Dear Future Algebra 2 Student,
We, your future teaches, desire for you to have a successful Algebra II experience. The Algebra II
Honors curriculum is rigorous, beginning with advanced skills such as graphing quadratic equations
as well as solving quadratics by factoring. These topics will be approached with the assumption you
have mastered the prerequisite skills learned in Algebra I and Geometry.
Your success is Algebra 2 will largely be dependent on your Algebra 1 and Geometry foundation and
your willingness to go above and beyond when the material is difficult.
In order to make sure you are properly placed next year you will need to take an Algebra 2 Honors
placement test. To prepare make sure to do the attached question set. The answers can be found
online at www.mrsstillman.com under the “Algebra I Review Assignment” tab.
You will take the placement exam in class on Thursday January 7, 2016. ALL students who desire to
enroll in Algebra 2 Honors next year MUST TAKE THE PLACEMENT EXAM!
If you have any questions, comments, or concerns email Jessica.stillman@browardschools.com.
~The Algebra 2 Honors Team
Algebra I Honors – Review Assignment
I.
Find the product.
a) ( 2x + 9) ( x +1)
(
b) ( 5x -1) ( 6x -10)
)(
c) 3x 2 - 4 3x 2 + 4
)
II.
The height of a rectangle is 3 units less than twice the width.
a) If the width of the rectangle is represented b) Write an expression for the area of the
by the variable w, write an expression for the rectangle in terms of w.
height in terms of w.
III.
Factor each polynomial completely.
2
7
b) 81x 2 - 36
a) 4x + 12x
2
e) 25x 2 - 20x + 4
d) x - 7x -18
8 12
6 16
2
g) 12x y - 75x y
h) 4x - 7x -15
3
2
4
3 2
5
j) 3n - 4n + 9n -12
k) 12a b -18a b + 24ab
3
2
2
m) 4x + 43x + 30x
n) 4x - x - 5
3
2
4
p) x -1
q) 5( x - 3) + 2( x - 3)
IV.
Evaluate each expression if
a) ab2 -d
V.
a)
3-
,
b)
2
,
ab 2
+d
c
Solve.
5x + 34 = 3- 2 (1- 7x )
c)
,
c) x -16x + 63
3
2
f) 2p + 5p + 6p + 15
2
i) x + 40x + 400
2
l) x + x + 0.25
2
t) 7x - 32x - 60
r) 50 - 2x 2
æx ö
1
( x - 8) = 3x - çè + 6 ÷ø
5
4
VI.
Sketch the graph.
a) y = 3x + 5
c) 4x - 3y =12
e) y = 7
g) y = x + 2 - 3
i) y = ( x + 2) - 3
2
b)
2
1
( 4x - 5) = ( 7 - 3x )
3
4
d)
x+5
=4
7x -1
x
-3
2
d) y -1= -4 ( x + 5)
b) y =
f) x = 7
h) y = x - 4 +1
j) y = x 2 + 2x -8
,
k) y = x + 3 +1
l) y = 2 - x
VII. Write the equation of a line in the specified form with the given characteristics.
a) Passes through (6, 1) and is perpendicular to the line 3x - 4y = 2. (STANDARD FORM)
b) Has an x-intercept of (9, 0) and a y-intercept of (0, -3). (POINT-SLOPE FORM)
c) Passes through the point (4, 7) and is parallel to the line that passes through the points (-1,
8) and (5, -6). (SLOPE-INTERCEPT FORM)
VIII.
a)
Solve each system.
b)
3x - 6y = 2
5x + 4y =1
c)
2x + y = 1
4x + 2y = 3
d)
x + 2y = 4
2x + 4y = 8
IX.
a)
Simplify. Your answer should contain only positive exponents.
b)
c)
-3
2
4
2
4
2x y × 4x y × 3x
2x 4 × 2x 4
3x -3 y 2
X.
Simplify the radical expression.
( )
a)
b)
121
(
d) 3 7
)
2
c)
27
(
)(
e) 2 + 13 2 - 13
)
(
State the quadratic formula.
XII.
Solve the quadratic equation using the indicated method.
(SQUARE ROOTS)
b) 3x 2 -16x =12
(QUADRATIC FORMULA)
8 + 125 - 32 +
f) 1- 3
XI.
a) 9x 2 +10 = 91
c) 3x 2 -11x - 3 = -x 2
(FACTORING)
Solve the literal equation for the indicated variable.
a+b+c
1
a) A =
, b=?
b) d = at 2 , a = ?
3
2
2 pm-1q 0 2m-1 p3
×
2p
q2
)
1
4
2
d) 2 ( x - 3) + 3 =13
2
(SQUARE ROOTS)
XIII.
1
1
c) A = ah - bh , h = ?
2
2
Answers
I.
a) 2x 2 +11x + 9
b) 30x 2 - 56x +10
II.
a) 2w - 3
c) 9x 4 -16
b) 2w 2 - 3w
III.
a) 4x 2 3x 5 +1
b) 9 (3x + 2) (3x - 2)
c) ( x - 9) ( x - 7)
d) ( x + 2) ( x - 9)
e) ( 5x - 2)
f) p 2 + 3 ( 2 p + 5)
(
)
(
)(
g) 3x 6 y12 2x + 5y 2 2x - 5y 2
(
)
)
(
2
h) ( 4x + 5) ( x - 3)
(
j) n 2 + 3 (3n - 4)
k) 6ab 2a3 - 3a 2 b + 4b 4
m) x ( 4x + 3) ( x +10)
n) ( 4x - 5) ( x +1)
(
)
p) x 2 +1 ( x +1) ( x -1)
IV.
a) 45
)
11
3
212
c) x =
59
i) ( x + 20)
2
l) ( x + 0.5)
2
t) ( 7x +10) ( x - 6)
r) ( 5+ x ) ( 5- x ) or - ( x + 5) ( x - 5)
q) ( x - 3) ( 5x -13)
2
b) 21
V.
a) x =
)
61
41
1
d) x =
3
b) x =
VI.
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
VII.
a) 4x + 3y = 27
VIII.
æ1 1 ö
a) ç , - ÷
è3 6ø
b) y =
1
1
( x - 9) OR y + 3 = x
3
3
b) no solution
7
c) y = - x + 49
3
c) Infinitely many
solutions. Any point
on the line x + 2y = 4 is
a solution to this
system.
d) (-60,-84)
IX.
a)
b) 8x 8 y 6
1
4x 8
c)
2 p3
m2q2
X.
a) 11
b) 3 3
c) -2 2 + 5 5 +
d) 63
e) -9
f) 4 - 2 3
1
2
XI.
x=
-b ± b2 - 4ac
2a
XII.
a) x = ±3
XIII.
2
b) x = - , 6
3
1
c) x = - , 3
4
d) x = 3± 5
a) b = 3A - a - c
b) a =
2d
t2
c) h =
2A
a-b