Chapter 5 Test Review Algebra II Chapter 5 Test Revie€¦ · · 2017-01-1810 Chapter 5 Test...

1 Chapter 5 Test Review

Algebra II – Chapter 5 Test Review Standards/Goals:

A.1.c./F.1.b.: I can factor a quadratic trinomial in the form of E.1.c./N.CN.7.: I can use the Conjugate Root Theorem to solve equations. E.2.b.: I can use transformations to consider the graph of a polynomial function (cubic). F.1.a./F.IF.7.c/A.APR.1.:

o I can identify the degree of a polynomial function. o I can evaluate and simplify polynomial expressions and equations for given input values.

F.1.b./A.SSE.2: o I can write polynomials in factored form. o I can factor polynomials using a variety of methods (synthetic & long division).

F.1.b./A.APR.2.:

I can use long division to divide two polynomials. F.2.a./A.APR.2.:

o I can determine the number and type of rational zeros for a polynomial function. o I can use the Rational Root Theorem to solve equations.

F.2.b./A.APR.3.: I can find all rational zeros of a polynomial function. F.2.c./F.IF.7.c.:

o I can use the graph of a polynomial function to find the zeros. o I can understand the relationship (and connection) between zeros, roots, solutions and x-

intercepts of polynomial equations. o I can find the multiplicity of the graph of a polynomial.

F.2.d./F.IF.7./F.IF.4.: I can use technology to graph a polynomial function and approximate the zeros. I can use technology to find the minimum and maximum values

I can use technology to determine the domain and range of a polynomial function. (POWER STANDARD REVIEW):

D.1.a.: I can solve a linear equation or inequality that involves absolute value.

D.1.a.: I can determine conceptually the values that would result in a linear equation or inequality involving absolute values to have no solution or infinitely many solutions.

(POWER STANDARD REVIEW): F.1.a.: I can evaluate polynomial expressions/equations for given input values.

(POWER STANDARD REVIEW):

E.1.a.: I can solve quadratic equations using the quadratic formula.

E.1.b.: I can use the discriminant to determine the number and types of roots/solutions/x-intercepts that a quadratic will have.

(POWER STANDARD REVIEW): H.2.a./A.SSE.4.:

I can identify whether a sequence is arithmetic or geometric.

I can derive the formula for sequence for both its explicit and recursive definitions. (ACT Algebra 1 Standards Review):

A.1.a.: I can use correct order of operations to simplify expressions.

A.1.b.: I can multiply binomials using the FOIL METHOD.

A.1.f.: I can write an equation into standard form from slope intercept form. (POWER STANDARDS REVIEW): C.1.d.: I can perform function composition and evaluate a function with

given input values in the process. (POWER STANDARDS REVIEW BLOCK): E.2.a./F.BF.3.:

I can determine whether a quadratic function has a maximum or a minimum.

I can determine the domain and range of a quadratic function and graph the function with and without technology.

#1. Find all solutions of the equation:


#2. Consider the factored polynomial function: f(x) ( ) ( ) Identify the zeros of this function and state the multiplicity of each.

a. _____________ is a zero of multiplicity _____________.

b. _____________ is a zero of multiplicity _____________.

c. State whether the graph crosses the x-axis or touches and turns around at each zero.

#3. Determine the degree, and identify the x and y intercepts: f(x) ( ) ( )( ) ANSWERS: SHOW ALL WORK HERE:

X-Intercepts:

Y-Intercepts:

#4. Use all available methods (in particular, the Conjugate Roots Theorem, if applicable) to factor the following polynomial equation completely, making use of the given zero. f(x) = ; is a zero Show work here:


#5. What are the real roots of: ?

#6. What is the factored form of: ?

#7. What are the zeros of: y = (x + 9)(4x + 2)(x – 8)?

#8. What is the multiplicity of f(x) = ( ) ?

#9. For this polynomial: ( ) , what type of behavior will the graph exhibit at the x-

intercept?

#10. A quintic polynomial has rational coefficients. If √ and 10 – i are roots of P(x) = 0, what

are the additional roots?

#11. Factor the following and determine the zeros and the multiplicities.

( )

#12. A polynomial with real coefficients has roots of: 7, -8, 10i, and √ . What must be some

other ROOTS of this polynomial?


#13. The following is the graph of a cubic function. How many ‘distinct’ zeros does it have?

How many zeros are ‘real’ and how many are complex?

#14. Evaluate this function for x = -2: f(x) = .

#15. A fourth degree polynomial, P(x) with real coefficients has 4 distinct zeros, 2 of them are

10 and 6 – i. What must be true about the other two?

