Advanced Precalculus Summer Assignment West Morris Mendham High School The following assignment contains important prerequisite topics for Precalculus. You will be responsible for the content when you return to school in September. Your teacher may collect this packet and grade it, randomly select problems in this packet to grade, or give a quiz or test on this material the first or second week of school. Your teacher will tell you what to expect during the first week of school.

Distance Formula

Factoring

Difference of two squares

( )( )bababa +−=− 22

Difference of two cubes

( )( )2233 babababa ++−=− Sum of Cubes

( )( )2233 babababa +−+=+

Arithmetic Sequence with a common difference d

The nth term

( )dnaa n 11 −+=

Sum of the first n terms.

( )2

1 nn

aanS +=

\Geometric Sequence with a common ratio r

The nth term

11

−= nn raa

Sum of the first n terms of the sequence

( )rraS

n

n −−

=111

Sum of an infinite geometric series.

11

1

<−

=

rwhenr

aSn

Change of base

ax

xb

ba log

loglog =

Advanced Pre-Calculus Name___________________________________

Algebra 2 Review Summer Assignment

Solve each inequality and graph its solution.

1)

10

r

− 7 − 8 ≤ 15

−4 −3 −2 −1 0 1 2 3 4 5

2)

10 −

3

9 − 2

r

< −11

−2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12

-1-

Find the common difference, the next three terms in the sequence, and the indicated term.

3) 10, 30, 50, 70, ...

Find

a

24

Solve each equation.

4)

−6 −

3

v

− 7 = −10

-2-

Use the information provided to write the standard form equation of each circle.

5) Center: (−8, −9)Radius: 10

-3-

Identify the center and radius of each. Then sketch the graph.

6)

x

2 +

y

2 = 25

x

y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2

2

4

6

8

7)

x

2 +

(

y

+ 2)2 = 19

x

y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2

2

4

6

8

-4-

Divide.

8)

(

x

3 + 7

x

2 − 26

x

− 75) ÷ (

x

+ 9) 9)

(

n

3 + 9

n

2 − 11

n

+ 1) ÷ (

n

− 1)

Simplify.

10)

3 5

5 −

5

-5-

Identify the domain and range of each.

11)

y

=

log

1

4

(

3

x

+ 14) + 3 12)

y

=

ln (

3

x

+ 2) − 1

Identify the domain and range of each.

13)

y

=

−5 +

x

− 1 14)

y

=

−3 +

x

− 1

-6-

Solve each equation.

15)

4

−2

n

− 1 =

43

n

16)

(

1

243 )3

b

=

34

17) log (

−

n

+ 10) = log −2

n

18)

−7 log4

(

a

+ 7) = 14

-7-

Solve each equation. Round your answers to the nearest ten-thousandth.

19)

log

x

+ log 8 = 3 20)

log

x

−

log 6 = log 21

Solve each equation.

21)

log4

2 −

log4

−

x

= log4

59 22)

ln 7 −

ln (

5

x

− 7) = 5

-8-

Solve each equation or state if there is no unique solution.

23)

−1 2

4 −3

X

= 6

1124)

−2 4

3 −1

C

+ −10 −3

1 11 =

−40 −47

11 32

Find all roots.

25)

x

3 +

x

2 +

x

+ 1 = 0 26)

x

4 − 8

x

3 + 17

x

2 = 0

-9-

27)

x

3 − 4

x

2 − 4

x

+ 16 = 0

Solve each equation by completing the square.

28)

a

2 − 8

a

− 29 = −5 29)

8

v

2 + 16

v

+ 89 = −8

-10-

Solve each equation by factoring.

30)

−8 −

x

=

2 − 2

x

2 31)

9

k

2 − 16

k

− 16 = −3

k

2

Solve each equation by taking square roots.

32)

5

x

2 − 9 = 116 33)

7

p

2 + 9 = 37

-11-

Solve each equation. Remember to check for extraneous solutions.

34)

x

− 2 =

60 − 5

x

35) 3 =

b

+ 7 − 4

Solve each equation. Round your answers to the nearest ten-thousandth.

36)

−9 ⋅

e

−5

r

− 1 − 6 = −61 37)

5 ⋅

e

1.3

x

+ 4 + 0.4 = 90

-12-

Factor each completely.

38)

15

mn

+ 3

m

− 20

n

− 4 39)

30

xy

− 35

x

− 12

y

+ 14

State the possible rational zeros for each function. Then factor each and find all zeros. One zero has been

given.

