Page 1
HUSD Middle School Algebra I Mid-Year Exam Study Guide
Page 1 of 6 MCC@WCCUSD (HUSD) 11/26/12
1 Example: Solving an Equation: 4 3 2 4
4 3 3 2 4 34 2 1
4 2 2 1 22 12 12 2
12
x xx x
x xx x x x
xx
x
+ = ++ − = + −
= +− = + −
=
=
=
5.0/7.EE.4, 8.EE.7
2 Example:
Solving an Inequality:
2 x −5( )− 3x − 2( ) ≤10
2 i x − 2 i5− 3x + 2 ≤102x −10− 3x + 2 ≤10−x −8 ≤10−x −8+8 ≤10+8−x ≤18x ≥ −18
5.0/7.EE.4, .7, A-REI-3
3 Example:
Exponents:
2.0/8.EE.1
1´ Practice: Solve the equations:
1) 27 113x= +
2) ( ) ( )3 4 5 3 2d d− − = + +
2´ Practice:
Solve the Inequality:
3) ( )12 30 93
w w− > +
Solve the inequality and graph the solution set on the number line:
4) 6 12 8 16y y+ − ≥
-5 -4 -3 -2 -1 0 1 2 3 4 5
3´ Practice: Simplify the expressions
5) g4 i g i g 2
6) 2xy2 i 3x3 y3
b3 i b2
= b3+2
= b5
b3 i b2
= b i b i b i b i b= b5
Page 2
HUSD Middle School Algebra I Mid-Year Exam Study Guide
Page 2 of 6 MCC@WCCUSD (HUSD) 11/26/12
4 Examples: Exponents:
a) b)
c)
2.0/8.EE.1
5 Example:
Simplify the Polynomial:
( ) ( )3 2 4 2
3 2 4 2
3 2 4 2
4 3 2
14 4 3 9 5
14 4 3 9 514 4 3 9 5
14 13 2
v v v v v
v v v v vv v v v v
v v v v
− − − − + + −
= − − + − − += − − + − − +
= + − − +
10.0
6 Example:
Multiply: ( )( )( )
( ) ( ) ( ) ( )( ) ( )
2
2
2
4 3
4 3 4 3
4 4 4 3 3 4 3 3
16 12 12 9
16 24 9
x
x x
x x x x
x x x
x x
−
= − −
= + − − − −
= + − − − −
= − +
10.0
4´ Practice: Simplify the expressions:
7) 2 44x y−
8) 8
3 5
1024x yx y z
9) ( )( )3 8 4 2
5 6
4 612
a b a ba b−
5´ Practice:
Simplify:
10) ( ) ( )2 25 3 9 8 5m m m m− − − + −
11) ( ) ( )7 3 6 3 11 8d d+ − + − +⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦
6´ Practice: Multiply:
12) ( )32 1c+
13) ( )( )2 4 3g g− +
5y−2z−3
= 5 i1y2 i
1z3
= 5y2z3
6x2 y−1
2xy3
= 2 i 3i x2−1 i y−1−3
2= 3x1y−4
= 3xy4
3 −2x4 y( )3
= 3 −2( )3x4( )3
y( )3
= 3 −8( )x12 y3
= −24x12 y3
Page 3
HUSD Middle School Algebra I Mid-Year Exam Study Guide
Page 3 of 6 MCC@WCCUSD (HUSD) 11/26/12
7 Example: Factoring: a) b) c)
d)
11.0/A-SSE-3
7´ Practice: Factor Completely:
14) r 2 −81
15) 2 4100 16m m−
16) 236 24 4x x+ +
17) 26 15 36y y− −
18) 28 10 3y y− −
�
5x 5 − 80x
= 5x x 4 −16( )= 5x x 2( )2 − 42[ ]= 5x x 2 + 4( ) x 2 − 4( )= 5x x 2 + 4( ) x 2 − 22( )= 5x x 2 + 4( ) x + 2( ) x − 2( )
�
144 − 25t 2
= 12( )2 − 5t( )2
= 12 + 5t( ) 12 − 5t( )
�
9y 2 −12y + 4
= 3y( )2 −12y + 22
= 3y − 2( ) 3y − 2( )= 3y − 2( )2
�
6w2 + 4w −10
= 2 3w2 + 2w − 5( )= 2 3w ± __( ) w ± __( )= 2 3w + 5( ) w −1( )
Page 4
HUSD Middle School Algebra I Mid-Year Exam Study Guide
Page 4 of 6 MCC@WCCUSD (HUSD) 11/26/12
8 Example Rational Expression Simplify:
10.0/A-APR-6
9 Example:
Divide:
10.0/A-APR-7
8´ Practice Simplify:
19) 2
2
3 4811 28y
y y−
− +
20) 2
4 22 10 28
kk k
−+ −
21) 2
2
16 16 33 28m m
m m+ +− −
9´ Practice:
22) 17 34 515 10 3 6
xx x
+÷− −
23) ( )( )
52
52
48 168 16 4
xx xx x x
−− + ÷+ + +
24) ( )6 4 2 224 42 72 6y y y y− − ÷
( )( )( )( )( )( )( )( )
2
2
2
2
3 34 12 16
3 1
4 3 4
3 1 14 1 4
3 14 4
aa a
a
a a
a aa a
aa
−− −
−=
− −
+ −=
+ −
−=
−
First look for GCF
Factor the numerator Binomial: difference of 2 squares
Factor the denominator Trinomial: Leading coefficient is 1
Make a product sum chart
Find equivalent forms of one.
