Algebra 1Quarter 3 Assessment Practice

Chapter 5-Exponents and PolynomialsChapter 6-Polynomials and Factoring

Chapter 10-Rational Expressions and Equations

Find the equivalent expression:1.) 2.)

9 2y y11

18

18

11

A)

B)

C) 2

D) 2

y

y

y

y

5 2 2( )a b7 4

9

10 4

14

A)

B)

C)

D)

a b

ab

a b

ab

Answer = A Answer = C

Find the exponential form of…

3

6

3) 2 2 2 2 y y y

A) 16

B) 8

C) 16

D) 2

y

y

y

y

2

2

4

4) 5 5 5

A) 125

B) 15

C) 35

D) 125

a a

a

a

a

a

Answer = A

Find the simplified form…2 4

4 6

205)

45

x y

x y6 10

2 2

2 2

6 6

4A)

94

B) 9

4C)

9

4D)

9

x y

x y

x y

x y

7

3

246)

12

x

x10

4

4

4

A) 2

2B)

2C)

D) 2x

x

x

x

B

D

Simplify

7) 4(-2)(-x)(x)(-x)(x)(x)

C

Which expression is equivalent to:

5 3 48) ( )c d

20 12 19

9 7 60

A) C)

B) D)

c d cd

c d cd

A

Which expression is equivalent to:43 33

9) 2

x y 7 7 12 12

12 12 7 7

81 81A) C)

16 16

12 12B) D)

8 8

x y x y

x y x y

C

Write the equivalent expression to:

22

4

510)

2

x

y

4

8

25

4

x

y

Simplify:6 2 211) (2 ) (4 )x xy

2 12 22 4x xy 12 24 4x xy

13 216x y

Simplify:

2 2 312) (3 ) (2 )a a b2 4 3 3 2a a b

4 3 9 2a a b 718a b

13) Multiply:

2 2 2( 2 )(12 )xy x y3 4 24x y

14) Multiply:

4 5( 4 )( 8 )x y xy 5 6 32x y

15) Multiply:

( 8)( 8)p p F.O.I.L ? Box Method ? Distribute? Difference of Squares?

2 64p

16) Factor Completely:

24 24x x

17) Factor Completely:

4 16x 2 2( 4)( 4)x x

That’s not all folks!!!!

2( 4)( 2)( 2)x x x

18) Multiply:

26 ( 7)x x x

19) Multiply:2 2(3 2 )(4 5 )x y x xy y

Distribute or use the rectangular box method

12x3 -15x2y 3xy2

-8x2y 10xy2 -2y3

4x2 -5xy y2

3x -2yCombine LIKE TERMS

3 2 2 312 23 13 2x x y xy y

20) DIVIDE!

8

3 2

14

28

x y

x y

5

2

x

y

21) DIVIDE

18 5

11 6

8

32

x y

x y

7

4

x

y

22) FACTOR

2 264 81x y

(8 9 )(8 9 )x y x y

23) Factor

2 49x ( 7)( 7)x x

24) Which of the following is a factor of

2 8 12?x x A) ( 6) C) ( 4)

B) ( 3) D) ( 2)

x x

x x

D

25) Factor

29 6 8a a Remember you can use DECOMPOSITION, or look at the answer choices and see which one multiplies to the trinomialIsn’t that lovely!But I say!!!! Challenge your mind…

Find A multiplied by CThen find what adds up to BDecomposeFactor by GroupingFind your Factors!!!

9 8 72

25) Factor

29 6 8a a 29 12 6 8a a a

3 (3 4) 2(3 4)a a a (3 4)(3 2)a a

26) FACTORLook…Four terms!

Two Binomials, may as well factor by grouping

3 23 2 6x x x

2 ( 3) 2( 3)x x x 2( 2)( 3)x x

27) Factor Completely!

3 210 28 14x x x 22 (5 14 7)x x x

Cannot factor further!

