algebra i(2) semester 2 - exam review 1 · part 2 - homework graph each line. you may need to solve...

Date: ________ Name: _______________________

exam review 1Algebra I(2)

SEMESTER 2 - EXAM REVIEW 1

PART 1

- CLASSWORKSimplify each expression.

1. 17 − 3 + 2( ) ⋅ 2( ) 2. 4 + 8 ÷ 2 + 6 ⋅ 3

3. 3 + 4 13 − 2 6 − 3( )[ ] 4. 5 2 8 + 5( ) −15[ ]

Solve each equation.5. 7 − 2n = n −14 6. 2 6 − 4d( ) = 16 − 9d

7. 4g + 7 = 5g −1− g 8. 8 − 3 p − 4( ) = 2 p

1

Solve each proportion.

9. x54

=263

10. 23=x18

11. 6y=37

12. −1.64

=−m10

Solve each system of equations. Use any method.

13. 3x + 5y = 3x + y = −1 14.

2x + 4y = 02x + 6y = 6

15. 2x + y = 4y = 4x +1 16.

6x − 3y = 6y = 2x + 5

2

PART 2

- HOMEWORK

Graph each line. You may need to solve for y first.

17. y = −12x + 3 18. 2y − 3x = −12

Solve each system of equations by graphing.

19. y = −x − 3y = −2x − 8 20.

y = 23x + 4

y = −13x − 2

3

Solve each quadratic equation using the quadratic formula. Round solutions to the nearest tenth.

Quadratic Formula:

x = −b ± b2 − 4ac2a

21. x2 + 2x −3 = 0 22. 2x2 − x −12 = 0

23. 3x 2 + 7x = 13 24. x2 − 3x +10 = 50

4

Date: ________ Name: _______________________



PART 1

- CLASSWORKSimplify each expression.

1. 5 8 + 2( ) + 3 11 − 7( ) 2. 12 6 + 309 − 3

⎛ ⎝ ⎜

⎞ ⎠ ⎟

3. 3 4 + 12( )2 7 − 3( ) 4. 14 ÷ 3 8 − 2( ) −11[ ]

Solve each equation.

5. −8 = h − 53

6. 5a + 7 − 3a

3= −9

Find each sum or difference. Write your answer in standard form.

7. 7x2 + 8x +1( ) + x2 − 5x − 3( ) 8. 8x 2 − 4x +1( ) − 3x2 + 6x − 4( )

9. 3y3 + 8y2 − 3( ) + 2y − 5y2( ) 10. 6x3 − 9 + 8x( ) − 2x2 + 6x −11( )

5

Find each product. 11. 2x2 x + 3( ) 12. 6x x −1( ) − 4 x2 − x( )

Factor each expression. If the expression is not possible to factor, label “not factorable”.

13.

�

x 2 −11x + 30 14.

�

x 2 +11x + 30

15. x2 + 6x − 27 16. x2 −11x − 60

17. 3x 2 + 8x + 5 18. x2 − 22x +121

19. 49x2 −144 20. x2 −1

21. n2 +16n − 36

6

PART 2

- HOMEWORK

Find each product.

22. x +1( ) x − 3( ) 23. 2x + 6( ) x − 8( )

24. 3x + 4( ) 2x −1( ) 25. 5x − 4( ) 2x + 3( )

26. Find the length of the missing side of each triangle: a) b)

27. Simplify. If you are stuck, write these in expanded form first.

a) 3x2y5

9x3y2 b) 2x5( )3 c) 5x3 • 3x5

7

28. Expand by multiplying. Then simplify your result if possible.

a) 3x − 2( )2 b) 2 x2 + 3x( ) − 4x2 x3 −10( )

29. Simplify each radical.

a) 240 b) 3 180 c) 1498

30. Solve by factoring. Set one side equal to zero if necessary. Then factor and solve:

a) n2 −16 = 0 b) 3x2 = 5 − 2x

31. Solve using the Quadratic Formula:

2x2 −11x + 9 = 0

x = __________ or __________

8

Quadratic Formula:

x = −b ± b2 − 4ac2a

Date: ________ Name: _______________________



PART 1

- CLASSWORK

Simplify the following radicals:

1. 150 2. 80 3. 1204

Solve for x. You may have 0, 1, or 2 answers!

