Name _________________________________________ Date _________ Per. _____/Teacher ____________________

A2TH – Common Core Review #1

1.

2.

3.

Name _________________________________________ Date _________ Per. _____/Teacher ____________________

A2TH – Common Core Review #2

3.

4. 5.

6.

7.

8.

9.

10.

11.

Parabolas

12.

13.

Name ________________________________________ Date__________________

Algebra 2

Regents Review Packet #2: Units 6-7 DIRECTIONS: Show all work in the space provided. All work must be shown or no credit will be given.

DUE: Thursday, 4/21

UNIT 6 – QUADRATIC EQUATIONS

1) A homeowner wants to increase the size of a rectangular deck that now measures 14 feet by 22

feet. The building code allows for a deck to have a maximum area of 800 square feet. If the

length and width are increased by the same number of feet, find the maximum number of whole

feet each dimension can be increased and not exceed the building code. [3 points]

2) Solve for x and express your answer in simplest form: [2 points]

#3

3) Which value of k will make a perfect square trinomial? [1 point]

1)

2)

3)

4)

4) Find the exact roots of by completing the square. [2 points]

5) Solve for x and express your answer in simplest radical form: 86)(x4

1 2 [2 points]

UNIT 7 – POLYNOMIAL FUNCTIONS

6) If a, b, and c are all positive real numbers, which graph could represent the sketch of the graph

of ( ) ( )( ) ? [1 point]

7) Use an appropriate procedure to show that is a factor of the function

( ) . Explain your answer. [2 points]

8) Solve algebraically for all values of x: . [3 points]

9) Solve algebraically for all values of x: [3 points]

10) Find four roots of the following equation: 2032 24 xx [3 points]

11) What are the zeros of the polynomial function graphed below? [1 point]

12) Use a graphing calculator to graph . Tell whether the function is odd, even, or neither.

Explain your answer. [2 points]

13) Sketch the graph of a polynomial with the given characteristics [2 points]

is increasing when .

is decreasing when

( ) when and .

( ) when .

1)

2)

3)

4)

14) Find the value of so that

has a remainder of 8. [2 points]

15) Write a polynomial function in standard form with least degree whose roots are given. [3 points]

√ , √ , ,

16) Consider the polynomial function [4 points]

( ) .

a) Verify that ( ) . Since ( ) , what must one of the factors of be?

b) Find the remaining two factors of and state the zeros of .

d) Sketch the graph of .

17) Consider the graph of a degree 5 polynomial shown to the right, with x-intercepts, , , , ,

and [3 points]

a) Write a formula for a possible polynomial function that the

graph represents using as the constant factor.

b) Suppose the -intercept is . Find the value of so that

the graph of has -intercept .

18) Solve the following system of equations algebraically: [4 points]

Name ________________________________________ Date__________________

Algebra 2

Regents Review Packet #4: Units 8-9

DUE: Friday, 4/29 DIRECTIONS: Show all work in the space provided. All work must be shown or no credit will be given.

UNIT 8 – RATIONAL EXPRESSIONS AND EQUATIONS

1) Solve for x:

[2 points]

2) Write (

)

(

) as an equivalent rational expression in lowest terms. [2 points]

3) A boat goes 240 miles downstream in the same time it can go 160 miles upstream. The speed of the current is 5 miles per hour. What is the speed of the boat in still water? [2 points]

4) What is the solution set of the equation ? [1 point]

1)

2)

3)

4)

5) Working by herself, Mary requires 16 minutes more than Antoine to solve a mathematics

problem. Working together, Mary and Antoine can solve the problem in 6 minutes.

Using the equation

how many minutes will it take Antoine to solve the problem if

he works by himself? [2 points]

6) Which expression is in simplest form? [1 point]

(1) x

x2 (3)

x

x

2 4

2

(2) 9

92x (4)

x x

x x

2

2

6 9

6

UNIT 9 – RATIONAL EXPONENTS AND RADICAL EXPRESSIONS /EQUATIONS

7) Use the properties of rational exponents to determine the value of y for the equation: [2 points]

√

( )

8) Solve algebraically for x: [2 points]

9) The expression 2

32 1

x is equivalent to [1 point]

(1)

(2)

(3)

(4)

10) Solve for b: 302)( 2/14/3 bb [2 points]

11) Rewrite the given expression in the form , where is a real number, is a positive real

number, and is rational. √

( √

) [2 points]

12) Show that for any rational number , the expression (

)

is equal to [2 points]

13) Express 3 53

3 95

7

378

ba

ba in simplest radical form. [2 points]

14) Simplify: [2 points]

15) Solve for all values of x:

√

[2 points]

Name ________________________________________ Date__________________

Algebra 2

Regents Review Packet #5: Unit 10 Parts 1 and 2

DUE: May 10th DIRECTIONS: Show all work in the space provided. All work must be shown or no credit will be given.

