IA2 Homework
Homework 2
Perform the indicated operation:
1. (x3 + 9x – 5) + (-4x3 – 12x + 5)
2.
3.
4.
5.
6.
7.
8.
(x2 – 33x + 15) + (-4x2 + 18x – 36)
Homework 3
Perform the indicated operation and simplify:
1. 5(d + 3) – 10
2.
3(2 – 3c) + 5c
3.
7 + 2(7x – 5)
4.
5x(2x – 3) + 9x
5.
(a + 2)(a + 3)
6.
(12 – r)(6 + r)
7.
(3d + 8)(3d – 8)
8.
(5x – 4 + 2x2)(3 + 4x)
9.
(x + 7)(x – 2) – x2
(3a2 – 2ab + 3b2) – (a2 – 5ab + 3b2)
(x2 – 6x + 5) – (3x2 – 2x – 2)
(x2 – 9) – (-2x2 + 5x – 3)
From 4x + 2y, subtract x – 4y.
Subtract 2x2 – 3x + 7 from x2 + 6x – 12.
2
Subtract 2c + 3c – 4 from 0.
IA2 Homework
Homework 4
Divide:
1. (10x + 20y) ÷ 5
2.
(tr – r) ÷ r
3.
12a − 6b
−2
4.
20x2 + 15x
5x
5.
− 2a3 − 3a2 + a
−a
6.
4.
The area of a rectangle is represented by
x2 – 8x – 9. If the length is represented by
x + 1, how can its width be represented?
Homework 6
Divide using synthetic division:
1. Divide x2 – 10x – 20 by x + 2
2.
Divide y2 + 2y – 7 by y – 2
3.
x + 6 x2 + 17x + 70
4.
One factor of x2 – 4x – 21 is x – 7. Find the
other factor.
15r 4s4 + 20r 3s3 − 5r 2s2
− 5r 2s2
Homework 5
Divide using synthetic division:
1. Divide s2 + 2s – 15 by s + 3
2.
x + 2 x2 + 6 x + 8
3.
Divide x2 – 64 by x – 8
IA2 Homework
Homework 7
Write each expression in factored form:
1. sr – st
2.
4x2 – 4y2
4.
2x – 4x3
5.
10xy – 15x2y2
7.
2ax2 – 2ax – 12a
7.
4x2 – 4
8.
63c2 – 7
p + prt
3.
6.
6.
Homework 9
Write each expression in factored form:
1. 2x2 + 5x + 2
2.
2x2 + 7x + 6
3.
3x2 10x + 8
4.
16x2 + 8x + 1
5.
2x2 + x – 3
6.
4x2 – 12x + 5
2
y – 64
2
t – 25
2
8.
4r – b
9.
2
2
9–m
4
10. 16a – 25b
11. s2 -
6
64
100
Homework 8
Write each expression in factored form:
1. a2 + 3a + 2
Homework 10
Write each expression in factored form:
1. by2 – 4b
2.
3x3 – 6x2 – 24x
2.
x2 – x – 2
3.
x4 – 16
3.
z2 + 9z – 36
4.
m2 – 81
4.
w2 – 16w + 64
5.
6x + 27b
5.
2x2 + 12x + 8
6.
x2 – 16h2
7.
abx2 - ab
IA2 Homework
Homework 11
Factor each expression:
1. x3 + 8
2.
3.
4.
27x3 + 1
2.
3y3 – 81
3.
2x3 + 54
4.
x2 – 100
5.
2x2 – 128x
6.
x2 – 19x + 90
8a6 + 64b3
x3 + y3
Homework 12
Factor each expression:
1. a3 – b3
2.
Homework 13
Factor each expression completely:
1. 64x3 + 125
x3 – 64
3.
8x3 – 27
4.
x6 – y9
IA2 Homework
Homework 14
Simplify each expression:
1.
15x2
3.
4.
4x − 20 3x2 + 30x
•
4x + 20 3x2 − 15x
35x4
2
2.
3.
2x − 6x
10x
4.
2b2 + 3b − 2
4b2 + 8b
•
8b3 − 8b2
2b2 − b
x2 − 16
x2 − 5x + 4
5.
x +1
, express
x+2
the area of the square in terms of x.