28) Simplify:

5 4 5 4(6 3 1) (8 3 1)x x x x x 5 4 5 46 3 1 8 3 1x x x x x

5 42 6 2x x x

29) What is the simplified form of:

5p + 8p - 3q - 6p

Combine Like Terms

= 7p – 3q

30) What is the simplified form of:

14) 16z - 3z - 3y - z

= 12z – 3y

31) Multiply:

2(5 3)x (5 3)(5 3)x x

225 15 15 9x x x 225 30 9x x

32) Simplify

3 3 2(3 2 4) (4 3 2)x x x x 3 3 23 2 4 4 3 2x x x x

3 27 3 2 2x x x

33) Simplify:2

2

2 6 4

4 12 16

t t

t t

2

2

2( 3 2)

4( 3 4)

t t

t t

2( 2)( 1)

2 2( 1)( 4)

t t

t t

2

2( 4)

t

t

34) Simplify:

5 15

5 15

x

x

5( 3)

5( 3)

x

x

( 3)

( 3)

x

x

35) Simplify:3 2

2

10 21

11 28

x x x

x x

2( 10 21)

( 7)( 4)

x x x

x x

( 7)( 3)

( 7)( 4)

x x x

x x

( 3)

4

x x

x

36) Simplify4 4

5 ( 5)( 5)x x x

4 4

5 ( 5)5 (

5

5)x x

x

x x

4 20 4

( 5)( 5)

x

x x

4 24

( 5)( 5)

x

x x

4( 6)

( 5)( 5)

x

x x

37) Simplify:

12 5 2 5a a

a a

2 512 5 aa

a a

12 5 2 5a a

a

10a

a 10

2 81What is 9 ?

3

xx

x

( 9)( 9) 9

3 1

x x x

x

( 9)( 9) 1

3 9

x x

x x

9

3

x

x

38)

39) Simplify

2

5( 3)

9

yy

y

( 3) ( 5)

1 ( 3)( 3)

y y

y y

5

3

y

y

40) SOLVE:

2 5

3x x

Rational

EQUATION

23 ( 3)

1

5

3 1( )

x x x

x x

x

2 5 15x x 5 5x x 3 15x

5x

15 15Solve: 2

2x x

2) 2 ( 2)

1

15 15 2

1 12 1

x x x

x

x x

x

x

215 30 15 2( 2 )x x x x 230 2 4x x 20 2 4 30x x

20 2( 2 15)x x

See the next slide to continue to solve

because the trinomial can factor further

41)

0 2( 3)( 5)x x

3 0 or 5 0x x

3, 5x

2 4 3 642)

3 2

x x

x x

( 2)( 2)3( 2)

3 ( 2)

x x x

x x

( 2)( 2)x x

x

2( 2)x

x

2

43) What are the solutions for

8 48 0x x

( 12)( 4) 0x x 12 0 or 4 0x x

12, 4x

4 3 2

44) What are the solutions for

3 15 18x x x GCF?

2 23 ( 5 6) 0x x x 23 ( 6)( 1) 0x x x

6 0 or 1 0x x

6 or 1x x

Remember to move into Standard Form Ax2+Bx+C=0

45) What are the solutions for

23 11 10?x x

23 11 10 0x x No GCF. Use Decomposition

11

30

6 5

3 2 5( 2) 0x x x ( 2)(3 5) 0x x

2 0 or 3 5 0x x 2 3 5x x

2

or

5

3

x

x

2

46) What is the factored form of

16x 40 25?x

2

4 5)(4 5

(4 5)

x x

x

Wow, a Perfect Square Trinomial!

47) It takes Mrs. Mangas 3 hours to grade papers and Mrs. Heath 5 hours to grade papers. How long would it take them to grade papers if they graded them together? 1 1 1

+ = 3 5 t

15 15 151 1 1

3 51 1 1

t t

t

t

5t 3t 15

5 3 15t t 8 15t

15 71 .

8 8t hrs

48) The scuba diving pool behind Sports Chalet can be filled in 18 hours by pipe A and 24 hours by pipe B. If both pipes are filling the pool at the same time, how long will it take to fill the pool?

1 1 1 + =

18 24 t

72 72 72

1 1

1 1 1

18 24 1

t

t

t t

4t 723t

4 3 72t t 7 72t

72 210

7 7t hrs