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: [email protected]
Renee Canagon
Email: [email protected]
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