If the side of a square measures
3y2 − 12
y3 − 8
Homework 16
Perform the indicated operation. Be sure to simplify
your answer!
5.
2b2 − 6b
2
2b − b − 15
Homework 15
Perform the indicated operation. Be sure to simplify your
answer!
1.
1.
2.
2
÷
x −1
1
x −1
m+3
6m
÷
3m
m+3
xy + 3y 2x2 − 6x
•
6x
x2 − 9
3.
2.
x2 + 1
x−y
5z
•
5z
y−x
2n2 − 8n
n2 − 16
÷
8n2
(n + 4)2
IA2 Homework
4.
2y2 + 11y + 5
4y2 + 4y + 1
÷
2y3 + 10y2
4y3
5.
5.
c3 − c2y
c2 − y2
÷
c3y
cy2 + y3
Homework 17
Perform the indicated operation. Be sure to simplify your
answer!
x2 − 100
x−2
1.
•
x −2
5x − 50
2.
2x + 6
x2
•
3x2
6x + 18
3.
x2 − 9 3x + 9
÷
4x
2x
4.
1
1
÷ 2
ab ab
3k − 3 12k − 12
÷
k
4k2
IA2 Homework
Homework 18
Perform the indicated operation and simplify your answer!
3x 4x 3x
+
+
1.
5
5
5
2.
4
x
−
x−4 x−4
3.
5x − 3
2x
−
4x − 4 4x − 4
4.
5.
2k2
k2 + 3k
x2 + 1
2
−
+
x − 16
5.
k2 + 3k
8.
y
18
−
y − 3 y2 − 9
9.
3m + 1
m2 − 16
+
m−2
2m + 8
Homework 20
Solve the fractional equation. Be sure to check your
answer(s)!
x
+2 = 6
1.
5
5x + 3
x2 − 16
c+2 c−3
+
2
3
2
3
+
x x +5
1
5
+
y−2 y−3
k2 + 9
Homework 19
Perform the indicated operation and simplify your answer!
3x x
+
1.
8
4
2.
7.
2.
1
1 1
+ =
12 y 4
3.
x
2
1
= +
x −1 x x −1
4.
2+
4
x
=
x−4 x−4
IA2 Homework
6.
y −2
4
= 2
y
y − 2y
IA2 Homework
Homework 21
Graph each line on the graph provided (be sure to label) and
rewrite each equation in standard form (Ax + By = C).
1. 4x – y – 7 = 0
Homework 22
Solve the linear system by graphing each line. Be
sure to label!
1. x + y = 4; x – y = 2
2.
y = -5x + 2
2.
y = -2x + 3; y =
3.
y=
3.
3x + y = 6; y = 3
−3
4
x+
5
4
1
2
x+3
IA2 Homework
4.
x + 4y = 6; x = 2
Homework 24
Solve each system of inequalities. Be sure to label!
1. x ≥ 1;
y > -2
Homework 23
Show the graph for each inequality.
1. 2y – 6x > 0
2.
3.
2.
y < x – 1;
x+y≥2
3.
x + 3y ≥ 6;
x+y–4≤0
x≤2
y–x≥5
IA2 Homework
Homework 25
Use the graph provided to graph each parabola.
1. y = x2 – 4x
2.
y = -x2 + 2x + 5
3.
y = x2 – 2x – 3
Homework 26
Solve the system of equations graphically.
1. y = x – 4;
y = x2 – 6x + 6
2.
y = -x2 + 3; y = 2
3.
y=
1
2
x2 + 1; x + y = 1
IA2 Homework
Homework 27
Solve the inequality using the graph provided.
1. y < x2
2.
y ≥ -x2 + 6x
3.
y ≤ 3x –
1
2
x2
IA2 Homework
Homework 28
Simplify the radical expressions.
75
1.
2.
3.
1.
180 − 80
2.
48x12 + x6 75
3.
700 + 8 7 − 3 28
4.
48 + 12 − 3
− 300
2 9y9
4.
a2b
5.
5 12x7
Homework 29
Simplify the radical expressions.
1.
Homework 30
Perform the indicated operation and simplify your
answer.
3
5.
3
250y3 − 3 16y3
6.
3
64x − 3 8x + 3 27x
24
2.
33
16x6
2
3.
