Algebra 2 Chapter 6 and 7 Test Review (part 1)

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1 Name: Class: Date: Algebra 2 Chapter 6 and 7 Test Review (part ). Find the annual percent increase or decrease that y = 0.35(2.3) x models. a. 230% increase c. 35% decrease b. 35% increase d. 65% decrease 2. An initial population of 820 quail increases at an annual rate of 23%. Write an exponential function to model the quail population. What will the approximate population be after 3 years? a. f(x) = 820(.23) x ; 526 c. f(x) = ( ) x ; 6,708,494 b. f(x) = 820(23) x ; 9,976,940 d. f(x) = 820(0.23) x ; The half-life of a certain radioactive material is 32 days. An initial amount of the material has a mass of 36 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5 days. Round your answer to the nearest thousandth. Ê a. y = x ˆ Ê ˆ 32 x Á 2 ; 0 kg c. y = 2 Á 36 ; kg Ê b. y = 36 ˆ 32 x Á 2 ; kg d. y = 2 Ê ˆ Á x ; 0.99 kg 4. The half-life of a certain radioactive material is 7 hours. An initial amount of the material has a mass of 722 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 7 hours. Round your answer to the nearest thousandth. a. y = Ê ˆ 7 x Ê ˆ 7 x 2 Á 722 ; 0.03 kg c. y = 2 Á 722 ; 0.44 kg Ê b. y = 722 ˆ 7 x Á 2 ; kg d. y = x Ê ˆ Á 2 ; 0 kg 5. Classify 2x 4 x 3 + 8x by degree. a. quartic c. quadratic b. quintic d. cubic 6. Classify 8x 4 + 7x 3 + 5x by number of terms. a. trinomial c. polynomial of 5 terms b. binomial d. polynomial of 4 terms 7. Write 2x 2 ( 5x 2 + 4x 3 ) in standard form. a. 8x 5 20x 4 c. 7x + 2x 4 b. 8x 5 + 0x 4 d. 7x 5 0x 4

2 Name: Consider the leading term of each polynomial function. What is the end behavior of the graph? 8. 3x 3 x a. The leading term is 3x 3. Since n is odd and a is negative, the end behavior is down and down. b. The leading term is 3x 3. Since n is odd and a is negative, the end behavior is up and up. c. The leading term is 3x 3. Since n is odd and a is negative, the end behavior is up and down. d. The leading term is 3x 3. Since n is odd and a is negative, the end behavior is down and up. 9. What is the graph of y = 4 x 3 a. c. b. d. 2

3 Name: 0. Graph y = 3(x + 2) 3 3 and describe the end behavior. a. c. The end behavior is up and down. The end behavior is down and up. b. d. The end behavior is down and up. The end behavior is up and down. Write the polynomial in factored form.. 6x 3 60x x a. 6x(x 6)(x + 4) c. 6x(x + 6)(x 4) b. 4x(x 6)(x + 6) d. 6x(x 4)(x 6) 2. x 3 + 2x 2 5x a. 5x(x + )(x 3) c. x(x + 5)(x + 3) b. x(x 3)(x + 5) d. 3x(x + 5)(x + ) 3

4 Name: What is the relative maximum and minimum of the function? 3. f(x) = x 3 + 3x 2 24x a. The relative maximum is at (4, 28) and the relative minimum is at ( 2, 80). b. The relative maximum is at ( 4, 80) and the relative minimum is at (2, 28). c. The relative maximum is at (4, 80) and the relative minimum is at ( 2, 28). d. The relative maximum is at ( 4, 28) and the relative minimum is at (2, 80). 4. f(x) = 2x 3 + x 2 x a. The relative maximum is at (.53, 8.3) and the relative minimum is at (.2, 2.0). b. The relative maximum is at (.53, 2.0) and the relative minimum is at (.2, 8.3). c. The relative maximum is at (.2, 8.3) and the relative minimum is at (.53, 2.0). d. The relative maximum is at (.2, 2.0) and the relative minimum is at (.53, 8.3). 5. Divide 4x 3 + 2x 2 + 3x + 4 by x + 4. a. 4x 2 4x + 59 c. 4x 2 4x + 59, R 232 b. 4x 2 + 8x 53, R 240 d. 4x 2 + 8x Divide 3x 3 2x 2 x 2 by x 2. a. 3x 2 + 4x + 5, R 32 c. 3x 2 8x 7 b. 3x 2 + 4x + 5 d. 3x 2 8x 7, R Divide x 3 + x 2 x + 2 by x + 4. a. x 2 3x +, R 42 c. x 2 + 5x 3 b. x 2 3x + d. x 2 + 5x 3, R 46 Divide using synthetic division. 8. Divide 6x 3 + 8x 2 7x 0 by (x 2). a. 6x 2 + 6x + 5 c. 6x x 9, R 20 b. 6x 2 6x 5 d. 6x 2 30x + 9, R Divide 4x 3 + 2x 2 23x + 6 by (x 4). a. 4x 2 + 5x 3, R 6 c. 4x x 43, R 8 b. 4x 2 5x + 3 d. 4x 2 37x Divide 4x x by (x + 4). a. 4x x 20 c. 4x 2 56x + 238, R 680 b. 4x 2 56x + 20 d. 4x x 238, R 680 4

