UMHS Algebra II - Summer Review
Summer Math assignments for current and incoming students
Algebra 2
All Algebra 2 students are required to have a
TI 84-Plus Graphing Calculator for this course.
The calculator will be used throughout this course, and in future math courses.
Please keep your eyes open for sales and purchase one before school begins.
Show All Work
Solving Equations
Solve each equation. SHOW ALL WORK.
Writing the Equation of a Line
- To find the equation of a line:
- Find the slope.
- Substitute one point and the slope into the equation of the line and solve for b.
- Rewrite the equation, only substituting in the slope and the y-intercept.
If you are doubling up and taking Geometry and Algebra 2 at the same time, you can skip the next three problems.
Find the equation of each line described/shown. SHOW ALL WORK.
6. Write the equation of the line with a slope of 3/4, passing through the point (8, 5).
EQUATION: ________________
7. Write the equation of the line passing through the points (3, −1) and (−2, −6).
EQUATION: ________________
Solving Systems of Linear Equations
A system of equations is two or more equations with two or more variables. There are four methods for solving systems of equations:
1) Graphing
2) Equal Values
3) Substitution
4) Elimination
There are many YouTube videos on all of these methods. If you need a refresher on one or more of these methods, please find a video or two to watch.
If you are doubling up and taking Geometry and Algebra 2 at the same time, you can skip the next three problems.
Solve each system of equations below using any method you choose. SHOW ALL WORK.
Multiplying Polynomials
In Algebra 1, you learned two methods for multiplying polynomials:
1) Distributive Property (used to multiply ONE term times a polynomial)
2) Generic Rectangle (used to multiply a polynomial times a polynomial)
If you are doubling up and taking Geometry and Algebra 2 at the same time, you can skip the next three problems.
Multiply by using the distributive property or by using a generic rectangle. SHOW ALL WORK.
Factoring Polynomials
In Algebra 1, you learned two methods for factoring.
1) GCF ➡️ Take out the greatest common factor
2) Diamond and Rectangle ➡️ Expression must look like the picture shown .
Find the outside of the generic rectangle.
1. Example: Factor
Step 1: Take out the GCF.
Factor using the diamond and rectangle.
Step 1: Put ax squared and c terms n the opposite corners of the generic rectangle.
Step 2: Multiply as squared and c. Put them in top of the diamond. Put bx in the bottom of the diamond. Find the two missing terms for the diamond.
Step 3: Put the terms from the diamond into the generic rectangle. Find the outside numbers.
Step 4: Write the factored form. 3(x+2) (x+1)
If you are doubling up and taking Geometry and Algebra 2 at the same time, you can skip the next three problems.
Factor completely. SHOW ALL WORK.
Solving Quadratic Equations
Solving Quadratics
STEP 1: Make the quadratic equation = 0.
STEP 2: Factor the polynomial.
STEP 3: Use the Zero Product Property to solve for x. (Set each factor = 0)
(Factor using a generic rectangle. Work not shown.)
Solve the following quadratic equations. SHOW ALL WORK.
Radicals
Simplifying Radicals ➡️ Simplifying a radical DOES NOT mean to turn it into a decimal.
METHOD #1: FACTOR TREES
STEP 1: Create a factor tree for the number inside the radical. (Cross out any numbers that you break down).
STEP 2: Circle numbers in PAIRS.
STEP 3: The numbers that you circle go in front of the radical (1 number per circle). The numbers that
aren’t crossed out or circled, stay inside the radical.
STEP 4: Multiply the outside numbers. Multiply the inside numbers.
METHOD #2: PERFECT SQUARES
STEP 1: Rewrite the radical as the product of a perfect square and another number. STEP 2: Find the square root of the perfect square.
If you are doubling up and taking Geometry and Algebra 2 at the same time, you can skip the next three problems.
Laws of Exponents
Use the laws of exponents to simplify each expression. Your final answer should NOT have negative exponents in it. SHOW ALL WORK.
The Pythagorean Theorem
The Pythagorean Theorem can used to solve for the missing side lengths in any right triangle. (hypotenuse = c)
Use the Pythagorean Theorem to find the missing side of each right triangle. Write your answers in simplified radical form. SHOW ALL WORK.
Absolute Value Equations
Solving Absolute Value Equations Absolute value equations can have 0, 1, or 2 solutions.
STEP 1: “Isolate” the absolute value on one side of the equation.
STEP 2: If the absolute value equals a positive number, rewrite the absolute value equation as two
equations.
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Inside = positive #
-
Inside = negative #
-
NEVER change the inside expression
STEP 2a: If the absolute value equals zero, set the inside equal to zero.
STEP 2a: If the absolute value equals an negative number, there is no solution. STEP 3: Solve the equation(s).
Solve each equation below. SHOW ALL WORK.
Domain and Range
DOMAIN: the input or “x” values
RANGE: the output or “y” values
Identify the domain and range of each relation.