SUMMER MATH WORK FOR STUDENTS
ENTERING ALGEBRA 2,
ADV. ALGEBRA 2 or
ALGEBRA/TRIGONOMETRY
The attached Math packet is assigned to you based on your registration for Algebra 2, Adv.
Algebra 2 or Algebra/Trigonometry for the upcoming school year.
Your assignment is to complete all of the problems in the packet (showing your work) and bring
the completed packet to your Math class on the first day of classes. The packet will be checked
for completeness at this time and you will receive a homework grade equivalent to three
regular homework assignments.
Over the first two days of classes, you will have an opportunity to ask questions and will review
the assigned summer work. During the following week you will be given a test on this material.
Directions:
--Students need to work in pencil and show their work in the packet or on lined
paper to accompany the packet. Round answers to the nearest tenth.
--A calculator may be used on any of the problems in this packet and a graphing
calculator is required for some.
Algebra 1 Skills Needed to be Successful in Algebra 2, Adv.
Algebra 2 or Algebra/Trigonometry
A. Simplifying Polynomial Expressions
Objectives: The student will be able to:
 Apply the appropriate arithmetic operations and algebraic properties needed to
simplify an algebraic expression.
 Simplify polynomial expressions using addition and subtraction.
 Multiply a monomial and polynomial.
B. Solving Equations
Objectives: The student will be able to:
 Solve multi-step equations.
 Solve a literal equation for a specific variable, and use formulas to solve
problems.
C. Rules of Exponents
Objectives: The student will be able to:
 Simplify expressions using the laws of exponents.
 Evaluate powers that have zero or negative exponents.
D. Binomial Multiplication
Objectives: The student will be able to:
 Multiply two binomials.
E. Factoring/Quadratic Functions
Objectives: The student will be able to:
 Identify the greatest common factor of the terms of a polynomial expression.
 Express a polynomial as a product of a monomial and a polynomial.
 Find all factors of the quadratic expression ax2 + bx + c by factoring and graphing
and the quadratic formula.
 Identify the zeroes or roots of a quadratic function as well as the vertex and axis
of symmertry.
F. Radicals
Objectives: The student will be able to:
 Simplify radical expressions.
G. Graphing Lines
Objectives: The student will be able to:
 Identify and calculate the slope of a line.
 Graph linear equations using a variety of methods.
 Determine the equation of a line.
H. Right angle trigonometry
Objectives: The student will be able to:
 Understand and use basic right triangle trigonometric functions such as sine,
cosine and tangent.
Problems to Work
A. Simplifying Polynomial Expressions
Combining Like Terms
- You can add or subtract terms that are considered "like", or terms that have the same
variable(s) with the same exponent(s).
Ex. 1:
5x - 7y + 10x + 3y
5x - 7y + 10x + 3y
15x - 4y
Ex. 2:
-8h2 + 10h3 - 12h2 - 15h3
-8h2 + 10h3 - 12h2 - 15h3
-20h2 - 5h3
Applying the Distributive Property
- Every term inside the parentheses is multiplied by the term outside of the parentheses.

Ex. 1: 3(9x4)
39x 34
27x 12
Ex. 2 : 4x2 (5x3 6x)
4x2 5x3 4x2 6x
20x5 24x3
Combining Like Terms AND the Distributive Property (Problems with a Mix!)
- Sometimes problems will require you to distribute AND combine like terms!!
Ex.1: 3(4x 2) 13x
34x 32 13x
12x 6 13x
25x 6
Ex. 2 : 3(12x 5) 9(7 10x)
312x 35 9(7) 9(10x)
36x 1563 90x
54x 48
Solving quadratic functions by factoring or quadratic formula
Find the roots of each by factoring.
1. x2 -7x – 8 = 0
2. x2 – 5x + 6 = 0
3. x2 = 144
4. x2 -21x = 0
5. 4x2 -16x + 16 = 0
6. 2x2 +8x + 6 = 0
7. x2 + 14x = 32
8. 9x2 + 6x + 1 = 0
Find the zeros of each function by using the quadratic formula.
1. x2 – 3x – 8 = 0
2. (x – 5)2 + 12 = 0
3. 2x2 – 10x +18 = 0
4. x2 + 3x + 3 = 0
5. x2 – 5x + 10 = 0
Properties of Quadratic Functions in Standard Form
For each function, a) determine whether the graph opens upward or downward, b)
find the axis of symmetry, c) find the vertex, d)find the y-intercept.
1. f(x) = x2 – 4x + 3
2. g(x) = x2 + 2x + 3
3. f(x) = x2 – 3x
4. f(x) = x2 – 2x + 4
1
2
Find the minimum or maximum value of each function.
1. x2 + 2x + 6
2. -2x2 – 8x + 10
Right Triangle Trigonometry
B
6.) Find sinA __________
26
24
m∠A _________
A
C
7.) Find tanA _________
m∠A __________
16
A
C
30
m∠A __________
15
12
A
C
m∠B __________