and –6Solve the equation. Check the solution.59.!2x 44x 313!6a.60. a2a ! 36a. –9b. 2a !6 !11831a 6b. –611
ID: AALGEBRA 2 FINAL EXAM REVIEWAnswer SectionMULTIPLE CHOICE1. ANS:OBJ:TOP:KEY:DOK:2. ANS:OBJ:TOP:KEY:DOK:3. ANS:OBJ:STA:TOP:KEY:4. ANS:OBJ:STA:TOP:KEY:5. ANS:REF:OBJ:STA:TOP:KEY:6. ANS:REF:OBJ:STA:TOP:DOK:7. ANS:OBJ:STA:TOP:DOK:8. ANS:OBJ:STA:TOP:DOK:APTS: 1DIF: L2REF: 5-1 Polynomial Functions5-1.1 To classify polynomialsSTA: MA.912.A.2.5 MA.912.A.4.55-1 Problem 1 Classifying Polynomialsdegree of a polynomial polynomial function standard form of a polynomial functionDOK 1DPTS: 1DIF: L2REF: 5-1 Polynomial Functions5-1.1 To classify polynomialsSTA: MA.912.A.2.5 MA.912.A.4.55-1 Problem 1 Classifying Polynomialsdegree of a polynomial polynomial function standard form of a polynomial functionDOK 1CPTS: 1DIF: L2REF: 5-1 Polynomial Functions5-1.2 To graph polynomial functions and describe end behaviorMA.912.A.2.5 MA.912.A.4.55-1 Problem 2 Describing End Behavior of Polynomial Functionspolynomial end behaviorDOK: DOK 1CPTS: 1DIF: L3REF: 5-1 Polynomial Functions5-1.2 To graph polynomial functions and describe end behaviorMA.912.A.2.5 MA.912.A.4.55-1 Problem 2 Describing End Behavior of Polynomial Functionspolynomial end behaviorDOK: DOK 1DPTS: 1DIF: L25-2 Polynomials, Linear Factors, and Zeros5-2.1 To analyze the factored form of a polynomialMA.912.A.4.3 MA.912.A.4.5 MA.912.A.4.7 MA.912.A.4.85-2 Problem 1 Writing a Polynomial in Factored FormDOK: DOK 2CPTS: 1DIF: L35-2 Polynomials, Linear Factors, and Zeros5-2.1 To analyze the factored form of a polynomialMA.912.A.4.3 MA.912.A.4.5 MA.912.A.4.7 MA.912.A.4.85-2 Problem 2 Finding Zeros of a Polynomial FunctionDOK 2CPTS: 1DIF: L2REF: 5-4 Dividing Polynomials5-4.1 To divide polynomials using long divisionMA.912.A.4.3 MA.912.A.4.4 MA.912.A.4.65-4 Problem 1 Using Polynomial Long DivisionKEY:DOK 2APTS: 1DIF: L3REF: 5-4 Dividing Polynomials5-4.2 To divide polynomials using synthetic divisionMA.912.A.4.3 MA.912.A.4.4 MA.912.A.4.65-4 Problem 3 Using Synthetic DivisionKEY: synthetic divisionDOK 21
ID: A9. ANS:REF:OBJ:STA:KEY:10. ANS:OBJ:TOP:DOK:11. ANS:OBJ:TOP:DOK:12. ANS:OBJ:TOP:DOK:13. ANS:REF:OBJ:TOP:DOK:14. ANS:REF:OBJ:TOP:DOK:15. ANS:REF:OBJ:TOP:DOK:16. ANS:REF:OBJ:TOP:DOK:17. ANS:REF:OBJ:TOP:DOK:18. ANS:OBJ:TOP:KEY:CPTS: 1DIF: L25-5 Theorems About Roots of Polynomial Equations5-5.1 To solve equations using the Rational Root TheoremMA.912.A.4.6 MA.912.A.4.7TOP: 5-5 Problem 1 Finding a Rational RootRational Root TheoremDOK: DOK 1CPTS: 1DIF: L2REF: 5-7 The Binomial Theorem5-7.1 To expand a binomial using Pascal's TriangleSTA: MA.912.A.4.125-7 Problem 1 Using Pascal's TriangleKEY: Pascal's Triangle expandDOK 