40)

f

(

x

) =

x

3 − 8

x

2 + 17

x

− 10; 5

-13-

Factor each completely.

41)

54

k

2 + 390

k

+ 84 42)

−24

k

2 + 28

k

+ 196

43)

18

b

2v

− 200

v

-14-

44)

u

4 − 7

u

2 + 10

A)

(

u

2 + 2)(

u

2 + 5)

B)

(

u

2 + 2)(

u

+ 3)(

u

− 3)C)

(

u

2 − 2)(

u

2 + 5)

D)

(

u

2 − 2)(

u

2 − 5)

45)

m

2 + 6

m

+ 9

46)

4

r

2 − 9 47)

27

a

3 − 8

-15-

48)

128

x

3 + 54

Evaluate each function.

49)

k

(

x

) =

x

− 1; Find

k

(

−1

2 ) 50)

h

(

x

) =

x

+

5

3

x

2; Find

h

(

2

3)

-16-

Find the inverse of each function. Then graph the function and its inverse.

51)

g

(

x

) =

−1

2

x

−

1

2

x

y

−6 −5 −4 −3 −2 −1 1 2 3 4 5 6

−6

−5

−4

−3

−2

−1

1

2

3

4

5

6

52)

g

(

n

) = 3

n

x

y

−6 −5 −4 −3 −2 −1 1 2 3 4 5 6

−6

−5

−4

−3

−2

−1

1

2

3

4

5

6

-17-

Perform the indicated operation.

53)

g

(

x

) =

−2

x

+ 2

h

(

x

) = −3

x

Find (

g

−

h

)(

x

)

54)

g

(

x

) =

x

2 + 3

x

h

(

x

) =

x

− 1

Find (

g

⋅

h

)(

x

)

55)

g

(

x

) =

x

2 − 2

h

(

x

) =

2

x

− 3

Find

g

(

h

(

x

))

56)

f

(

x

) =

x

3 − 5

x

g

(

x

) =

x

+ 3

Find (

f

+

5

g

)(

x

)

-18-

Find the common ratio and the 8th term.

57)

3, 9, 27, 81, ...

Find the sum of the first n terms of each geometric series described.

58)

−2

3 −

2

15 −

2

75 −

2

375...,

n

= 659)

−4 − 12 − 36 − 108...,

n

= 9

-19-

Find the sum of each infinite geometric series described.

60)

−96 − 48 − 24 − 12... 61)

2 −

2

5 +

2

25 −

2

125...

-20-

Sketch the solution to each system of inequalities.

62)

x

− 3

y

< −6

4

x

+ 3

y

> −9

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

63)

y

<

−2

x

− 2

y

<

−1

2

x

+ 1

−5 −4 −3 −2 −1 0 1 2 3 4 5

−5

−4

−3

−2

−1

1

2

3

4

5

-21-

Solve each compound inequality and graph its solution.

64)

9

20

b

>

−27

40 and

b

+

3

2 ≤

7

2

−3 −2 −1 0 1 2 3 4

-22-

Write the slope-intercept form of the equation of the line through the given points.

65) through: (−2, −4) and (−1, −1)

Write the slope-intercept form of the equation of the line described.

66) through: (−4, 4), parallel to

y

=

−2

x

67) through: (3, −3), perp. to

x

= 0

-23-

Use a calculator to approximate each to the nearest thousandth.

68) log3

48

Condense each expression to a single logarithm.

69)

5 log 5 +

log 11

2

-24-

Expand each logarithm.

70) log7

(

x

y

2 )6 71) log

2

3

x

⋅

y

⋅

z

Simplify. Write "undefined" for expressions that are undefined.

72)

3

a

a

6

b

−

5

b

6

b

−5

b

+ −1 −5

a

2

a

-25-

73)

−4

−1 4

y

xy

−2

−5

xy

⋅ 2

y

3

2 −5

x

74) Heather and Adam each improved their yards by planting grass sod and geraniums. They bought theirsupplies from the same store. Heather spent $180 on 12 ft² of grass sod and 12 geraniums. Adam spent

$104 on 8 ft² of grass sod and 6 geraniums. Find the cost of one ft² of grass sod and the cost of one

geranium.

