Honors Algebra 2 2018 - 2019

Honors Algebra 2 is a rigorous course that requires the use of Algebra 1 skills. The summer

work is designed to maintain and reinforce these prerequisite skills so as to prepare you for the upcoming school year. If you need help with a topic, use the online Algebra 1 textbook as a resource (the link is on our Google Classroom).

Complete the summer packet in pencil only

Show all necessary work

Due on the first day of class

A test on the summer packet will be given on the first day of class

Please join Google Classroom using the code

3skgnr5

Google Classroom will be used for future postings and information throughout the summer.

For the 2018-2019 school year, you will be required to bring the following supplies to class every day

TI-84 Plus or TI-84 CE graphing calculator

1

inch 3-ring binder with 8 dividers

Red pen

Mechanical pencils

Loose leaf paper

Colored pencils

Honors Algebra 2 Summer Packet Name ________________________________________ Pencil only!

Show all necessary work to receive credit. Due: First day of class.

Chapter 1: Solving Linear Equations

1) 173106 aa 1) ______a

2) 12745 ww 2) ______w

3) 15154124

3 cc 3) ______c

4) 77444411 ppp 4) ______p

5) 7105

26

5

3 ee 5) ______e

Solving Proportions

1) Solve: 9

43

x 1) x = ______

2) Solve: 1

4

1

3

xx 2) x = ______

Determine if each equation has no solution or an infinite number of solutions.

1) 232224 xx 1) ___________

2) 933

2446 mmm 2) ___________

Rewriting Equations and Formulas

t.PM 021

1) The formula above gives the amount of money M earned after P dollars is invested for t years. Which of the following gives P in terms of M and t?

A) t.MP 021 B) t.

MP

021 C) t.MP 021 D) t.MP 021

t.,a 0810521

2) The speed of a sound wave in air depends on the air temperature. The formula above shows the relationship between a , the speed of a sound wave, in feet per second, and t, the air temperature, in degrees Fahrenheit. Which of the following expresses the air temperature in terms of the speed of a sound wave?

A) 081

0521

.

,at

B)

081

0521

.

,at

C)

081

0521

.

a,t

D)

0521

081

,a

.t

CByAx

3) The equation above represent the standard form of a line. Which of the following expresses y in terms of A, B, C, and x?

A) BAxCy B) B

AxCy

C)

Ax

BCy

D)

B

AxCy

Chapter 2: Solving and Graphing Inequalities

Write an inequality that represents the graph.

1) ___________ 2) ___________

Solve each inequality.

3) 142

x

3) __________________

4) 11256 xx 4 __________________

5) What is the solution to the inequality ?11252 x

A) 7x

B) 7x

C) 18x

D) 18x

Determine if each inequality has no solution or an infinite number of solutions.

1) 53862

1 xx 1) _________________

2) 82634 xxx 2) _________________

Compound Inequalities

Graph the compound inequality.

1) 3x or 4x 2) 31 x

Choose the compound inequality represented by the graph.

3) 4)

A) 30 x A) 3x or 3x

B) 30 x B) 3x or 3x

C) 30 x C) 33 x

D) 0x or 3x D) 33 x

Solve the compound inequality and graph the solution.

5) 1112 x or 123 x 6) 1156 x

Chapter 3: Graphing Linear Equations

Give the slope of each line.

1) m = ____________ 2) m = _____________ 3) m = _____________ 4) m = _____________

5a) What is the x-intercept of the graph of the equation ?yx 662

A) 1

B) 2

C) 3

D) 6

5b) What is the y-intercept of the graph of the equation ?yx 662

A) 1

B) 2

C) 3

D) 6

6) What is the x-intercept of the line with equation 62 xy ? 6) ___________

7) Find the slope of the line passing through the given points.

a) 14, and 62, a) ___________

b) 42, and 44, b) ___________

c) 41 , and 72 , c) ___________

d) 36, and 86, d) ___________

8) Which of the following is the slope-intercept form of ?yx 843

A) 24

3 xy B) 2

4

3 xy C) 2

3

4 xy D) 2

3

4 xy

A B C D

Graph each line using the slope and y-intercept.

9) 4 3y x 10) 1

52

y x

slope ______ y-int ______ slope ______ y-int ______

Graph each horizontal or vertical line.