2DPTS: 1DIF: L4REF: 6-1 Roots and Radical Expressions6-1.1 To find nth rootsSTA: MA.912.A.10.36-1 Problem 1 Finding All Real RootsKEY: nth rootDOK 1DPTS: 1DIF: L3REF: 6-1 Roots and Radical Expressions6-1.1 To find nth rootsSTA: MA.912.A.10.36-1 Problem 2 Finding RootsKEY: radicand index nth rootDOK 1DPTS: 1DIF: L26-2 Multiplying and Dividing Radical Expressions6-2.1 To multiply and divide radical expressionsSTA: MA.912.A.6.2 MA.912.A.10.36-2 Problem 1 Multiplying Radical ExpressionsKEY:DOK 1APTS: 1DIF: L46-2 Multiplying and Dividing Radical Expressions6-2.1 To multiply and divide radical expressionsSTA: MA.912.A.6.2 MA.912.A.10.36-2 Problem 1 Multiplying Radical ExpressionsKEY:DOK 2APTS: 1DIF: L36-2 Multiplying and Dividing Radical Expressions6-2.1 To multiply and divide radical expressionsSTA: MA.912.A.6.2 MA.912.A.10.36-2 Problem 2 Simplifying a Radical ExpressionKEY: simplest form of a radicalDOK 1BPTS: 1DIF: L36-2 Multiplying and Dividing Radical Expressions6-2.1 To multiply and divide radical expressionsSTA: MA.912.A.6.2 MA.912.A.10.36-2 Problem 3 Simplifying a ProductKEY: simplest form of a radicalDOK 2APTS: 1DIF: L26-2 Multiplying and Dividing Radical Expressions6-2.1 To multiply and divide radical expressionsSTA: MA.912.A.6.2 MA.912.A.10.36-2 Problem 4 Dividing Radical ExpressionsKEY: simplest form of a radicalDOK 1CPTS: 1DIF: L2REF: 6-3 Binomial Radical Expressions6-3.1 To add and subtract radical expressionsSTA: MA.912.A.6.26-3 Problem 1 Adding and Subtracting Radical Expressionslike radicals DOK: DOK 12
ID: A19. ANS:OBJ:TOP:DOK:20. ANS:OBJ:TOP:DOK:21. ANS:OBJ:TOP:22. ANS:OBJ:TOP:23. ANS:OBJ:TOP:24. ANS:OBJ:TOP:KEY:25. ANS:OBJ:TOP:KEY:26. ANS:OBJ:TOP:KEY:27. ANS:REF:OBJ:STA:TOP:DOK:28. ANS:REF:OBJ:STA:TOP:DOK:29. ANS:OBJ:TOP:30. ANS:OBJ:TOP:APTS: 1DIF: L3REF: 6-3 Binomial Radical Expressions6-3.1 To add and subtract radical expressionsSTA: MA.912.A.6.26-3 Problem 3 Simplifying Before Adding or SubtractingDOK 2BPTS: 1DIF: L2REF: 6-3 Binomial Radical Expressions6-3.1 To add and subtract radical expressionsSTA: MA.912.A.6.26-3 Problem 4 Multiplying Binomial Radical ExpressionsDOK 1APTS: 1DIF: L3REF: 6-3 Binomial Radical Expressions6-3.1 To add and subtract radical expressionsSTA: MA.912.A.6.26-3 Problem 5 Multiplying ConjugatesDOK: DOK 1CPTS: 1DIF: L3REF: 6-3 Binomial Radical Expressions6-3.1 To add and subtract radical expressionsSTA: MA.912.A.6.26-3 Problem 6 Rationalizing the DenominatorDOK: DOK 1DPTS: 1DIF: L2REF: 6-3 Binomial Radical Expressions6-3.1 To add and subtract radical expressionsSTA: MA.912.A.6.26-3 Problem 6 Rationalizing the DenominatorDOK: DOK 1CPTS: 1DIF: L3REF: 6-4 Rational Exponents6-4.1 To simplify expressions with rational