5 Algebra 2 Chapter 6 and 7 Test Review (part ) Answer Section. ANS: A PTS: DIF: L3 REF: 7- Exploring Exponential Models OBJ: 7-. To model exponential growth and decay NAT: CC A.SSE..b CC A.CED.2 CC F.IF.7.e A..b A.2.f A.2.g TOP: 7- Problem 2 Identifying Exponential Growth and Decay KEY: exponential decay exponential function exponential growth 2. ANS: A PTS: DIF: L3 REF: 7- Exploring Exponential Models OBJ: 7-. To model exponential growth and decay NAT: CC A.SSE..b CC A.CED.2 CC F.IF.7.e A..b A.2.f A.2.g TOP: 7- Problem 3 Modeling Exponential Growth KEY: exponential growth exponential function 3. ANS: B PTS: DIF: L3 REF: 7-2 Properties of Exponential Functions OBJ: 7-2. To explore the properties of functions of the form y = ab^x NAT: CC A.SSE..b CC A.CED.2 CC F.IF.7 CC F.IF.7.e CC F.IF.8 CC F.BF. CC F.BF..b N.3.f G.2.c A..b A.2.d A.2.h STA: 4.2 TOP: 7-2 Problem 3 Using an Exponential Model KEY: exponential function 4. ANS: B PTS: DIF: L3 REF: 7-2 Properties of Exponential Functions OBJ: 7-2. To explore the properties of functions of the form y = ab^x NAT: CC A.SSE..b CC A.CED.2 CC F.IF.7 CC F.IF.7.e CC F.IF.8 CC F.BF. CC F.BF..b N.3.f G.2.c A..b A.2.d A.2.h STA: 4.2 TOP: 7-2 Problem 3 Using an Exponential Model KEY: exponential function 5. ANS: A PTS: DIF: L2 REF: 5- Polynomial Functions OBJ: 5-. To classify polynomials NAT: CC A.SSE..a CC F.IF.4 CC F.IF.7 CC F.IF.7.c STA: 2. TOP: 5- Problem Classifying Polynomials KEY: degree of a polynomial polynomial function standard form of a polynomial function 6. ANS: D PTS: DIF: L2 REF: 5- Polynomial Functions OBJ: 5-. To classify polynomials NAT: CC A.SSE..a CC F.IF.4 CC F.IF.7 CC F.IF.7.c STA: 2. TOP: 5- Problem Classifying Polynomials KEY: degree of a polynomial polynomial function standard form of a polynomial function 7. ANS: B PTS: DIF: L3 REF: 5- Polynomial Functions OBJ: 5-. To classify polynomials NAT: CC A.SSE..a CC F.IF.4 CC F.IF.7 CC F.IF.7.c STA: 2. TOP: 5- Problem Classifying Polynomials KEY: degree of a polynomial polynomial function standard form of a polynomial 8. ANS: C PTS: DIF: L2 REF: 5- Polynomial Functions OBJ: 5-.2 To graph polynomial functions and describe end behavior NAT: CC A.SSE..a CC F.IF.4 CC F.IF.7 CC F.IF.7.c STA: 2. TOP: 5- Problem 2 Describing End Behavior of Polynomial Functions KEY: polynomial end behavior turning point 9. ANS: D PTS: DIF: L2 REF: 5- Polynomial Functions OBJ: 5-.2 To graph polynomial functions and describe end behavior NAT: CC A.SSE..a CC F.IF.4 CC F.IF.7 CC F.IF.7.c STA: 2. TOP: 5- Problem 3 Graphing Cubic Functions KEY: polynomial function end behavior turning point