43
5
− 125y5
Homework 31
Perform the indicated operation and simplify your
answer.
1.
5 7 + (− 175)
2.
12 3 +(−3 12)
3.
4.
3
n7
4.
5.
20 + 5 + 150 − 96
3
4a 56a11
3
a3 3 0 − − 64a12
IA2 Homework
Homework 32
Perform the indicated operation and simplify.
Homework 33
Perform the indicated operation and simplify.
5 • 20
1.
1.
2.
5
3 32 • 2
2.
3.
80
5
1
3
24 48
4 6
• 18
3.
303 128
63 2
x • x5
4.
5.
3
3
5 • 25
6.
3
9x 2 • 3 6 x
7.
3 ( 4 3 + 12 )
8.
3 2 (2 8 − 3 )
9.
(2 + 7)(3 + 7 )
10. (5 + 2 3)(5 − 2 3)
4.
5.
75 + 48
3
2 5 + 6 15
2 5
IA2 Homework
Homework 34
Solve and check each solution.
1.
x =3
2.
6x = 3
3.
3 x =6
4.
x−2 =5
5.
5+ y =9
6.
7.
2y − 1 + 7 = 4
5.
5 + 4y − 2 = 2
6.
y = 3 + 30 − 2y
Homework 36
Graph each radical equation on the graph provided.
1.
y = 2x
2.
y = x +3
3.
y = x−4
x =1+ x +5
Homework 35
Solve and check each solution.
1.
y = 2 2y − 3
2.
x= x
3.
y=
6y + 16
IA2 Homework
4.
x = 4 + 2x − 8
IA2 Homework
Homework 37
Write the given power of i in simplest terms as 1, i, -1, or -i.
1. i12
2.
7.
2d − 75d5
8.
3
i7
−8
49
3.
i
4.
i72
5.
i54
6.
i99
7.
i300
8.
i246
9.
i91
Homework 39
Write each number in terms of i, perform the
indicated operation, and write the answer in simplest
terms.
10. i2001
1.
− 64 + − 36
2.
3 − 4 − − 121
Homework 38
Express each number in terms of i and simplify.
1.
− 36
3.
1
2
2.
− − 81
4.
− 2 − 18 −
3.
2 − 48
5.
8 − 3 + − 12
4.
2
3
5.
6.
−9
− 200 − − 32
1
5
Homework 40
Write each number in terms of i, perform the
indicated operation, and write the answer in simplest
terms.
1.
− 49 • − 1
2.
− 2 • − 18
3 − 11
− 20x
− 50
4
IA2 Homework
3.
−4 −3 • −3
4.
− 3 − 10 • 2 − 10
5.
6.
7.
− 400
− 25
− 98
−2
− − 48
4 −3
IA2 Homework
Homework 41
Perform the operation and express the result in
a + bi form.
1. (10 + 3i) + ( 5 + 8i)
2.
Multiply the conjugates and write the product as a
real number.
6. (4 + i)(4 – i)
(7 – 2i) + (3 – 6i)
3.
(4 – 2i) + (-3 + 2i)
4.
(6 + 3i) – (2 + i)
5.
(-8 + 5i) – (5 – 7i)
6.
(9 – 2i) – (9 – 5i)
7.
Subtract 2 – 13i from 7 – 5i.
7.
(1 + 5i)(1 – 5i)
8.
(7 – 2i)(7 + 2i)
9.
( 5 + i)( 5 − i)
10. ( 6 + 3i)( 6 − i3)
8.
Express the sum of 9 + − 9 and − 5 − − 16 in
simplest a + bi form.
Homework 42
Write the product of the given numbers in a + bi form.
1. (3 + i)(4 + i)
2.
2.
4 – 8i
3.
2 −i 3
4.
7 – 5i
(5 – i)(3 + i)
3.
(1 + 3i)(2 – i)
4.
(4 – 5i)(2 + i)
5.
Homework 43
State the conjugate of each complex number:
1. 3 + i
Perform the indicated operation.
5 − 3i
5.
1−i
6.
7 − 4i
1 − 2i
7.
21 + i
5−i
(1 – 3i)(5 – 3i)
IA2 Homework
8.
2 − 3i
5 − 7i
9.