-26-

75) Nicole and Mike are selling flower bulbs for a school fundraiser. Customers can buy packages of tulip

bulbs and bags of daffodil bulbs. Nicole sold 2 packages of tulip bulbs and 14 bags of daffodil bulbs fora total of $232. Mike sold 8 packages of tulip bulbs and 7 bags of daffodil bulbs for a total of $193.

What is the cost each of one package of tulips bulbs and one bag of daffodil bulbs?

Simplify.

76)

10 + 7i

−6 − i

-27-

-28-

Answers to Algebra 2 Review Summer Assignment

1)

−8

5 ≤

r

≤ 3 : −4 −3 −2 −1 0 1 2 3 4 5

2)

r

< 1 or

r

> 8 : −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12

3) Common Difference:

d

= 20

Next 3 terms: 90, 110, 130

a

24 = 470

4)

{

11

3, 1} 5)

(

x

+ 8)2 +

(

y

+ 9)2 = 100

6)

x

y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2

2

4

6

8 Center: (0, 0)Radius: 5

7)

x

y

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2

2

4

6

8 Center: (0, −2)Radius: 19

8)

x

2 − 2

x

− 8 −

3

x

+ 9

9)

n

2 + 10

n

− 110)

3 5 + 3

411) Domain:

x

>

−14

3

Range: All reals

12) Domain:

x

>

−2

3

Range: All reals

13) Domain:

x

≥ 1

Range:

y

≥ −5

14) Domain:

x

≥ 1

Range:

y

≥ −315)

{

−1

5}

16)

{

−4

15} 17) {−10}18)

{

−111

16 } 19) {125}

20) {126}21)

{

−2

59} 22)

{

7 + 7

e

5

5

e

5 } 23) 8

7

24) 1 4

−7 −9

25) {−1, i, −i} 26)

{0 mult. 2,

4 + i,

4 − i}

27) {4, −2, 2} 28)

{

4 +

2 10 ,

4 −

2 10}29)

{

−4 +

i 178

4,

−4 −

i 178

4 }30)

{

5

2, −2} 31)

{

−2

3, 2} 32) {5, −5} 33) {2, −2}

34) {7} 35) {42} 36) −0.562 37) −0.857

38)

(

3

m

− 4)(

5

n

+ 1) 39)

(

5

x

− 2)(

6

y

− 7) 40) Possible rational zeros: ± 1, ± 2, ± 5, ± 10

Factors to:

f

(

x

) =

(

x

− 2)(

x

− 1)(

x

− 5)Zeros: {2, 1, 5}

41)

6(

k

+ 7)(

9

k

+ 2) 42)

−4(

2

k

− 7)(

3

k

+ 7) 43)

2

v

(

3

b

+ 10)(

3

b

− 10)44) D 45)

(

m

+ 3)2 46)

(

2

r

+ 3)(

2

r

− 3)47)

(

3

a

− 2)(

9

a

2 + 6

a

+ 4) 48)

2(

4

x

+ 3)(

16

x

2 − 12

x

+ 9)49)

−1

2

50)

38

27

-29-

51)

x

y

−6 −4 −2 2 4 6

−6

−4

−2

2

4

6

g

−1(

x

) =

−2

x

− 1

52)

x

y

−6 −4 −2 2 4 6

−6

−4

−2

2

4

6

g

−1(

n

) =

n

3

53)

x

+ 2 54)

x

3 + 2

x

2 − 3

x

55)

4

x

2 − 12

x

+ 7 56)

x

3 + 15

57) Common Ratio:

r

= 3

a

8 = 6561

58)

−2604

3125

59) −39364

60) −19261)

5

3

62)

−4 −2 0 2 4

−4

−2

2

4

63)

−4 −2 0 2 4

−4

−2

2

4

64)

−3

2 <

b

≤ 2 : −3 −2 −1 0 1 2 3 4

65)

y

=

3

x

+ 2 66)

y

=

−2

x

− 4 67)

y

= −3 68) 3.524

69) log (

55

11) 70)

6 log7

x

−

12 log7

y

71)

log2

x

3 +

log2

y

3 +

log2

z

3

72)

3

a

− 5

b

− 1

−4

a

− 6

b

11

b

+ 2

a

73)

−24

y

12 + 80

yx

−8

xy

2 + 16

−12

xy

− 40

x

40

y

− 8

xy

60 + 20

x

2y

74) ft² of grass sod: $7, geranium: $8

75) package of tulips bulbs: $11, bag of daffodil bulbs: $15

76)

−67

37 −

32i

37