6 0. ANS: C PTS: DIF: L4 REF: 5- Polynomial Functions OBJ: 5-.2 To graph polynomial functions and describe end behavior NAT: CC A.SSE..a CC F.IF.4 CC F.IF.7 CC F.IF.7.c STA: 2. TOP: 5- Problem 3 Graphing Cubic Functions KEY: polynomial function end behavior turning point. ANS: D PTS: DIF: L3 REF: 5-2 Polynomials, Linear Factors, and Zeros OBJ: 5-2. To analyze the factored form of a polynomial NAT: CC A.SSE. CC A.APR.3 CC F.IF.7 CC F.IF.7.c CC F.BF. STA: 2. TOP: 5-2 Problem Writing a Polynomial in Factored Form 2. ANS: B PTS: DIF: L2 REF: 5-2 Polynomials, Linear Factors, and Zeros OBJ: 5-2. To analyze the factored form of a polynomial NAT: CC A.SSE. CC A.APR.3 CC F.IF.7 CC F.IF.7.c CC F.BF. STA: 2. TOP: 5-2 Problem Writing a Polynomial in Factored Form 3. ANS: B PTS: DIF: L3 REF: 5-2 Polynomials, Linear Factors, and Zeros OBJ: 5-2. To analyze the factored form of a polynomial NAT: CC A.SSE. CC A.APR.3 CC F.IF.7 CC F.IF.7.c CC F.BF. STA: 2. TOP: 5-2 Problem 5 Identifying a Relative Maximum and Minimum KEY: relative maximum relative minimum 4. ANS: B PTS: DIF: L3 REF: 5-2 Polynomials, Linear Factors, and Zeros OBJ: 5-2. To analyze the factored form of a polynomial NAT: CC A.SSE. CC A.APR.3 CC F.IF.7 CC F.IF.7.c CC F.BF. STA: 2. TOP: 5-2 Problem 5 Identifying a Relative Maximum and Minimum KEY: relative maximum relative minimum 5. ANS: C PTS: DIF: L2 REF: 5-4 Dividing Polynomials OBJ: 5-4. To divide polynomials using long division NAT: CC A.APR. CC A.APR.2 CC A.APR.6 N..d A.3.c A.3.e TOP: 5-4 Problem Using Polynomial Long Division 6. ANS: D PTS: DIF: L3 REF: 5-4 Dividing Polynomials OBJ: 5-4. To divide polynomials using long division NAT: CC A.APR. CC A.APR.2 CC A.APR.6 N..d A.3.c A.3.e TOP: 5-4 Problem Using Polynomial Long Division 7. ANS: A PTS: DIF: L2 REF: 5-4 Dividing Polynomials OBJ: 5-4. To divide polynomials using long division NAT: CC A.APR. CC A.APR.2 CC A.APR.6 N..d A.3.c A.3.e TOP: 5-4 Problem Using Polynomial Long Division 8. ANS: A PTS: DIF: L3 REF: 5-4 Dividing Polynomials OBJ: To divide polynomials using synthetic division NAT: CC A.APR. CC A.APR.2 CC A.APR.6 N..d A.3.c A.3.e TOP: 5-4 Problem 3 Using Synthetic Division KEY: synthetic division 9. ANS: A PTS: DIF: L3 REF: 5-4 Dividing Polynomials OBJ: To divide polynomials using synthetic division NAT: CC A.APR. CC A.APR.2 CC A.APR.6 N..d A.3.c A.3.e TOP: 5-4 Problem 3 Using Synthetic Division KEY: synthetic division 2

7 20. ANS: A PTS: DIF: L2 REF: 5-4 Dividing Polynomials OBJ: To divide polynomials using synthetic division NAT: CC A.APR. CC A.APR.2 CC A.APR.6 N..d A.3.c A.3.e TOP: 5-4 Problem 3 Using Synthetic Division KEY: synthetic division 3

8 Algebra 2 Chapter 6 and 7 Test Review (part ) [Answer Strip] _ C 0. _ A. _ C 8. _ B 3. _ A 2. _ B 3. _ D 9. _ B 4. _ B 4. _ C 5. _ D 6. _ A 7. _ A 5. _ D 6. _ D. _ A 8. _ B 7. _ B 2. _ A 9. _ A 20.