Algebra II CP

Midterm Exam Review Packet

Name:______________________

Hour:______________

ALGEBRA II-CP Name___________________________________

Midterm Review - Ch. 1, 2,3

Solve each equation.

1. 8(–12y + 10) = 92 – 6(16y + 2) 2. 7x + 3 = 2(x – 1) 3. 10

4

5

x

4. 95

3 x 5. 4t – 12 = –t + 11 6. 6x – 10 – (x + 5) = 0

7. What is the slope of the line whose equation is 4x – 5y = 10?

8. What is the slope of the line passing through (2, 6) and (-9, 8)?

9. For which pair of equations are the lines perpendicular?

A. 2x – y = 1 and xy2

1 B. 6x + 3y = 10 and 3x – 6y = 10

C. y = 5x and y = -5x D. 3x + 2y = 1 and 2y = 3x + 8

10. For which pair of equations are the lines parallel?

A. y – 5 =3x and 2y – 6x = –12 B. 5x + 3y = 15 and 3x + 3y = 15

Find the equation of the line in any form satisfying the following conditions.

11. Passes through ( 2 , 6 ) and is parallel 12. m = 0 passes through ( 1 , -8 )

to -5x + 2y = 7

13. Passes through ( -1 , 2 ) and ( -5 , -3 ) 14. Passes through ( 0 , 4 ) and is perpendicular to y = 6x - 7

Solve by these systems by graphing by hand (please sketch graph).

15. –2x + y = –7 16. x + 4y = 4

3x – 4y = 8 y = -4

1x + 5

Solve by substitution

17. 2x – y = –1 18. 5x + 3y = 8 19. x + 2y = 12

y + x = 4 5x + y = 16 4x + 8y = -19

Solve by elimination 20. x – y = 7 21. 5x – 7y = –2

2x + y = 5 3x + 2y = 36

22. For which system are there infinitely many solutions?

A. 3x + 5y = 7 B. x – 5y = 7 C. 3x – y = 8 D. 2x – y = 1

6x + 10y = 14 2x = 10y + 15 3x + y = 10 y = 2x – 3

Define TWO variables, write TWO equations and solve by substitution or elimination. Show all work for full credit!

23. The sum of two numbers is 106. One number is five less than twice the other.

What are the two numbers?

24. At McDonald’s, 2 burgers and 2 fries cost $5.50. If you order 3 burgers and 4 fries it cost $9.25.

How much does one burger cost? One order of fries?

25. The perimeter of a rectangular garden is 168 ft. The length of the garden is 30 more than 5 times the width.

What are the dimensions of the garden? (You must have two equations!)

26. Ticketmaster sells pavilion and lawn tickets to Pine Knob. A total of 5,000 tickets were sold for a concert. The

pavilion tickets cost $20 each and the lawn tickets cost $15 each. The sales for all tickets totaled $82,500. How many of

each type of ticket were sold?

Algebra II: Chapter 4 Midterm Review Name _______________________________________________

Multiple Choice: Select the letter that best answers the question.

1. Determine the vertex and axis of symmetry of the

following quadratic:

12642 xy

2. Determine the vertex and the maximum or minimum

value of the following quadratic:

32

1 2 xxy

1. _____

2. _____

A. Vertex: 12,6

Axis: 6x

B. Vertex: 12,6

Axis: 12x

A. Vertex: 5.1,1

Max. Value: 5.1

B. Vertex: 3,1

Max. Value: 3

C. Vertex: 12,6

Axis: 6x

D. Vertex: 12,6

Axis: 6x

C. Vertex: 5.4,1

Min. Value: 5.4

D. Vertex: 5.3,1

Min. Value: 5.3

Determine whether the equation is in Vertex, Intercept, or Standard form. Then, find the indicated values and graph each equation. Don’t forget to draw the axis of symmetry!

3. 4123 2 xxy

4. 3105 2 xxy

Vertex or Intercept or Standard Vertex or Intercept or Standard

Opens __________ Opens __________

Vertex ,

Vertex ,

Axis of Symmetry __________

Maximum or Minimum

Value ___________

Axis of Symmetry __________

Maximum or Minimum

Value ___________

Determine whether the given equation is in Vertex, Intercept, or Standard Form.