( )( )( )( )
( )( )( )( )
( )( )( )( )( )( )( )( )
2 2
2 2
2 2
2 2
2
2
20 10 257 12 6 9
20 6 97 12 10 254 5 3 33 4 5 5
4 5 33 4 5
35
k k k kk k k kk k k kk k k kk k k kk k k k
k k kk k k
kk
− − − +÷+ + + +− − + += •+ + − ++ − + +
= •+ + − −
+ − +=
+ + −
+=
−
Multiply by the Reciprocal of the Divisor Factor Find Equivalent forms of one
Page 5
HUSD Middle School Algebra I Mid-Year Exam Study Guide
Page 5 of 6 MCC@WCCUSD (HUSD) 11/26/12
10 Example: Adding & Subtracting Rational Expressions Simplify: *Must have common denominator
Note: Numerator is not factorable
10.0/A-APR-7
10´ Practice: Add or subtract and simplify if possible
25) 1 32 2y y
−− −
26) 5 34 3 12z z+
+ +
27) 2 2
25 6 3 2x
x x x x−
+ + + +
End of Study Guide
( ) ( )
( )( )( )
( ) ( )
( )
3 3 14 20 6 303 3 1
4 5 6 5
3 13 3 24 5 3 6 5 29 6 2
12 5 12 515 212 5
d dd dd dd d
ddd dd dd ddd
++− −
+= +− −
+⎛ ⎞ ⎛ ⎞= • + •⎜ ⎟ ⎜ ⎟− −⎝ ⎠ ⎝ ⎠+= +
− −+=−
Factor to find the LCD LCD is 2(2)(3)(d-5) Multiply each term by a form of one
Add and simplify
Page 6
HUSD Middle School Algebra I Mid-Year Exam Study Guide
Page 6 of 6 MCC@WCCUSD (HUSD) 11/26/12
HUSD Algebra 1 Mid-Year Exam Study Guide Answer Key
Item Number Answer! CA!Standard/!CCSS!1! ! 5.0/7.EE.4, 8.EE.7 2! ! 5.0/7.EE.4, 8.EE.7 3! !
number!line!5.0/7.EE.4, .7, A-REI-3
4! !number!line!
5.0/7.EE.4, .7, A-REI-3
5! ! 2.0/8.EE.1 6! ! 2.0/8.EE.1 7!
!
2.0/8.EE.1 8!
!2.0/8.EE.1
9! ! 2.0/8.EE.1 10! ! 10.0 11! ! 10.0 12! ! 10.0 13! ! 10.0 14! ! 11.0/A-SSE-3 15! ! 11.0/A-SSE-3 16! ! 11.0/A-SSE-3 17! ! 11.0/A-SSE-3 18! ! 11.0/A-SSE-3 19!
!10.0/A-APR-6
20!!
10.0/A-APR-6
21!!
10.0/A-APR-6
22!!
10.0/A-APR-7
23!!
10.0/A-APR-7
24! ! 10.0/A-APR-7 25!
!10.0/A-APR-7
26!!
10.0/A-APR-7
27!!
10.0/A-APR-7