UNIT 10 Part 1 – Exponential and Logarithmic Functions

1)

[2 points]

2) What is the inverse of the function y = log 3 x

(1) 3 y = x (3) x 3 = y

(2) 3 x = y (4) y = x 3

[2 points]

3) If and , the expression is equivalent to

1) 3)

2) 4)

[2 points]

4) Which expression is not equivalent to log ?b 36

(1) 6 2logb (3) 2 6logb

(2) log logb b9 4 (4) log logb b72 2

[2 points]

5) The expression 1

2log log3

x y is equivalent to:

(1) 3

logx

y (2)

2

3log

x

y (3) 3log xy (4) 3log( )x y

[2 points]

6) If 2

2

abd

c , then log d is equal to:

(1) 1

log (log log )2

a b c (3) log 2(log log )a b c

(2) log log loga b c (4) 1 1

log log log2 2

a b c

[2 points]

7) Solve for x:

[2 points]

8) Todd invests $7,000 at an annual interest rate of 4.2% compounded continuously. Use the formula rtPeA

to determine how many years, to the nearest tenth of a year, it will take for Todd’s investment to triple.

[4 points]

9) Use the change of base rule to solve for x: )3(log)22(log 525 xx

[4 points]

10) Solve for x: 2)5(log)32(log )3()3( xx xx

[4 points]

11) Solve for x to the nearest hundredth: 10055 3 xx [4 points]

UNIT 10 Part 2 – Exponential and Logarithmic Functions

12)

[2 points]

13) A savings account initially has a balance of $500. The number of years, t, that the money must be in

the account for it to grow to a balance of b dollars is shown in the accompanying table.

Balance (b)

500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

Years (t)

0 13.9 21.9 27.7 32.2 35.8 38.9 41.6

(a) Determine a logarithmic regression equation that models this data. Round coefficients to the nearest hundredth.

(b) Use the regression equation found in part a to predict, to the nearest tenth of a year, the number of years the money must be left in the account for it to grow to a balance of $7,500.

[4 points] 14) Find the inverse of the following function and state the domain and range of the original function and inverse function.

2)( xexf

[4 points]

15) Suppose that you would like to buy a home priced at 220,000. You plan to make a payment of of the purchase price and pay of the purchase price into an escrow account annually. Compute the total monthly payment of the loan for a -year mortgage at 4.6% annual interest.

[4 points]

16)

[4 points]

17) [4 points]

Name ________________________________________ Date__________________

Algebra 2

Regents Review Packet #6: Units 11 – 13

DUE: May 20, 2016 DIRECTIONS: Show all work in the space provided. All work must be shown or no credit will be given.

UNIT 11 – Sequences and Series

1) Write an explicit formula for the nth term of the recursively defined sequence below.

For what values would when {4 points}

2) What is the common ratio of the sequence ?

1)

2)

3)

4)

{1 point}

3) Write the sum without using summation notation, and find the sum.

∑

{2 points}

4) Find the sum of the following geometric series:

{2 points} 5) Write a rule for the nth term of sequence 57, 48, 39, 30, …

{2 points}

Unit 12 – Intro to Trig 6) Find the degree measure of an angle of 2.75 radians to the nearest tenth. {2 points}

7) Use the Pythagorean identity , where is any real number, to find

the following:

, given

for

.

{2 points}

8) Simplify the expression:

{1 point} 9) In which quadrant does the terminal side of lie when {1 point} 10) Find the exact value of sec(-120°)

{2 points}

11) Point 1),5Q( is on a circle of radius r whose center is at the origin. If is an angle in

standard position whose terminal ray passes through point Q, find the value of:

f) cos

b) sin c) csc

d) cot

e) tan f) sec

{4 points}

Unit 13 – Trig Graphs

12) Which statement is incorrect for the graph of the function [

] ?

(1) The period is 8. (2) The amplitude is 6. (3) The range is [-6, 6] (4) The midline is

{1 point} 13) Write an equation to represent the graph below.

{2 points} 14) Which of the following functions has a maximum value of 25?

(1) (3)

(2) (4)

{1 point}

15) Suppose that a Ferris wheel is feet in diameter and rotates counterclockwise. When a

passenger car is at the bottom of the wheel, it is located feet above the ground. It takes 6 minutes

to go around the Ferris wheel one time.

a. Sketch a graph of a function that represents the height of a passenger car that starts at the top

of the wheel for one turn.

b. The sketch you created in part (a) represents a graph of a function. What is the domain of the

function? What is the range?

c. Find the equation for the function in part (a).

{6 points}