#16. A fifth degree polynomial has been factored to be:

( ) ( )( ) ( ) . How many x-intercepts does it have?


#17. What are the zeros of: ( ) ( )( )( )?

#18. Factor: . State the domain and range of the quadratic function, as well.

#19. The following polynomials have a degree of 5. How many ‘distinct’ real zeros are there for

each graph? How many are real and how many are complex/imaginary?

#1. #2. #3.

#20. What numbers are zeros and what are their multiplicities for:


#21. F.2.c.: Consider the graph of the function: f(x) = , which has one x-

intercept at (-4,0). Find all the other zeros of the function algebraically. Show your work, and

explain how you found all your answer. Additionally, name the intervals where the function

both INCREASES and DECREASES.


#22. Consider the graph of the function shown below:

a. Write the intervals in which the function is INCREASING or DECREASING.

b. Where are the approximate zeros of this function?

c. Identify the relative minimum and maximum values.

d. Are there any zeros for this function that might possibly have a multiplicity greater than 1? If so, where at?


What are the zeros for the following polynomial functions? Additionally, state the degree of each, and determine the # and types of zeros (real, imaginary, distinct). How many x-intercepts will each function have? #23. f(x) = x(x - 8)( ) ( )

ANSWERS: List ALL of the Zeros:

Degree:

# of Real Zeros:

# of Imaginary Zeros:

# of Distinct REAL Zeros:

# of x-intercepts:

#24. f(x) = ( ) ( )(2x – 10)

ANSWERS: List ALL of the Zeros:

Degree:

# of Real Zeros:

# of Imaginary Zeros:

# of Distinct REAL Zeros:

# of x-intercepts:


FLASHBACK: Solve, graph and write each in interval form: #1. | | #2. | | #3. | | #4. | | #5. Consider the following quadratic: Determine the number and type of roots for this equation using the discriminant. State the domain and range, as well.


Consider the following function: #6. What is the vertex of the function?

#7. What is the axis of symmetry?

#8. Does the parabola have a minimum or a maximum and where at? State the domain and range

#9. Where is the y-intercept? Let m = 5 – 7i and h = 2 + 9i #10. Find m – 6h #11. Find m · h

#12. What is

? #13. What is m + h?

Use the following functions to answer the questions: f(x) = 3x – 2 g(x) = h(x) = 4x + 8 k(x) =

#14. Find (

)( ). #15. Find (g – k)(5)


#16. F.IF.2.: If f(x) = , find f(-5) a. -17 b. 18 c. 33 d. 17

#17. F.IF.1.: Which graph does NOT represent a function?

a. b.

c. d.


#18. F.IF.2.: For f(x) = -5x – 2, evaluate f(5). a. -32 b. -27 c. 23 d. -15

#19. F.IF.2.: Suppose that g(x) = x + 9 and f(x) = 2x + 10. Find f(x) + g(x)

a. 22x b. 3x + 1 c. 3x + 19 d. 3x – 10

#20. F.IF.2.: Evaluate the function f(x) = 2x + 8 when x = 6.

a. 16 b. 20 c. 28 d. 96

#21. F.1.a.: Which expression is equivalent to ( ) ( )?

a. b. c. d.

#22. F.1.a.: Which expression is equivalent to ( ) ( )?

a. b. c. d.

#23. F.1.a.: Find the product of 2x + 5 and 3x – 4.

a.

b.

c.

d. #24. F.2.d./F.IF.7./F.IF.4.: How many times does the graph of cross the x-axis?

a. 0 b. 1 c. 2 d. 4


#25. F.2.c.: Which graph could represent a cubic function with 2 distinct real zeros?

#26. F.1.a.: 3p4(4p4 + 7p3 + 4p + 1) a. 12p8 + 3p7 + 4p5 + p4

b. 12p8 + 21p7 + 12p5 + 3p4

c. 7p8 + 10p7 + 7p5 + 4p4

d. 12p16 + 21p12 + 15p4

#27. A certain ninth degree polynomial function can be factored as:

( )( ) ( )( ) How many x-intercepts does this function have?

#28. If m<QRT = and m<TRS = , write a polynomial that represents the measures of <QRS.


FLASHBACK: Quadratics/Discriminant: FIRST: Find the discriminant of each and then state the number and type of roots that each will have. SECOND: Solve each using the quadratic formula: #1. #2.

Chapter 5 Test Review Algebra II Chapter 5 Test Revie€¦ · · 2017-01-1810 Chapter 5 Test...

Documents

Transcript of Chapter 5 Test Review Algebra II Chapter 5 Test Revie€¦ · · 2017-01-1810 Chapter 5 Test...