5. 152 xxy

6. 232

1)( 2 xxxf

7. 334

1 2 xy

Vertex or Intercept or Standard Vertex or Intercept or Standard Vertex or Intercept or Standard

Multiple Choice: Select the letter that best answers the question. 8.

Simplify xx 8326 4

8. ______

A. xx248

B. xx296 C. xx96

D. xx 4192 2

9.

Simplify 526134

9. ______

A.

532026624

B.

532026624

C.

5514624

D.

532026624

10.

Simplify ii 763217

11. _____

A. i2335

B. i191 C. i923 D. i2325

11.

Simplify i

i

3

254

12. _____

A. 3

2

3

54

i

B. 3

2

3

54

i C.

3

2

3

54 ii D.

3

2

3

54 i

Use what you know about simplifying square roots and the properties of i to answer the following questions. Make sure that all denominators are rationalized and each root is completely simplified.

12. ii 3623

13. 511511

14.

54

2

15. i

i

12

153

Answer: ____________________

Answer: ____________________ Answer: ____________________ Answer: ____________________

16.

Simplify: 21

7

17.

Simplify: i

i

8

102

18.

Find the value of the discriminant and describe the zeros of: 823 2 xx

18._____

A. D = 100

2 real zeros

B. D = 100

1 double zero/root

C. D = − 94

2 imaginary zeros

D. D = 96

2 real zeros

19.

Find the solutions/zeros of: 2x2 − 4x + 3 = 0

19._____

A. 22 i B. i1 C. 22 i

D. 2

21

i

20.

Find the solutions/zeros of: 2x2 − 5x − 3 = 0

Algebra II: Chapter 5 Midterm Review Name _______________________________________________

Evaluate or simplify the expression completely. 1.

2405 57 eheh

2.

2

6

05

db

a

3.

23

56

16

34

dc

dc

Answer: ______________________________

Answer: ______________________________ Answer: ______________________________

4.

3274yx

5.

1811 310 xwxw

6.

04

73

13

39

cb

cb

Answer: ______________________________

Answer: ______________________________ Answer: ______________________________

7.

Which of the following expressions is equivalent to: cab

bca3

12

12

8

7. _____

A. 3

2 22cab

B. 223

2

cb

a C.

23

2

b

a D.

bc

a

3

2

8.

Which of the following expressions is equivalent to: 23624 223 aaaa

8. _____

A. 854 23 aaa B. 44 23 aaa C. 837 23 aa

D. 854 23 aaa

9.

Which of the following expressions is equivalent to: 4912 2 xxx

9. _____

A.

B.

C.

D.

Use the graph to describe the end behavior, determine the number of real zeros, and estimate the indicated value. 10.

______)(,

______)(,

xfxAs

xfxAs

11.

______)(,

______)(,

xfxAs

xfxAs

Number of real zeros: _________

Local Maximum: ,

Number of real zeros: _________

Local Minimum: ,

Identify all of the factors of each polynomial.

12. 18 3 y

13. xx 542 4

Factors: _________________________________

Factors: _________________________________

14. 283 24 xx

15. xxx 10122 35

Factors: _________________________________

Factors: _________________________________

Use synthetic division to divide the following polynomials.

16. 54413112 23 xxxx

17. 2101525 24 xxxx

Answer: ___________________________________________________ Answer: ____________________________________________________

Given polynomial xf and a factor of xf , factor xf completely.

18. One factor of 2425 23 xxxxf is 2x .

Find the remaining factors.

19. One factor of 673 xxxf is 1x . Find the

remaining factors.

Remaining Factors: __________________________________________ Remaining Factors: __________________________________________

20.

Find two of the zeros of the function: 362753 234 xxxxxf

20._____

A. 4,3 B. 1,3 C. 4,3i D. 4,3 i

21.

Find two of the zeros of the function: 42355 234 xxxxxf

21._____

A. 7,6 B. 5.3,1 C. 7,6 i D. 7,1 i

Write an equation in standard form with the following zeros:

22. ixandx 59

23. 74 xandix

Equation: ___________________________________________________ Equation: ___________________________________________________

24. The function whose graph is shown has _____.

24. ____

A. two local maximums B. no local maximums C. two local minimums D. one local minimum

Algebra II: Chapter 6 Midterm Review Name _______________________________________________

Evaluate the expression.