4+i
2 − 3i
Homework 44
State the additive and multiplicative inverse of each complex
number in simplest a + bi form.
4+i
1.
4−i
2.
2 + 3i
2 − 3i
3.
−i
2+i
Homework 45
State the additive and multiplicative inverse of each complex
number in simplest a + bi form.
1. 3 + i
2.
5 + 6i
3.
4 – 3i
4.
-2 + 4i
Homework 46
Use the graph provided to graph each complex
number as a vector.
1. 2 + 3i
2. 5 + i
3. 3 – i
4. -2 – 6i
5. -4 + i
IA2 Homework
1.
Homework 47
On a flat panel tv that cost $500, the sales tax is $43.75.
Find the sales tax on a tv that cost $689.
1.
Homework 48
Direct variation is a _____________________
between y and x.
2.
If y varies directly as x then ______________
where k is the __________________________.
2.
3.
4.
3.
If y varies directly as x, and
y = 12 when x = 2, find the constant of
variation.
4.
If y varies directly as x, and
y = 20 when x = 40, find the constant of
variation.
5.
Find the relationship in the direct variation
below if y varies directly as x:
Steve shoveled 20 driveways and earned $450. At this
rate, how many more driveways would Steve have to
shovel to earn a total of $1057.50?
At your annual holiday party, you ran out of punch
really quickly. You estimated that 2 gallons served 15
people. At this rate, how many more gallons would you
have needed if 105 people were at your party?
The football team is ordering sweatshirts. Each
sweatshirt is $40 but if the team orders 25 or more, they
are reduced by 10%. If the team orders 50 or more, they
are reduced another 10%. If 55 were ordered, what was
the price of one sweatshirt?
X
1
2
3
4
5
Y
3
6
9
12
15
IA2 Homework
Homework 49
Find the constant of variation and fill in the missing values
in each direct variation below.
1. y varies directly as x:
x
3
-1
?
-5
y
-30
?
40
50
2.
What is the equation for #1?
3.
b varies directly as a:
B
-3
5
?
12
A
-15
?
25
60
4.
What is the equation for #3?
5.
x varies directly as y:
x
2
8
?
10
y
1
?
12
5
6.
What is the equation for #6?
IA2 Homework
1.
2.
3.
Homework 50
If x varies inversely as y and x = 24 when
y = 6, what is the value of y when x = 12.
1.
Homework 51
A company that produces personal computers
has determined that the number of computers it
can sell (n) is inversely proportional to the price
(p) of the computer. Three thousand computers
can be sold when the price of a computer is
$1200. Approximately how many computers
can be sold when the price is $2000?
If x varies inversely as y and x = 45 when
y = 4, find x when y = 3.
2.
The pressure (p) of a gas varies inversely as the
volume (v). If the pressure is 25lb/in2 when the
volume is 400ft3, find the pressure when the
volume is 150ft3.
3.
The number of people at Amanda’s party is
inversely proportional to the amount of
watermelon slices they get. If 60 people get 5
watermelon slices each then how many slices
will each person get if there are 100 people at
the party?
If a varies inversely as b, find the missing value in the
table:
A
3
9
B
270
90
27
81
10
IA2 Homework
Homework 52
Solve each equation below.
1. (x - 3)(2x + 1) = 0
2.
Homework 53
Solve each equation using the quadratic formula.
1. x2 – 6x + 7 = 0
x2 – 13x + 42 = 0
2.
x2 + 10x -11 = 0
3.
x2 = 2x -5
2
3.
x + 12x = 28
4.
2x2 - 11x = x2 - 3x +12
IA2 Homework
Homework 54
Solve each equation by completing the square.
1. a2 – 8a = 20
Homework 55
Solve each equation by completing the square.
1. x2 – 9x + 18 = 0
2.
x2 – 2x = 3
2.
x2 – 7x + 12 = 0
3.
x2 + 12x + 35 = 0
3.
x2 + 5x – 6 = 0
IA2 Homework
Homework 56
State the center and radius of each circle equation given.
1. (x – 3)2 + (y – 5)2 = 16
2.
(x + 1)2 + (y – 7)2 = 25
3.
x2 + (y + 4)2 = 9
4.
(x - 2)2 + (y + 4)2 = 12
5.
