Welcome to Algebra 2:
Here are the guidelines to making sure you are ready for Algebra 2. This is your summer homework that
will make sure Algebra 2 runs smoothly and on-track. This is material you should already know and have
mastered before Algebra 2. You will complete the problems, outlines, definitions, etc given from each
section.
I.
Equations and Inequalities:
A. Properties of Real Numbers: (Define and give an example of each)
i.
Real Numbersiv.
Integersii.
Rational Numbersv.
Whole Numbersiii.
Irrational NumbersB. Properties of Addition and Multiplication: (Define and give an example of each)
i.
Commutativeiv.
Inverseii.
Associativev.
Distributiveiii.
IdentityC. Defining Subtraction and Division
i.
Definition of Subtraction- adding the opposite (a-b) = a + (-b)
ii.
Definition of division- multiplying by the reciprocal (or multiplication inverse);
a/b= a*1/b
D. Unit Analysis (Complete the following problems)
i.
You work 4 hours and earn $36. What is your earning rate? ___________
ii.
You travel 2.5 hours at 50 mph. How far did you go? _______________
iii.
You drive 45 miles per hour. What is your speed in feet per second? __________
E. Evaluating and Simplifying Algebraic Expressions
i.
Orders of Operations-PEMAS (Using Orders of Operations; solve the following)
a. 1 + 82 ∙ (12 − 6) = ___________
b. 3 − 6 ∙ 22 + (4 − 6) = ____________
c. 3 (4 − 6)2 = _______________
F. Solving Algebraic Expressions with variables
i.
Substitute a number in for a variable and simplify
ii.
Examples to solve:
a. −3𝑥 + 2𝑥 − 6; 𝑤ℎ𝑒𝑛 𝑥 = 2 ________________________________
b.
4𝑥−3
; 𝑤ℎ𝑒𝑛
2𝑥+8
2
𝑥=4
____________________________________
c. 9𝑥 + 9𝑥; 𝑤ℎ𝑒𝑛 𝑥 = −1 __________________________________
G. Combining like terms:
i.
An expression is simplified if it contains no grouping symbols and all like terms
are combined. Like terms are terms that have the same variable parts
ii.
Examples: (Combine like terms for the following)
a. 9𝑥 + 11𝑥 = _________________________
b. 6𝑝2 + 4𝑝 − 3𝑝2 + 2𝑝 − 5 = _______________________
c. 5𝑧 + 3𝑧 − 2𝑧 (2𝑧 + 4) =__________________________
H. Solving Linear Equations
i.
Define:
a. Equationb. Linear Equationii.
Solving equations with a variable on one-side: (Solve the following)
a. 2𝑥 − 6 = 12
x = ________________________
b. 4𝑥 − 3 = 11
x = ________________________
iii.
Solving equations with variables on both sides: (Solve the following)
a. 2𝑥 + 2 = 3𝑥 + 6
x= _________________________
b. 3 (2𝑥 + 3) = 5𝑥 + 12 x= _________________________
c. 7𝑥 + 3 = 7𝑥 − 3
x = _________________________
I. Formulas: (Write the following formulas and give an example of each)
Quantity
Formula
Example
Distance
d=rt
50 = 10r; r = 5
Area of Triangle
Area of a Rectangle
Area of a Trapezoid
Area of a Circle
Circumference of a Circle
i.
J.
Solve for a variable: (Simplify and solve the following)
a. Solve the formula D = RT for R. Then find the Rate with a Distance of 25 and
a Time of 5. _______________________________
b. Solve the formula: A= ½ BH for H. Then find the Height with an Area of 24
and a Base of 3. _____________________________
c. Solve the formula: A= πr² for r. Then find the radius of a circle with an area
of 120 inches². ______________________________
Solving Linear Inequalities
i.
Linear Inequalities- one variable can be written in one of the following
forms, where a and b are real numbers and a ≠ 0:
ax + b< 0
ax + b > 0
ii.
ax + b ≤ 0
ax + b≥ 0
Graph the following on a number line:
a. x < 3
b. x > 0
c. x ≤-2
iii.
Solving and Graphing linear inequalities: (Solve and graph the following)
a. 3𝑥 − 12 < 6
II.
III.
b. −2𝑥 ≤ −12
Linear Functions
A. Define:
i.
Domainiv.
Slopeii.
Rangev.
Slope-Interceptiii.
Functionvi.
Point-SlopeB. Graph: (On a sheet of graph paper: graph and label each graph).
1
iii.
𝑦 − 6 = 2 (𝑥 − 4)
i.
𝑦 = 2𝑥 + 4
iv.
2x +3y = 6
ii.
𝑦 = −2𝑥 − 6
Triangles:
A. Right Triangles
i.
Pythagorean Theorem (𝑎2 + 𝑏 2 = 𝑐 2 )
a. List the Pythagorean Triples: ________; _________; ____________
b. 30, 60, 90 Triangles: (Draw an example of this triangle with side lengths
labeled)
c. 45, 45, 90 Triangles: (Draw an example of this triangle with side lengths
labeled)
d. Trig Ratios:
e. Solve the following for the missing leg:
i.
ii.
IV.
iii.
Circles:
A. Define:
i.
Circlev.
ii.
Center of a circlevi.
iii.
Radiusvii.
iv.
DiameterB. Standard Equation of a circle with a center at the origin:
i.
𝑥2 + 𝑦2 = 𝑟2
ii.
𝐸𝑥: 𝑥 2 + 𝑦 2 = 4
a. Center (0,0); Radius = 2
iii.
Find the center and radius of the following:
a. 𝑥 2 + 𝑦 2 = 16
b. 𝑥 2 + 𝑦 2 = 14
C. Standard Equation of a circle with a center not at the origin:
i.
(𝑥 − 2)2 + (𝑦 − 3)2 = 16
a. Center (2, 3); Radius = 4
ii.
Find the center and radius of the following:
a. (𝑥 − 2)2 + (𝑦 − 6)2 = 9
i.
Center: ______________
ii.
Radius: ______________
2
b. (𝑥 − 4) + (𝑦 − 3)2 = 12
i.
Center: ______________
ii.
Radius: ______________
ChordSecantTangent line-