homework packet

IA2 Homework

Homework 2

Perform the indicated operation:

1. (x3 + 9x – 5) + (-4x

3 – 12x + 5)

2. (x2 – 33x + 15) + (-4x

2 + 18x – 36)

3. (3a2 – 2ab + 3b

2) – (a

2 – 5ab + 3b

2)

4. (x2 – 6x + 5) – (3x

2 – 2x – 2)

5. (x2 – 9) – (-2x

2 + 5x – 3)

6. From 4x + 2y, subtract x – 4y.

7. Subtract 2x2 – 3x + 7 from x

2 + 6x – 12.

8. Subtract 2c2 + 3c – 4 from 0.

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

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.

IA2 Homework

Homework 7

Write each expression in factored form:

1. sr – st

2. p + prt

3. 4x2 – 4y

2

4. 2x – 4x3

5. 10xy – 15x2y

2

6. y2 – 64

7. t2 – 25

8. 4r2 – b

2

9. 9 – m2

10. 16a4 – 25b

6

11. s2 - 10064

Homework 8


1. a2 + 3a + 2

2. x2 – x – 2

3. z2 + 9z – 36

4. w2 – 16w + 64

5. 2x2 + 12x + 8

6. 2ax2 – 2ax – 12a

7. 4x2 – 4

8. 63c2 – 7

Homework 9


1. 2x2 + 5x + 2

2. 2x2 + 7x + 6

3. 3x2 10x + 8

4. 16x2 + 8x + 1

5. 2x2 + x – 3

6. 4x2 – 12x + 5

Homework 10


1. by2 – 4b

2. 3x3 – 6x

2 – 24x

3. x4 – 16

4. m2 – 81

5. 6x + 27b

6. x2 – 16h

2

7. abx2 - ab

IA2 Homework

Homework 11

Factor each expression:

1. x3 + 8

2. 27x3 + 1

3. 8a6 + 64b

3

4. x3 + y

3

Homework 12

Factor each expression:

1. a3 – b

3

2. x3 – 64

3. 8x3 – 27

4. x6 – y

9

Homework 13

Factor each expression completely:

1. 64x3 + 125

2. 3y3 – 81

3. 2x3 + 54

4. x2 – 100

5. 2x2 – 128x

6. x2 – 19x + 90

IA2 Homework

Homework 14

Simplify each expression:

1. 4

2

x35

x15

2. x10

x6x2 2

3. 4x5x

16x2

2

4. 8y

12y33

2

5. 15bb2

b6b22

2

Homework 15

Perform the indicated operation. Be sure to simplify your

answer!

1. 9x

x6x2

x6

y3xy2

2

2. xy

z5

z5

yx

3. x15x3

x30x3

20x4

20x42

2

4. bb2

b8b8

b8b4

2b3b22

23

2

2

5. If the side of a square measures 2x

1x, express

the area of the square in terms of x.

Homework16

Perform the indicated operation. Be sure to simplify

your answer!

1. 1x

1

1x

1x2

2

2. 3m

m6

m3

3m

3. 2

2

2

2

)4n(

n8

16n

n8n2

IA2 Homework

4. 3

23

2

2

y4

y10y2

1y4y4

5y11y2

5. 32

3

22

23

ycy

yc

yc

ycc

Homework 17

Perform the indicated operation. Be sure to simplify your

answer!

1. 50x5

2x

2x

100x2

2. 18x6

x3

x

6x2 2

2

3. x2

9x3

x4

9x2

4. 2ab

1

ab

1

5. 2k4

12k12

k

3k3

IA2 Homework

Homework 18

Perform the indicated operation and simplify your answer!

1. 5

x3

5

x4

5

x3

2. 4x

x

4x

4

3. 4x4

x2

4x4

3x5

4. k3k

9k

k3k

k22

2

2

2

5. 16x

3x5

16x

1x22

2

Homework 19

Perform the indicated operation and simplify your answer!

1. 4

x

8

x3

2. 3

3c

2

2c

5. 5x

3

x

2

7. 3y

5

2y

1

8. 9y

18

3y

y2

9. 8m2

2m

16m

1m32

Homework 20

Solve the fractional equation. Be sure to check your

answer(s)!

1. 625

x

2. 4

1

y12

1

3. 1x

1

x

2

1x

x

4. 4x

x

4x

42

IA2 Homework

6. y2y

4

y

2y2

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 = 45

43 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 = 21 x+3

3. 3x + y = 6; y = 3

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

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 = 21 x

2 + 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 – 21 x

2

IA2 Homework

Homework 28

Simplify the radical expressions.

1. 75

2. 300

3. 9y92

4. ba2

5. 7x125

Homework 29

Simplify the radical expressions.

1. 3 24

2. 3 6

23 x16

3. 3 5

54 y125

4. 3 7n

5. 3 11a56a4

Homework 30

Perform the indicated operation and simplify your

answer.

1. 80180

2. 75xx48 612

3. 28378700

4. 31248

5. 3 33 3 y16y250

6. 333 x27x8x64

Homework 31

Perform the indicated operation and simplify your

answer.