2(x + 9)2 + 2(y – 5)2 = 72
Homework 57
Complete the square to find the standard equation
for the circle AND the center and radius.
1. x2 + y2 + 6x + 8y + 9 = 0
2.
x2 + y2 - 6x + 4y + 4 = 0
3.
x2 + y2 - 10x + 8y + 40 = 0
IA2 Homework
Homework 58
Complete the square to find the standard equation for the
circle AND the center and radius.
1. x2 + y2 – 2x + 4y – 20 = 0
2.
x2 + y2 – 4x + 8y + 4 = 0
3.
x2 + y2 – 6x + 10y + 25 = 0
IA2 Homework
Homework 59
Determine whether each of the below graphs represent a function.
a.
Homework 60
The graph of function f is shown at the
right. Find the following:
f(-1)
b.
f(1)
c.
f(0)
d.
f(3)
2.
If a function g is defined by g(x) = 2x +
15, find the value of g(-3).
3.
a.
If a function k is defined by
6−x
k(x) =
, find the value of
x −3
k(2)
b.
k(9)
c.
k(0)
d.
k(6)
e.
k(-3)
f.
k(3)
1.
IA2 Homework
Homework 61
Given f(x) = x3 and g(x) = x + 1, determine:
1. f ○ g(0)
2.
Homework 62
Find the composition of the given functions.
1. f ○ g(x) when f(x) = x2 and g(x) = x + 1.
g [ f(0) ]
3.
f [ g(1) ]
4.
g ○ f(-1)
5
and g(x) = 2x.
x+1
2.
f ○ g(x) when f(x) =
3.
g ○ f(x) when f(x) = 3x + 4 and g(x) = 2x
– 1.
4.
g ○ f(x) when f(x) = x - 1 and
g(x) = 2x2 + x – 1.
Given f(x) = 2x - 5 and g(x) = 5x + 2, determine:
5. f ○ g(0)
6.
g [ f(0) ]
7.
f [ g(3) ]
8.
g ○ f(-2)
IA2 Homework
IA2 Homework
Homework 63
Graph each function:
1. y = 2x3
2.
y=|x|+2
3.
y=|x+2|
4.
y=
2x − 1
IA2 Homework
Homework 64
Graph each function.
1. y = x2
2.
y = x3
3.
y = (x - 2)2 + 1
4.
y = x3 - 5
IA2 Homework
Homework 65
Graph each function.
1. y = (x - 3)2 + 1
2.
y=|x+1|
3.
y=
x −4 −2
IA2 Homework
Homework 66
Graph each function:
1. y = x2
2.
2
y = y = (x - 2) + 1
3.
y = (x + 3)2 - 4
4.
y = (x + 5)2
IA2 Homework
Homework 67
Graph each parent function.
1. y = x3
2.
y = (x + 2)3
3.
y = (x - 2)3 - 3
4.
y = x3 - 5
IA2 Homework
Homework 68
Graph each function.
1.
y=
x −1
2.
y=
x +4
3.
y=
x −4 −2
Homework 69
Graph each function.
1. y = | x |
2.
y=|x–1|
3.
y=|x+3| +5
IA2 Homework
Homework 70
Determine whether each function shown below is oneto-one.
1.
2.
3.
Homework 71
Find the inverse of each function provided.
1. (2, 3) (4, 5) (6, 7)
2.
(0, 0) (1, 1) (2, 4)
3.
(4, 2) (9, 3) (16, 4)
4.
Draw a sketch of a function and its inverse, which
should also be a function below.
IA2 Homework
Homework 72
Find the inverse of each function provided.
1. y = x – 6
2.
y=
3.
4.
5.
1
2
x
Homework 73
Find the inverse of each function provided.
1. y = 2x + 5
1
2
2.
y=
y = 3x – 6
3.
y = .75x – .25
y=
x
5
4.
y=
y=
3x + 2
4
+3
x-6
10x + 20
5
IA2 Homework
Homework 74
Find the inverse of the given function. Graph both the
given function and its inverse.
1. y = x + 1
2.
y = 3x
3.
y = -2x – 5
Homework 75
Find the inverse of the given function. Graph both the
given function and its inverse.
1. y = 14 x
2.
y = 2x+ 5
3.
y = x2
IA2 Homework
Homework 76
Simplify:
1. x3 ● x5
2.
