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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