exponents STA: MA.912.A.6.3 MA.912.A.6.46-4 Problem 1 Simplifying Expressions with Rational Exponentsrational exponentsDOK: DOK 1BPTS: 1DIF: L2REF: 6-4 Rational Exponents6-4.1 To simplify expressions with rational exponents STA: MA.912.A.6.3 MA.912.A.6.46-4 Problem 1 Simplifying Expressions with Rational Exponentsrational exponentsDOK: DOK 1APTS: 1DIF: L2REF: 6-4 Rational Exponents6-4.1 To simplify expressions with rational exponents STA: MA.912.A.6.3 MA.912.A.6.46-4 Problem 2 Converting Between Exponential and Radical Formrational exponentsDOK: DOK 1BPTS: 1DIF: L26-5 Solving Square Root and Other Radical Equations6-5.1 To solve square root and other radical equationsMA.912.A.6.4 MA.912.A.6.5 MA.912.A.10.36-5 Problem 1 Solving a Square Root EquationKEY: square root equationDOK 2CPTS: 1DIF: L36-5 Solving Square Root and Other Radical Equations6-5.1 To solve square root and other radical equationsMA.912.A.6.4 MA.912.A.6.5 MA.912.A.10.36-5 Problem 2 Solving Other Radical EquationsKEY: radical equationDOK 2DPTS: 1DIF: L3REF: 6-6 Function Operations6-6.1 To add, subtract, multiply, and divide functionsSTA: MA.912.A.2.7 MA.912.A.2.86-6 Problem 1 Adding and Subtracting FunctionsDOK: DOK 2CPTS: 1DIF: L3REF: 6-6 Function Operations6-6.1 To add, subtract, multiply, and divide functionsSTA: MA.912.A.2.7 MA.912.A.2.86-6 Problem 2 Multiplying and Dividing FunctionsDOK: DOK 23
ID: A31. ANS:OBJ:TOP:32. ANS:OBJ:TOP:DOK:33. ANS:REF:OBJ:TOP:DOK:34. ANS:REF:OBJ:TOP:DOK:35. ANS:REF:OBJ:STA:TOP:DOK:36. ANS:REF:OBJ:STA:TOP:DOK:37. ANS:REF:OBJ:STA:TOP:DOK:38. ANS:REF:OBJ:STA:TOP:KEY:39. ANS:REF:OBJ:STA:TOP:DOK:DPTS: 1DIF: L3REF: 6-6 Function Operations6-6.1 To add, subtract, multiply, and divide functionsSTA: MA.912.A.2.7 MA.912.A.2.86-6 Problem 2 Multiplying and Dividing FunctionsDOK: DOK 2APTS: 1DIF: L3REF: 6-6 Function Operations6-6.2 To find the composite of two functionsSTA: MA.912.A.2.7 MA.912.A.2.86-6 Problem 3 Composing FunctionsKEY: composite functionDOK 2APTS: 1DIF: L36-7 Inverse Relations and Functions6-7.1 To find the inverse of a relation or functionSTA: MA.912.A.2.116-7 Problem 2 Finding an Equation for the InverseKEY: inverse relationDOK 2DPTS: 1DIF: L36-7 Inverse Relations and Functions6-7.1 To find the inverse of a relation or functionSTA: MA.912.A.2.116-7 Problem 2 Finding an Equation for the InverseKEY: inverse relationDOK 2DPTS: 1DIF: L27-1 Exploring Exponential Models7-1.1 To model exponential growth and decayMA.912.A.8.1 MA.912.A.8.3 MA.912.A.8.77-1 Problem 1 Graphing an Exponential FunctionKEY: exponential functionDOK 2DPTS: 1DIF: L27-2 Properties of Exponential Functions7-2.2 To graph exponential functions that have base eMA.912.A.2.5 MA.912.A.2.10 