Supplies needed for your first day of class

and every day after:

3 Ring Binder or Notebook

Filler Paper

Pencils/Erasers

Scientific Calculator (such as a TI-34)

We STRONGLY recommend you have a

Graphing Calculator (TI 84).

Contact a teacher:

John Marks

Email: jmarks@rahway.net

Renee Canagon

Email: rcanagon@rahway.net

Summer 2015

Due date: September 8th

This packet was created

to help you succeed in

your upcoming

Precalculus class. Many

of the concepts were

taught to you in

previous classes. In your

upcoming math class we

will be building on these

concepts covered in this

packet.

You may find that you

have forgotten some of

these concepts. There

are many resources

available to you on the

internet to refresh your

memory. If you are

confused, be sure to

take the time to ask for

the help needed to

complete them.

This packet will count towards your first marking period grade. The packet will be graded for completeness and accuracy. Your teacher will be looking for supporting work to see that you understand each concept. We have given you our email addresses so you can contact one of us if you have questions. Please do not wait until the first day of school to ask for help! On Tuesday, September 8th, you will be given an assessment on the topics included in this packet to check for understanding. Have a great summer!

GUIDELINES FOR COMPLETING

THE ASSIGNMENT

RAHWAY HIGH SCHOOL

MATHEMATICS DEPARTMENT

Honors PRECALCULUS

Summer Assignment

1

Order of Operations.

1. Perform operations in Parentheses.

2. Evaluate numbers with Exponents.

3. Multiply or Divide from left to right.

4. Add or Subtract from left to right

Evaluate the expression.

1. 8 + 2 · 5 2. 40 ÷ 8 – 7 3. 5 · 42 ÷ 8

4. 1 – 7 + 52 5.

6. (12 – 8)2 ÷ 25

7. 4 · 32 8. 10 ÷ 5 · 2 9. 32 ÷ 8 + 2 · 82

10. 4(3 + 8) – 82 ÷ 32 11. 10(3 – 6)3 + 41 12. (2-5)2 – (4·5)2

2

Factor the following polynomials completely:

Formulas: Difference of 2 squares: a2 – b2 = (a + b) (a – b)

Sum of 2 cubes: a3 + b3 = (a + b) (a2 – ab + b2)

Difference of 2 cubes: a3 - b3 = (a - b) (a2 + ab + b2)

1) b 2 + 8b + 7 2) n 2 − 11n + 10 3) m 2 + m – 90 4) n 2 + 4n – 12

5.) n 2 − 10n + 9 6) b 2 + 16b + 64 7.) 2n2 + 6n − 108 8.) 5n 2 + 10n + 20

9.) 2n2 + 3n – 9 10.) 5n2 + 19n + 12 11.) 4n 2 − 15n − 25

3

12) 4x2 − 35x + 49 13) −6a2 − 25a – 25 14) 16b2 + 60b – 100

15) 36k2 − 1 16) p2 – 49 17.) 3n2 − 75 18.) 25 – m2

19.) 9x 2 − 16y2 20.) 4x 2 − 4x + 1 21.) 3 + 6b + 3b2

22) 2x4 + 22x3 + 56x2 23.) x3 – 64 24.) 27 + 8x3

4

Properties of Rational Exponents

Let a and b be real numbers and let m and n be rational numbers , such that the quantities in

each property are real numbers.

Property Name: Definition:

1. Product of Powers 1. am · an = am + n

2. Power of a Power 2. (am)n = amn

3. Power of a Product 3. (ab)m = ambm

4. Negative Exponent 4. a-m =

, a ≠ 0

5. Zero Exponent 5. a0 = 1, a ≠ 0

6. Quotient of Powers 6. am/ an = am-n, a≠ 0

7. Power of a Quotient 7. (

) m = am / bm , b≠ 0

Simplify completely. Use only positive exponents.

1) 2m2 ⋅ 2m3 2) m4 ⋅ 2m-3 3) 4r-3 ⋅ 2r2 4) 4n4 ⋅ 2n-6

5) 2k4 ⋅ 4k 6) 2x3 y-3 ⋅ 2x-1 y3 7) (x2)0 8) (2x2)-4

5

9) (2x4 y-3)-1 10) 2 3

3 34 2h g h 11) 2 7

4 6 6 314a b a c

12) 36

2

r

r 13)

18 5

11 3

21

7

d e

d e 14)

4

6

3w

g

15)

342

4

d

e

16)

311 16

6 6

d f

d f

17)

1 427

18) 1 4

10

10 19)

1 55

5

6

9

20) 1

3 4 1 47 7

21.) 3 75 22.) 3 381 9 23.) 5

80

6

Solve the following equations:

1. 8 43

t

2.