11) 3y 12) 3x

13) The total amount of water, w, in gallons, left in a tank can be modeled by the equation

tw 5300 , where t is the number of hours since the tank started leaking. Which of the

following is the best interpretation of the number 5 in the equation? A) The tank is empty after 5 hours B) The tank loses 5 gallons of water each hour

C) The tank continues to lose water until 5 gallons are left D) Each hour, the tank loses 5 less gallons of water than it did in the previous hour

1518 ta

14) A bank customer made an initial deposit into a savings account, and then deposited a fixed amount each week into the account. The equation above models the amount, a, in dollars after t weeks. What was the dollar amount of the initial deposit? $ ________

Chapter 4: Writing Linear Equations

Write the equation of each line in slope-intercept form.

1) ________________ 2) __________________

Write the equation of each line.

3) _____________ 4) ______________

Write the slope-intercept form of the equation with the given characteristics.

5) slope = 4

1; passes through (0, 2) 5) __________________

6) What is the equation of the line that has a slope of 4 and passes through the point (3, -10)?

A) 224 xy

B) 224 xy

C) 434 xy

D) 434 xy

Write the slope-intercept form of the equation with the given characteristics. 7) passes through (2, 1) and (3, -5) 7)__________________ 8) parallel to 53 xy ; passes through (-4, 6) 8) _________________

9) perpendicular to 82

1 xy ; passes through (0, 6) 9) __________________

10) a horizontal line that passes through (3, -5) 10) ________________ 11) The table below shows the distance covered by a spaceship in 11) _________________ outer space. Write an equation in slope-intercept form that represents the distance traveled as a function of time.

12) Which point-slope equation represents a line that passes through (5, -3) with slope 6?

A) 365 xy

B) 365 xy

C) 563 xy

D) 563 xy

13) Rewrite the equation below in standard form CByAx 13) _____________________

43

2 xy (A, B, and C are integers and A > 0)

Chapter 5: Solving Systems of Equations

1) Give the (x, y) solution to the system graphed below. 1) ________________

2) Find the (x, y) solution to the system of equations by graphing. 2) ________________

42

13

xy

xy

3) Which of the following ordered pairs (x, y) is a solution of the system below?

2

1053

yx

yx

A) 02, B) 20, C) 42, D) 64,

4) Write a system of equations for the system graphed below.

Find the (x, y) solution to the system of equations.

5)

142

3

yx

yx 5) __________

____________________

____________________

6)

2

2042

xy

yx 6) __________

7) An online movie club has an initiation fee of $10 plus $4 per movie rented.

Another club has an initiation fee of $20 plus $2 per movie rented.

The equations below model the memberships for the two clubs.

202

104

mc

mc

a) After how many movies will the memberships cost the same amount? a) ___________

b) What is that cost? b) ___________

8) Solve the system.

622

1432

yx

yx 8) ___________

9) What is the solution to the system solved below?

124

524

yx

yx

0 = 6

A) (0, 6)

B) (6, 0)

C) No solution

D) Infinitely many solutions

10) Find the (x, y) solution to the system of equations.

822

103

yx

yx 10) __________

Graphing Linear Inequalities

1) Graph the linear inequality. Use a color pencil to shade the solution.

43

1 xy

2) Is 54, a solution of the inequality 32

1 xy ? Show your work!

3) Which one of the following points is not a solution of the inequality graphed below?

A) 11,

B) 12 ,

C) 32,

D) 41,

4) Which of the following linear inequalities is graphed below?

A) 12 xy

B) 12 xy

C) 12 xy

D) 12 xy

Systems of Linear Inequalities

1) Is 32, a solution of the system of linear inequalities below? Show your work!

82

43

xy

xy

2) Graph the system of linear inequalities. Use 2 different color pencils to shade. Clearly label

the solution region.

3

2

1

12

xy

xy

3) Choose the system of inequalites graphed below.

32

1

12

1

xy

xy)A

32

1

12

1

xy

xy)B

32

1

12

1

xy

xy)C

32

1

12

1

xy

xy)D

Chapter 6.1: Exponents.

1) The product of 336 yx and yx22 is

A) 23xy B)

458 yx C) 4512 yx D)

3612 yx

2) 24

A) 16

1 B) 16 C) 8 D)

8

1

3) 4x

x

A) 3x B) 3

1

x C)

3

x D) 3x

4) For any nonzero value of x, 24x

A) 8x B)

8

1

x C)

2x D) x8

5) Expressed in simplest form, ac

ca

4

12 3

is equivalent to

A) 28a

B) 23a

C) ca23

D) ca33

6) Which expression is equivalent to 2

246

2

2182

x

xxx ?

