2. IA2 Homework
Homework 4
Divide:
1. (10x + 20y) ÷ 5
2. (tr – r) ÷ r
3.
2
b6a12
4.
x5
x15x20 2
5.
a
aa3a2 23
6. 22
223344
sr5
sr5sr20sr15
Homework 5
Divide using synthetic division:
1. Divide s2
+ 2s – 15 by s + 3
2. 8x6x2x 2
3. Divide x2
– 64 by x – 8
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. 70x17x6x 2
4. One factor of x2
– 4x – 21 is x – 7. Find the
other factor.
9. 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
2. y = -5x + 2
3. y = 4
5
4
3
x
Homework 22
Solve the linear system by graphing each line. Be
sure to label!
1. x + y = 4; x – y = 2
2. y = -2x + 3; y = 2
1
x+3
3. 3x + y = 6; y = 3
10. IA2 Homework
4. x + 4y = 6; x = 2
Homework 23
Show the graph for each inequality.
1. 2y – 6x > 0
2. x ≤ 2
3. y – x ≥ 5
Homework 24
Solve each system of inequalities. Be sure to label!
1. x ≥ 1; y > -2
2. y < x – 1; x + y ≥ 2
3. x + 3y ≥ 6; x + y – 4 ≤ 0
11. 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 = 2
1
x2
+ 1; x + y = 1
17. IA2 Homework
Homework 37
Write the given power of i in simplest terms as 1, i, -1, or -i.
1. i12
2. i7
3. i49
4. i72
5. i54
6. i99
7. i300
8. i246
9. i91
10. i2001
Homework 38
Express each number in terms of i and simplify.
1. 36
2. 81
3. 482
4. 93
2
5. 113
6. 4
x20
7. 5
d75d2
8. 3
8
Homework 39
Write each number in terms of i, perform the
indicated operation, and write the answer in simplest
terms.
1. 3664
2. 12143
3. 322002
1
4. 50182 5
1
5. 1238
Homework 40
Write each number in terms of i, perform the
indicated operation, and write the answer in simplest
terms.
1. 149
2. 182
19. IA2 Homework
Homework 41
Perform the operation and express the result in
a + bi form.
1. (10 + 3i) + ( 5 + 8i)
2. (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.
8. Express the sum of 99 and 165 in
simplest a + bi form.
Homework 42
Write the product of the given numbers in a + bi form.
1. (3 + i)(4 + i)
2. (5 – i)(3 + i)
3. (1 + 3i)(2 – i)
4. (4 – 5i)(2 + i)
5. (1 – 3i)(5 – 3i)
Multiply the conjugates and write the product as a
real number.
6. (4 + i)(4 – i)
7. (1 + 5i)(1 – 5i)
8. (7 – 2i)(7 + 2i)
9. )i5)(i5(
10. )3i6)(i36(
Homework 43
State the conjugate of each complex number:
1. 3 + i
2. 4 – 8i
3. 3i2
4. 7 – 5i
Perform the indicated operation.
5.
i1
i35
6.
i21
i47
7.
i5
i21
20. IA2 Homework
8.
i75
i32
9.
i32
i4
Homework 44
State the additive and multiplicative inverse of each complex
number in simplest a + bi form.
1.
i4
i4
2.
i32
i32
3.
i2
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
21. IA2 Homework
Homework 47
1. On a flat panel tv that cost $500, the sales tax is $43.75.
Find the sales tax on a tv that cost $689.
2. 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?
3. 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?
4. 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?
Homework 48
1. Direct variation is a _____________________
between y and x.
2. If y varies directly as x then ______________
where k is the __________________________.
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:
X 1 2 3 4 5
Y 3 6 9 12 15
22. 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?
23. IA2 Homework
Homework 50
1. If x varies inversely as y and x = 24 when
y = 6, what is the value of y when x = 12.
2. If x varies inversely as y and x = 45 when
y = 4, find x when y = 3.
3. If a varies inversely as b, find the missing value in the
table:
A 3 9 27 81
B 270 90 10
Homework 51
1. 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?
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?
26. 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
27. 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
28. IA2 Homework
Homework 59
Determine whether each of the below graphs represent a function.
Homework 60
1. The graph of
function f is shown
at the right. Find the
following:
a. 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. If a function k is
defined by
3x
x6
)x(k , find
the value of
a. k(2)
b. k(9)
c. k(0)
d. k(6)
e. k(-3)
30. IA2 Homework
Homework 61
Given f(x) = x3
and g(x) = x + 1, determine:
1. f ○ g(0)
2. g [ f(0) ]
3. f [ g(1) ]
4. g○ f(-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)
Homework 62
Find the composition of
the given functions.
1. f ○ g(x) when f(x) =
x2
and g(x) = x + 1.
2. f ○ g(x) when f(x) =
1x
5
and g(x) =
2x.
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.
37. IA2 Homework
Homework 68
Graph each function.
1. y = 1x
2. y = 4x
3. y = 24x
Homework 69
Graph each function.
1. y = | x |
2. y = | x – 1 |
3. y = | x + 3 | + 5
38. IA2 Homework
Homework 70
Determine whether each function shown below is one-
to-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.
39. IA2 Homework
Homework 72
Find the inverse of each function provided.
1. y = x – 6
2. y = 2
1
x
3. y = 3x – 6
4. y = 5
x
+3
5. y =
4
2x3
Homework 73
Find the inverse of each function provided.
1. y = 2x + 5
2. y = 2
1
x - 6
3. y = .75x – .25
4. y =
5
20x10
40. 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 = 4
1
x
2. y = 2x+ 5
3. y = x2
42. IA2 Homework
Homework 79
Memorize these log rules:
logab = x ax
= b
log ab log a + log b
log b
a
log a – log b
log ax
x ● log a
Expand each expression:
1. log ab
2. log (a ÷ b)
3. log (a2
b)
4. log b
a
5. log ba
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 - 2
1
log b
Homework 80
Write the exponential equation in logarithmic form:
1. 24
= 16
2. 32
= 9
3. 10-2
= 0.01
4. 120
= 1
5. 3
1
8 =2
6. 2
1
5 = 5
7. 6-1
= 6
1
8. 4a
= b
9. x3
= y
10. 5c
= d
11. ba
= 8
46. IA2 Homework
Homework 86
Evaluate the given expression.
1. 5P3
2. 3P1
3. 4P4
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?
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
3. 12C0
4. 52C2
5. 26C2
6. 4C2
7. 4C3
Homework 88
Evaluate each expression using your calculator.
1. 8C3
2. 12C7
3. 6C0
4. 52C3
5. 25C2
6. 5C2
7. 5C3
Homework 89
Write the expansion of the given binomial.
1. (x + y)4
2. (x - y)7
3. (x + y)10
47. 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