MA.912.A.8.1 MA.912.A.8.3 MA.912.A.8.77-2 Problem 5 Continuously Compounded InterestKEY: continuously compounded interestDOK 2DPTS: 1DIF: L37-2 Properties of Exponential Functions7-2.2 To graph exponential functions that have base eMA.912.A.2.5 MA.912.A.2.10 MA.912.A.8.1 MA.912.A.8.3 MA.912.A.8.77-2 Problem 5 Continuously Compounded InterestKEY: continuously compounded interestDOK 2BPTS: 1DIF: L27-3 Logarithmic Functions as Inverses7-3.1 To write and evaluate logarithmic expressionsMA.912.A.2.5 MA.912.A.2.11 MA.912.A.8.1 MA.912.A.8.37-3 Problem 1 Writing Exponential Equations in Logarithmic FormlogarithmDOK: DOK 2CPTS: 1DIF: L37-3 Logarithmic Functions as Inverses7-3.1 To write and evaluate logarithmic expressionsMA.912.A.2.5 MA.912.A.2.11 MA.912.A.8.1 MA.912.A.8.37-3 Problem 2 Evaluating a LogarithmKEY: logarithmDOK 24
ID: A40. ANS:REF:OBJ:STA:TOP:DOK:41. ANS:REF:OBJ:STA:TOP:DOK:42. ANS:OBJ:TOP:43. ANS:OBJ:TOP:44. ANS:OBJ:TOP:45. ANS:OBJ:TOP:46. ANS:OBJ:TOP:DOK:47. ANS:REF:OBJ:TOP:KEY:48. ANS:REF:OBJ:TOP:KEY:49. ANS:REF:OBJ:TOP:DOK:50. ANS:REF:OBJ:TOP:DOK:APTS: 1DIF: L27-3 Logarithmic Functions as Inverses7-3.1 To write and evaluate logarithmic expressionsMA.912.A.2.5 MA.912.A.2.11 MA.912.A.8.1 MA.912.A.8.37-3 Problem 2 Evaluating a LogarithmKEY: logarithmDOK 2BPTS: 1DIF: L47-3 Logarithmic Functions as Inverses7-3.1 To write and evaluate logarithmic expressionsMA.912.A.2.5 MA.912.A.2.11 MA.912.A.8.1 MA.912.A.8.37-3 Problem 2 Evaluating a LogarithmKEY: logarithmDOK 2APTS: 1DIF: L3REF: 7-4 Properties of Logarithms7-4.1 To use the properties of logarithmsSTA: MA.912.A.8.2 MA.912.A.8.67-4 Problem 1 Simplifying LogarithmsDOK: DOK 2APTS: 1DIF: L2REF: 7-4 Properties of Logarithms7-4.1 To use the properties of logarithmsSTA: MA.912.A.8.2 MA.912.A.8.67-4 Problem 1 Simplifying LogarithmsDOK: DOK 2APTS: 1DIF: L2REF: 7-4 Properties of Logarithms7-4.1 To use the properties of logarithmsSTA: MA.912.A.8.2 MA.912.A.8.67-4 Problem 2 Expanding LogarithmsDOK: DOK 2CPTS: 1DIF: L3REF: 7-4 Properties of Logarithms7-4.1 To use the properties of logarithmsSTA: MA.912.A.8.2 MA.912.A.8.67-4 Problem 2 Expanding LogarithmsDOK: DOK 2APTS: 1DIF: L3REF: 7-4 Properties of Logarithms7-4.1 To use the properties of logarithmsSTA: MA.912.A.8.2 MA.912.A.8.67-4 Problem 3 Using the Change of Base FormulaKEY: Change of Base FormulaDOK 2CPTS: 1DIF: L47-5 Exponential and Logarithmic Equations7-5.1 To solve exponential and logarithmic equations STA: MA.912.A.8.57-5 Problem 1 Solving an Exponential Equation – Common Baseexponential equationDOK: DOK 2CPTS: 1DIF: L27-5 Exponential and Logarithmic Equations7-5.1 To solve exponential and logarithmic equations STA: MA.912.A.8.57-5 Problem 1 