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 2017

Due date: September 9th

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 Friday, September 9th, 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.) 5 · 42 ÷ 8 2.) 3−(−9)

−10+6 3.) 32 ÷ 8 + 2 · 82

4.) 10(3 – 6)3 + 41 5.) (2-5)2 – (4·5)2

2

Adding or subtracting fractions with different denominators.

Find equivalent fractions with the same denominator:

1. Find the smallest multiple (LCM) of both numbers.

2. Rewrite the fractions as equivalent fractions with the LCM as the

denominator.

Evaluate the expression.

2.) 1.)

3.) 4.)

5.) 6.) 3

4+

1

2

3

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.) n 2 − 10n + 9 2.) b 2 + 16b + 64

3.) 2n2 + 6n − 108 4.) 2n2 + 3n – 9

5.) 5n2 + 19n + 12 6.) −6a2 − 25a – 25

7.) p2 – 49 8.) 9x 2 − 16y2

9.) 2x4 + 22x3 + 56x2 10.) x3 – 64

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 = 1

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. ( 𝑎

𝑏 ) m = am / bm , b≠ 0

Simplify completely. Use only positive exponents.

1.) 2m2 ⋅ 2m3 2.) 2x3 y-3 ⋅ 2x-1 y3 3.) (x2)0

4.) (2x2)-4 5.) 36

2

r

r 6.)

18 5

11 3

21

7

d e

d e

5

7.)

311 16

6 6

d f

d f

8.)

1 4

10

10

9.) 3 75 10.) 5

80

Solve the following equations:

1.) 8 43

t

2.)

59

2

p

3.) 12 5 3 2 17r 4.) 3 2 5 2 16x x

6

5.) 3 4 4 5w w 6.) 8 3 2 3 3 5 4 2g g g

Solve the following quadratic equations . Factor if possible. Use the quadratic

formula if necessary. Check your solutions.

Quadratic formula: 𝑥 =−𝑏±√𝑏2−4𝑎𝑐

2𝑎

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

2 16y

4.) 26 4 2x x 5.) 2x2 – x = 7

7

Solve the following systems:

1. ) 10 2

4

y x

x y

2.) 11 4

3 2 0

y x

x y

3.) 4 5

3 9

x y

x y

4.) 0

3 3 6

x y

x y

5.) 2 2 8

4

x y

x y

8

Solve and check the following rational equations.

1.3 1

4 2x x

2.)

3 5

1 5

x

x x

3.)4 1 1

5 5

x

x x x

4.)

2

12 3 3

2 2x x x x

9

Perform the indicated operation:

1.) 3

4

2 1 3

1

x x x x

x x

2.)

2 2

2 2

4 5 2 6

6 9 3 2

x x x x

x x x x

3.) 4 9

7 5

28

2

x y y

y x 4.)

2

14 6

7 18 9x x x

10

Given the function 𝒇(𝒙) = 𝟑𝒙 − 𝟓𝒙𝟐 − 𝒙𝟑 and 𝒈(𝒙) = 𝟔𝒙𝟐 − 𝟒𝒙. Find the

following:

1) (𝑓 + 𝑔)(𝑥) 2) (𝑓 − 𝑔)(𝑥)

3) (𝑓 + 𝑔)(−1) 4) (𝒇 − 𝒈)(−𝟏)

Given the function 𝒇(𝒙) = 𝟒𝒙𝟓 and 𝒈(𝒙) = 𝟐𝒙𝟑. Find the following:

1) (𝑓𝑔)(𝑥) 2) (𝑓

𝑔)(𝑥)

3) (𝑓𝑔)(−2) 4) (𝒇

𝒈) (0)

11

Logarithms

Rewrite the equation in exponential form.

1. 2log 8 3 2. 7log 7 1

Rewrite the equation in logarithmic form.

3. 05 1 4. 1 16

6

Evaluate the logarithm.

5. 2log 16 6. 6log 6 7. 515

log

Expand the logarithmic expression.

8. 4log 7x 9. 6

2log

x

y

Condense the logarithmic expression.

10.) log 10 log 5 11.) 3 ln 9 ln x y

12

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

12.) 5log 3 13.) 2log 11

Solve the logarithmic/exponential equation. For the logarithmic equations, check for extraneous solutions.

14.) 5 3 4x xe e 15.) 1 33 9x x

16.) 8 35x . 17.) ln 3 8 ln 6x x

18.) 6log 5 4 2x 19.) 2 2log log 3 2x x

20.) ln ln 4 3x x