Summer Packet – 2015 - Students entering Algebra 2
This packet is intended for students who will be taking Algebra 2 in the 2015-2016 school year. This
packet includes material and practice which students should know before entering the Algebra 2 course
at Franklin High School. Although this packet is not mandatory homework over the summer, students
are strongly encouraged to review the necessary material to be as successful as possible in Algebra 2.
Students will be given an assessment on this material by the end of the first week of school to assess
their strengths and weaknesses of these skills and concepts. This will help teachers support students
earlier in the year to eliminate or minimize gaps in understanding.
You may find this list of online resources helpful:
http://www.ixl.com
http://www.purplemath.com
http://www.mathway.com
http://www.amathsdictionaryforkids.com
The following is a list of mathematical terms that students should know:
Absolute Value
Additive Inverse
Fraction
Integer
Model
Multiplicative inverses
Percent rate of change
Polynomial
Prime factorization
Prime number
Proportion
Quadratic equation
Quadratic expression
Quadratic function
Radical
Ratio
Rational numbers
Real numbers
Repeating decimal
Scientific notation
Significant figures
Simultaneous equations
Terminating decimal
Variable
Whole number
Intercept
The following is a list of rules, properties and theorems that students should know:
Associative Property of Addition
Commutative Property
Properties of Equality
Properties of Operations
Associative Property of Multiplication
Order of Operations
Properties of Inequality
Pythagorean Theorem
The following is a list of standards from Grade 8 Mathematics and Algebra 1 that students
should know, along with practice problems.
1. A-SEE.3c - Rewrite expressions involving rational exponents using properties of
exponents.
Multiply:
a. 5 x 2  x  2 x 4 
b.
 4 x 
2
 2x 
5
Simplify:
1
4
a. x  x
2
3
b. x10
1
x7
Simplify:
a.
x 4 y8
x3 y 2
b.
r 7 s 4t 2
r 2 s 5t
2. A – APR – 1 – Add, subtract, multiply polynomials.
Multiply and write in standard form:
a.
 x  7  x  3
a.
 2x  5 x 1
Multiply and write in standard form:
a.
 x  5
2
b.
 3x  4 
b.
1
2
1
x x x
5
3
2
2
Combine like terms:
a. 8 
1
4
1
x  x  x 5
4
12
2
3. A – REI - 3 – Solve equations and inequalities in one variable.
Solve:
a. 3x  6  9
b. 1  4 x  7
Solve:
a. 4(7 x  2)  3(5 x  1)
b. 2( x  3)  4( x  8)
Solve:
a.
1
3 3
x 
x4
2
5 20
b.
5
3 1
x  x2
6
4 3
4. A – REI - 6 – Solve systems of linear equations exactly.
Solve the system algebraically and graphically.
a.
2x  y  0
2 x  3 y  8
b.
5x  2 y  3
3 x  4 y  7
5. A – CED – 1,2 – Create equations in one variable. Graph equations on coordinate axes
with labels and scales.
Write an equation of the line that passes through the points.
a. (4, 2) and (1, 3)
b. (3, 5) and (1,  6)
Write an equation of the function shown in the graph.
a.
b.
Graph each equation on the coordinate plane.
a.
y
3
x2
4
b. 4 x  5 y  20
6. F – IF – 2 – Use function notation and evaluate functions for inputs in their domains.
a. Find f (3) if f  x   x3  x2  5x  1.
b. Find f (-1) if f  x    x4  5x2  x .
7. F – IF – 6 – Calculate and interpret the average rate of change of a function (presented
symbolically or as a table) over a specified interval.
a. Darrin set out on a trip. At 1 hour into his trip, he noted he had driven 40 miles. At 3
hours into his trip, he noted he had driven 168 miles.
i. State the rate of change of Darrin’s driven miles with respect to time. Use
appropriate units.
ii. Assuming he maintains this rate, at how many hours into his trip will he have
driven 500 miles?
b. At 5am, the temperature outside was 65°. At noontime, the temperature outside was
88°.
i. State the rate of change of temperature with respect to time. Use appropriate
units.
ii. Assuming the change in temperature maintains this rate, what time will the
temperature reach 100°?