Solving an Exponential Equation – Common Baseexponential equationDOK: DOK 2APTS: 1DIF: L27-5 Exponential and Logarithmic Equations7-5.1 To solve exponential and logarithmic equations STA: MA.912.A.8.57-5 Problem 5 Solving a Logarithmic EquationKEY: logarithmic equationDOK 2BPTS: 1DIF: L38-3 Rational Functions and Their Graphs8-3.1 To identify properties of rational functionsSTA: MA.912.A.5.68-3 Problem 3 Finding Horizontal AsymptotesKEY: rational functionDOK 25
ID: A51. ANS:OBJ:TOP:DOK:52. ANS:OBJ:TOP:DOK:53. ANS:OBJ:TOP:DOK:54. ANS:OBJ:TOP:DOK:55. ANS:REF:OBJ:TOP:56. ANS:REF:OBJ:TOP:57. ANS:REF:OBJ:TOP:DOK:58. ANS:REF:OBJ:TOP:DOK:59. ANS:OBJ:KEY:60. ANS:OBJ:KEY:BPTS: 1DIF: L28-4.1 To simplify rational expressions8-4 Problem 1 Simplifying a Rational ExpressionDOK 2CPTS: 1DIF: L38-4.1 To simplify rational expressions8-4 Problem 1 Simplifying a Rational ExpressionDOK 2BPTS: 1DIF: L28-4.2 To multiply and divide rational expressions8-4 Problem 2 Multiplying Rational ExpressionsDOK 2DPTS: 1DIF: L38-4.2 To multiply and divide rational expressions8-4 Problem 3 Dividing Rational ExpressionsDOK 2APTS: 1DIF: L28-5 Adding and Subtracting Rational Expressions8-5.1 To add and subtract rational expressions8-5 Problem 2 Adding Rational ExpressionsDPTS: 1DIF: L38-5 Adding and Subtracting Rational Expressions8-5.1 To add and subtract rational expressions8-5 Problem 3 Subtracting Rational ExpressionsAPTS: 1DIF: L28-5 Adding and Subtracting Rational Expressions8-5.1 To add and subtract rational expressions8-5 Problem 4 Simplifying a Complex FractionDOK 2CPTS: 1DIF: L38-5 Adding and Subtracting Rational Expressions8-5.1 To add and subtract rational expressions8-5 Problem 4 Simplifying a Complex FractionDOK 2DPTS: 1DIF: L28-6.1 To solve rational equations TOP: 8-6 Problemrational equationDOK: DOK 2APTS: 1DIF: L48-6.1 To solve rational equations TOP: 8-6 Problemrational equationDOK: DOK 26REF: 8-4 Rational ExpressionsSTA: MA.912.A.10.3KEY: rational expression simplest formREF: 8-4 Rational ExpressionsSTA: MA.912.A.10.3KEY: rational expression simplest formREF: 8-4 Rational ExpressionsSTA: MA.912.A.10.3KEY: rational expression simplest formREF: 8-4 Rational ExpressionsSTA: MA.912.A.10.3KEY: rational expression simplest formDOK: DOK 2DOK: DOK 2KEY: complex fractionKEY: complex fractionREF: 8-6 Solving Rational Equations1 Solving a Rational EquationREF: 8-6 Solving Rational Equations1 Solving a Rational Equation
a. -10 b. -2 c. 2 d. 10 Write the expression as a single logarithm. _ 42. 3 log b q 6 log b v a. log b (q3 v6) c. (3 6) log b ÊËÁÁq vˆ b. log b qv3 6 Ê Ë ÁÁ ÁÁ ˆ d. log b q3 v6 Ê Ë ÁÁ ÁÁ ˆ _ 43. log 3 4 ! log 3 2 a. log 3 2 b. log 3 2 c. log 2 d. log 2 Expand the .