1. 3

4

27

2. 25 32

Use the properties of rational exponents to simplify. Express in simplest radical form.

3. 2

8

2

5

44

4.

5

4

5

7

m

m

5.

7

2

2

3

4

1

55

6.

7

3

3

1

5

2

xx

7.

7

12

7

4

x

x

8. 5

8

10

1

bb

9.

Which of the following expressions is equivalent to: 276752185

9. _____

A. 323 B. 38215 C. 21531054 D. 38215

10.

Which of the following expressions is equivalent to: 3 93427 zyx

10. ____

A.

33 33 xxyz B. 333 xxyz C.

33 39 xxyz D. 33 93 xxyz

Simplify the expression using the properties of radicals.

11. 4 54 8285 xx

12. 4 44 3 271096 yy

13.

If 932

xxh and ,53 32

xxxm find: xmxh ?

13. _____

A. 934 32

xx B. 934 32

xx C. 34

63 xx D. 97 37

x

14.

If 932

xxh and ,53 32

xxxm find: xhxm ?

14. _____

A. 934 32

xx B. 934 32

xx C. 34

63 xx D. 97 37

x

Let 32,95 xxgxxf . Perform the indicated operation.

15. xgf

16. xfg

Find the inverse of the function.

17. 23

4)( xxf

18. 92 xxf

Let 3,5 xxgxxf , 3

1

xxj , and 11 xxm . Find only the domain of each.

19.

)(xf

xg

20. xm

xj

Domain: ______________________ Domain: ______________________

Find the solution(s) to the equation:

21. 34 xx

22. xx 188

23. 13 xx

Algebra II: Chapter 7.1-7.3 Midterm Review Name _____________________________________________ Determine whether each function represents exponential growth, decay, or neither.

1.

x

y

3

25

2. xy 2

2

1

3. xy 410

Match the function with the graph.

4. 33

4

x

y ____

5. 23 xy ____

6. 141 1 xy ____

A.

B.

C.

Match the function with the graph.

7.

2

3

2

x

y ____

8.

x

y

2

11 + 3 ____

9. 23

22

1

x

y ____

A.

B.

C.

Determine the a, b, h, k, as well as the equation for the Horizontal Asymptote, the Domain, and the Range. Then, fill out the table

and graph the function.

10. 23 4 xy

a = _______

b = _______

Growth or Decay or Neither

h = _______

______________________

k = _______

Domain: ________________________________

Range: ________________________________

HA = _______________

x y

−1

,

0

,

1

,

2

,

11.

53

21

2

x

y

a = _______

b = _______

Growth or Decay or Neither

h = _______

______________________

k = _______

______________________

Domain: ________________________________

Range: ________________________________

HA = _______________

x y

−1

,

0

,

1

,

2

,

12. 328.0 xey

a = _______

b = _______

r = _______

Growth or Decay

h = _______

______________________

k = _______

______________________

Domain: _______________________________

Range: ________________________________

HA = _______________

x y

−2

,

−1

,

0

,

1

,

Use the formulas to solve the following story problems. You will need to have these on your notecard for the exam.

tray 1 tray 1

nt

n

rPA

1

rtPeA

13. A computer system depreciates at a rate of 15% per year. If you originally bought the computer for $4000, how much would it be worth 5 years from now?

14. Brian buys a new car for $24,000. The car depreciates in value 17% per year. How much would the car be worth 8 years from now?

15. The student enrollment of a high school was 1500 in 2010 and has increased by 8% per year since then. Let t be the number of years since 2000. How many students are enrolled in the year 2015?

16. The length l (in centimeters) of a tiger shark can be

modeled by the function, tel 178.0276337 , where t is the shark’s age (in years). Use the model to estimate the length of a shark that is 3 years old.

17. Suppose you deposit $1,000 in an account paying 6.5% annual interest compounded continuously. What is the balance after 6 years?

18. You deposit $10,000 in an account paying 6.5% annual interest compounded continuously. What is the balance after 6 years?

19. You deposit $15,000 in an account that earns 5.1% annual

interest. Find the balance after 1 year if it’s compounded daily?

20. You deposit $100 in an account that pays 6% annual interest. How much will be in the account if it’s compounded monthly?