3.
Homework 78
Solve each exponential equation:
1. 2x-1 = 82
b12
b7
(x4)2
Evaluate f(x) with the given value:
4. f(x) = 2x
f(2)
5.
f(x) = 4x-1
6.
f(x) = 32x+1
7.
f(x) =
1 x
2
2.
9x+1 = 27x
3.
16x-3 = 4x-3
4.
32x-1 = 3x+2
5.
53x = 25x+1
6.
6x = 2164x-4
7.
4x = 16
8.
22x=64
9.
3x-1=27
f(3)
f(3)
f(-1)
Homework 77
Graph each exponential function:
1. f(x) = 2x
2.
f(x) = 3x+1
IA2 Homework
Homework 79
Memorize these log rules:
logab = x
⇔
ax = b
log ab
⇔
log a + log b
log ba
⇔
log a – log b
log ax
⇔
x ● log a
Expand each expression:
1. log ab
2.
3.
Homework 80
Write the exponential equation in logarithmic form:
1. 24 = 16
2.
32 = 9
3.
10-2 = 0.01
4.
120 = 1
5.
8 3 =2
6.
52 = 5
7.
6-1 =
8.
4a = b
9.
x3 = y
log (a ÷ b)
log (a2b)
1
4.
log
a
b
1
5.
6.
log a b
1
6
log (ab)2
Condense each expression:
7. 2log x – log y
8.
log 2x – log 2y
9.
3(log x + log y)
10. log a -
1
2
log b
10. 5c = d
11. ba = 8
IA2 Homework
Homework 81
Write the logarithmic equation in exponential form:
1. log2 64 = 6
Solve for n:
6. log327 = n
2.
log10 1000 = 3
7.
log216 = n
3.
log27 9 =
8.
log5
9.
logn27 = 3
4.
5.
6.
2
3
1
25
=n
5
2
log4 32 =
log 1 3 = - 12
9
logbc -
10. logn49 = 2
1
5
11. logn125 =
Homework 82
Solve for x:
1. log2x = 4
2.
log5x = 2
3.
log3x = -2
4.
log7x = 0
5.
log81x =
1
2
3
2
IA2 Homework
Homework 83
Find x to the nearest tenth.
1. 2x = 7
Homework 84
Find x to the nearest tenth.
1. 4.08x = 2.02
2.
5x = 47.6
2.
7x = 615
3.
1.06x = 1.14
3.
4.7x = 10.2
4.
2.5x = 9.88
4.
3.8x = 2.9
5.
3x = 15.6
5.
2.75x = 3.72
6.
15x = 295
7.
4.5x = 1.57
IA2 Homework
Homework 85
Find x to the nearest tenth.
1. 3x = 4
2.
5x = 3.6
3.
x1.5 = 15
4.
2x = 1.5
5.
4x = 21
6.
x0.4 = 1.6
IA2 Homework
Homework 86
Evaluate the given expression.
1. 5P3
6.
4C2
7.
4C3
2.
3P 1
3.
4P 4
Homework 88
Evaluate each expression using your calculator.
1. 8C3
4.
A child playing with blocks places the letters N, C,
E, A, and D together at random. How many
difference words can be made?
2.
12C7
3.
6C0
4.
52C3
5.
25C2
6.
5C2
7.
5C3
5.
A signal is made by arranging a red, a white, a blue,
and a yellow flag on a vertical pole. How many
different signals can be made?
Homework 87
Write out the evaluation of each given expression.
1. 8C5
2.
12C12
Homework 89
Write the expansion of the given binomial.
1. (x + y)4
3.
12C0
4.
52C2
5.
26C2
2.
(x - y)7
3.
(x + y)10
IA2 Homework
Homework 90
Write in simplest form the third term of the expansion.
1. (a + b)4
2.
(a - b)5
Write in simplest form the fourth term of the expansion.
3. (c - d)4
Homework 91
Write the expansion of the given binomial.
1. (3a + 1)3
2.
(x - 2)4
3.
(1 - b)5
Write in simplest form the third term of the expansion.
4. (a - 7)6
5.
(2 + y)7
Write in simplest form the fourth term of the expansion.
6. (2a - 3)5
IA2 Homework