59

2

p

3. 3 2 60k k

4. 43 12 6p p 5. 28 8 13 35b b 6. 11 6 3 30j j

7. 12 5 3 2 17r 8. 3 2 5 2 16x x 9. 4 7 3x x

10. 8 2 3 12b b 11. 8 5 3 8 4h h h 12. 10 7 15 3g g g

7

13. 3 4 4 5w w 14. 8 3 2 3 3 5 4 2g g g

Solve the following quadratic equations . Check your solutions.

Quadratic formula:

1. 2 6 5 0x x 2. 2 6 9 0x x 3. 2 25 0x

4. 2 4 12 0x x 5. 212 4x 6. 3x2

+ 5x = 8

7. 2 64g 8. 2

2 16y 9. 2 1 0x

8

10. 26 4 2x x 11. 2x2 – x = 7 12. 24 3 1x x

Solve the following systems:

1. 10 2

4

y x

x y

2. 4 1

5

y x

x y

3. 11 4

3 2 0

y x

x y

4. 3 2

2 3

x y

x y

5. 4 5

3 9

x y

x y

6. 2 5 7

2 3 1

x y

x y

9

7. 7

5 2 8

x y

x y

8. 7 6 9

5 2 19

x y

x y

9. 0

3 3 6

x y

x y

10. 2 2 8

4

x y

x y

11. 3

2 5

2 6

y

x y

x y z

Solve and check the following rational equations.

1.3 1

4 2x x

2.

4 6

2 2x x

3.

3 5

1 5

x

x x

10

4.4 2

43 x 5.

4 1 1

5 5

x

x x x

6.

2

12 3 3

2 2x x x x

Perform the indicated operation:

1.4 2 3 2

4 5 3

54

9

x y x y

y x y 2.

3

4

2 1 3

1

x x x x

x x

3.

2 25 4 3

3

x x x x

x x

4.2 2

2 2

4 5 2 6

6 9 3 2

x x x x

x x x x

5.

4 9

7 5

28

2

x y y

y x

11

6.2

4 3 3

6 3

3 6 6

x x x

x x x

7.

7 3

2 2

x

x x

8. 2

7 4

2 3x x 9.

2

14 6

7 18 9x x x

10. 2 6 1 3x x x 11. 23 11 4 1x x x

12

Find f g x and f g x . Then evaluate f g and f g

for the given value of x.

1. 3 34 ; 9 4 ; 2f x x g x x x

2. 2 3 23 5 ; 6 4 ; 1f x x x x g x x x x

Find fg x and f

xg

. Then evaluate fg and f

g for the

given value of x.

;

4. 2 1 43 ; 5 ; 16f x x g x x x

13

Logarithms

Rewrite the equation in exponential form.

1. 2log 8 3 2. 7log 7 1 3. 5log 25 2

Rewrite the equation in logarithmic form.

4. 24 16 5. 05 1 6. 1 16

6

Evaluate the logarithm.

7. 2log 16 8. 5log 125 9. 6log 6

10. 515

log 11. 9log 1 12. 218

log

Expand the logarithmic expression.

13. 2log 5x 14. 4log 7x 15. 6

2log

x

y

14

Condense the logarithmic expression.

16. 7 7log 3 log 5 17. log 10 log 5

18. 3 ln 9 ln x y 19. 2 212

log 9 log y

Use the change-of-base formula to evaluate the logarithm.

20. 5log 3 21. 2log 11 22. 6log 10

15

Solve the equation.

1. 7 2 36 6x x 2. 5 3 4x xe e 3. 1 33 9x x

4. 8 35x . 5. ln 3 8 ln 6x x 6. 3 3log 9 2 log 4 3x x

7. log 4 1 log 25x 8. 6log 5 4 2x

16

Solve the equation. Check for extraneous solutions.

1. 2 2log log 3 2x x 2. 3 3log 3 log 2 1 2x x

3. ln ln 4 3x x 4. 26 6log 2 log 3 2x