1. )175(75

2. )123(312

3. 96150520

4. 3 1233 a640a

IA2 Homework

Homework 32

Perform the indicated operation and simplify.

1. 205

2. 2323

3. 18531

4. 5xx

5. 33 255

6. 33 2 x6x9

7. )1234(3

8. )382(23

9. )73)(72(

10. )325)(325(

Homework 33

Perform the indicated operation and simplify.

1. 5

80

2. 64

4824

3. 3

3

26

12830

4. 3

4875

5. 52

15652

IA2 Homework

Homework 34

Solve and check each solution.

1. 3x

2. 3x6

3. 6x3

4. 52x

5. 9y5

6. 471y2

7. 5x1x

Homework 35

Solve and check each solution.

1. 3y22y

2. xx

3. 16y6y

5. 22y45

6. y2303y

Homework 36

Graph each radical equation on the graph provided.

1. x2y

2. 3xy

3. 4xy

IA2 Homework

4. 8x24x

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. 932

5. 113

6. 4x20

7. 5d75d2

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. 3220021

4. 5018251

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

IA2 Homework

3. 334

4. 102103

5. 25

400

6. 2

98

7. 34

48

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

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

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

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


5. x varies directly as y:

x 2 8 ? 10

y 1 ? 12 5


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?

IA2 Homework

Homework 52

Solve each equation below.

1. (x - 3)(2x + 1) = 0

2. x2 – 13x + 42 = 0

3. x2 + 12x = 28

4. 2x2 - 11x = x

2 - 3x +12

Homework 53

Solve each equation using the quadratic formula.

1. x2 – 6x + 7 = 0

2. x2 + 10x -11= 0

3. x2 = 2x -5

IA2 Homework

Homework 54

Solve each equation by completing the square.

1. a2 – 8a = 20

2. x2 – 2x = 3

3. x2 + 12x + 35 = 0

Homework 55

Solve each equation by completing the square.

1. x2 – 9x + 18 = 0

2. x2 – 7x + 12 = 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 + y

2+6x + 8y + 9 = 0

2. x2 + y

2-6x + 4y + 4 = 0

3. x2 + y

2-10x + 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 + y

2 – 2x + 4y – 20 = 0

2. x2 + y

2 – 4x + 8y + 4 = 0

3. x2 + y

2 – 6x + 10y + 25 = 0

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)

IA2 Homework

f. k(3)

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.

IA2 Homework

IA2 Homework

Homework 63

Graph each function:

1. y = 2x3

2. y = | x | + 2

3. y = | x + 2 |

4. y = 1x2

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


1. y = (x - 3)2 + 1

2. y = | x + 1 |

3. y = 24x

IA2 Homework

Homework 66

Graph each function:

1. y = x2

2. y = y = (x - 2)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


1. y = 1x

2. y = 4x

3. y = 24x

Homework 69


1. y = | x |

2. y = | x – 1 |

3. y = | x + 3 | + 5

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.

IA2 Homework

Homework 72


1. y = x – 6

2. y = 21 x

3. y = 3x – 6

4. y = 5x +3

5. y = 4

2x3

Homework 73


1. y = 2x + 5

2. y = 21 x - 6

3. y = .75x – .25

4. y = 5

20x10

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 = 41 x

2. y = 2x+ 5

3. y = x

2

IA2 Homework

Homework 76

Simplify:

1. x3 ● x

5

2. 7

12

b

b

3. (x4)

2

Evaluate f(x) with the given value:

4. f(x) = 2x f(2)

5. f(x) = 4x-1

f(3)

6. f(x) = 32x+1

f(3)

7. f(x) = 2

1 x f(-1)

Homework 77

Graph each exponential function:

1. f(x) = 2x

2. f(x) = 3

x+1

Homework 78

Solve each exponential equation:

1. 2x-1

= 82

2. 9x+1

= 27x

3. 16x-3

= 4x-3

4. 32x-1

= 3x+2

5. 53x

= 25x+1

6. 6x = 216

4x-4

7. 4x = 16

8. 22x

=64

9. 3x-1

=27

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 (a2b)

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

IA2 Homework

Homework 81

Write the logarithmic equation in exponential form:

1. log2 64 = 6

2. log10 1000 = 3

3. log27 9 = 3

2

4. log4 32 = 2

5

5. log9

1 3 = -2

1

6. logbc - 5

1

Homework 82

Solve for x:

1. log2x = 4

2. log5x = 2

3. log3x = -2

4. log7x = 0

5. log81x = 2

1

Solve for n:

6. log327 = n

7. log216 = n

8. log525

1 = n

9. logn27 = 3

10. logn49 = 2

11. logn125 = 2

3

IA2 Homework

Homework 83

Find x to the nearest tenth.

1. 2x = 7

2. 5x = 47.6

3. 1.06x = 1.14

4. 2.5x = 9.88

5. 3x = 15.6

6. 15x = 295

7. 4.5x = 1.57

Homework 84


1. 4.08x = 2.02

2. 7x = 615

3. 4.7x = 10.2

4. 3.8x = 2.9

5. 2.75x = 3.72

IA2 Homework

Homework 85


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

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

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

homework packet

Technology