4. 3 x − 4 = 11 5. 5 3− 4x2( ) = 10

6. 11x2 − 22

2= 11 7.

17 − 2x2

−1+10 = 19

9

For the following, set up a system of equations and solve. Don’t forget to define your variables>

8. The sum of one number and twice the second is 28. The first number is one more than the second. Find the two numbers.

9. Five deluxe pizzas and six standard pizzas cost $102. Six deluxe pizzas and twelve standard pizzas cost $156. How much does one deluxe pizza cost? How much does one standard pizza cost?

10. Five gallons of regular unleaded gas and eight gallons of premium gas cost $17.15. Five gallons of regular unleaded and two gallons of premium cost $8.75. Find the cost of each kind of gasoline.

11. Mark has twice as many starbursts as Chris. Together they have 108. How many does each have?

10

PART 1

-HOMEWORK

12. Suzanne buys 10 shirts total. Some cost $5 and the rest cost $9. If she spends $82 on shirts, how many of each type of shirt did she buy?

13. Simplify the following expressions:

a) 3 4x − 2( ) − 2 x + 6( ) b) 2x − 7( ) x + 3( )

c) 3x − 2( )2 d) x − 3( ) x + 2( ) + 4 2x − 7( )

14. Solve the following systems of equations.

a) 3x + y = 102x − y = 5 b)

2x + 3y = 83x + y = 5 c)

y = 3 − x5x + 3y = −1

11

15. Solve by graphing: y = 3

4x + 2

y = −12x + 7

16. Solve:

a) 3x5

+32=7x10

b) 4x+32x

=116

17. Solve by factoring:

a) 2x2 − 7x + 3 = 0 b) x2 + 6x = 2x + 21

12

Date: ________ Name: _______________________



Practice Final

- CLASSWORK

Solve for x:1. 25 − 3x2 = −23 2. 9 + 2x − 2 = 11

x = ________ or ________ x = _________

3. Solve by SUBSTITUTION: 4. Solve by ELIMINATION:

2x + 2y = 3x − 4y = 1

3x + 5y = 6−4x + 2y = 5

Set up a system of equations and solve.5. In one week, a music store sold 7 violins for a total of $1600. Two types of violins were sold. One type cost $200 and the other type cost $300. How many of each type of violin were sold?

Let x = the number of violins for $200 Let y = the number of violins for $300

13

Simplify.

6. −2 −2( )4 = 7. 50 = 8. x3 • x5 • x7 =

9. 5−2 = 10. −2x3y6( )3 = 11. 8

12. 200 13. 3 50 14. 2575

15. Solve by factoring: 16. Multiply:

2x2 + 7x + 3 = 0 3x − 5( ) x + 6( )

14

17. Find the length of the diagonal:

18. Subtract: −2x3 − x2 + 5x + 7( ) − 3x3 + 7x − 9( )

19. Factor:

a) x2 +16x + 63 b) x2 −15x + 56

c) x2 −12x − 28 d) x2 + 7x − 60

15

20. The weights (in pounds) of ten freshmen are recorded below:! ! 112! ! 129! ! 172! ! 100! ! 114! ! 162! ! 145! ! 137! ! 145! ! 118

! (a) Draw a stem and leaf plot below.

!

! (b) Find the mean. ! ! _______!! (c) Find the median. ! ! _______

! (d) Find the mode. !! _______!! (e) Find the range.! ! ! _______

! (f) Find the first quartile. ! ! _______

! (g) Find the third quartile.!_______

! (h) Use this data to make a “box-and-whiskers”plot below:

!

!

21. Josie has a current average of 78 on four tests. If three of the grades are 81, 85, and 86, what was her fourth test grade?

16

algebra i(2) semester 2 - exam review 1 · part 2 - homework graph each line. you may need to solve...

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