A) 23 9xx B)

24 9xx C) 19 23 xx D) 19 24 xx

7) 342x

A) 128x B)

78x C) 76x D)

126x

8) 25 yx

A) 5

2

x

y B)

2

5

y

x C)

25

1

yx D)

25 yx

9) 03

A) 0 B) 1 C) 3 D) 3

1

Chapter 7: Polynomials

1) Write 32 423 xxx in descending order for the variable x. 1) ________________________

625253 22 xxxx

2) What is the sum of the two polynomials above?

A) 478 2 xx

B) 478 2 xx

C) 478 24 xx

D) 478 24 xx

222222 3353 yxyyxxyyyx

3) Which of the following is equivalent to the expression above?

A) 224 yx

B) 22 68 yxy

C) 22 22 xyyx

D) 222 682 yxyyx

4) Find each product.

a) 1453 2 xxx a) ________________________

b) 24322 72 xyyxyx b) ________________________

5) Find each product.

a) 43 xx a) _________________________

b) 17 xx b) _________________________

c) 66 xx c) _________________________

d) 3232 xx d) _________________________

e) 24x e) _________________________

6) Which trinomial is equivalent to 413 xx ?

A) 4113 2 xx

B) 4113 2 xx

C) 4133 2 xx

D) 4113 2 xx

Factoring a Polynomial

1) ___x___xxx 1072

2) 22 96 ___xxx

3) ___x___xxx 50152

3) The polynomial 16249 2 xx factors to 2bax . What are the values of a and b?

a = _____ b = _____ Factor the polynomial.

4) 20122 xx 4) _____________________________

5) 1582 xx 5) _____________________________

6) 322 xx 6) _____________________________

7) 642 x 7) _____________________________

8) 22 yx 8) _____________________________

9) 4925 2 x 9) _____________________________

Factor as the square of a binomial.

10) 1682 xx 10) _____________________________

11) 93025 2 xx 11) _____________________________

Factor using the GCF.

12) 204 x 12) _____________________________

13) xx 62 2 13) _____________________________

14) yxyx 452 14) _____________________________

Factor completely.

15) 502 2 x 15) _____________________________

16) 30213 2 xx 16) _____________________________

17) Which represents the complete factorization of ?xx 122 2

A) 122 xx

B) xx 62 2

C) 62 xx

D) xx 1212 2

18) Which represents the complete factorization of ?xx 1452

A) 72 xx

B) 72 xx

C) 141 xx

D) 141 xx

19) Which binomial is a factor of ?xx 652

A) 6x

B) 2x

C) 3x

D) 1x

Chapter 3.1 – 3.3: Functions

1) Determine whether each relation represents a function. If it is not, circle elements that fail

Use the Vertical Line Test (VLT) to determine if each graph represents a function.

2) 3) 4)

5) 6) 7)

8) What number(s) can be placed in the empty cell so that the table of values satisfies the definition of a function? Select all that apply. A. -5 B. -1 C. 0 D. 2 E. 11 F. 17

Function f is graphed at the right.

9) Find 5f .

10) For what value of x does ?xf 6

The table represents a function f.

11) _______f 1

12) For what value of x does ?xf 2

13a) What is the x-intercept of the function? _________ b) What is the y-intercept of the function? _________ c) Write an equation in slope-intercept form to represent the function. ____________________

14) If f is a function defined by ,52 xxf for what value of x 14) ___________

does ?3xf

15) Let 23 xxf and 4 xxg . Find the following:

a) 3f a) _________________

b) 1g b) _________________

c) xf2 c) _________________

d) xgxf d) _________________

e) xgxf e) _________________

f) xgxf f) _________________

x f(x)

-1 -2

0 -1

1 2

2 0

16) The function f is defined by axxf 2 , where a is a constant. If ,71 f

what is the value of a? A) 5 B) 7 C) 8 D) 9

17) Graph the function 42 xxf using the slope and the y-intercept.

18) Give the domain and range of the function.

19) Give the domain and range of each function.

Domain ____x___ Domain ____x___ Domain ___x___ Domain ____x

Range ____y___ Range ____xf___ Range ____y___ Range ____y

Domain ______________

Range _______________

20) What is the domain of the function graphed below?

A) 1x

B) 3x

C) 1x

D) all real numbers

21) What is the range of the function graphed below?

A) 1y

B) 3y

C) 3y

D) all real numbers

22) What is the range of the function graphed below?

A) 2y

B) 0y

C) 0y

D) all real numbers