2020 Summer Break Assignment for Students Entering Algebra II Name: _ - MCSM

2020 Summer Break Assignment for
     Students Entering Algebra II

Name: ____________________________
    Due Date: September 8th, 2020

Algebra II Supply List 2020-2021
Part of your summer assignment is also checking off the supply list below.
These supplies you will need through the entire course of the Algebra 2.

  Ø TI 84+family(TI84+ or TI84+CE) Graphing Calculator.

  Ø Sharpened Pencils/Erasers

  Ø Graph Paper

  Ø Ruler

  Ø 8.5 X 11 in Ringed Binder

  Ø Dividers

  Ø Loose leaf paper

  Ø One set of colored markers

A. REAL NUMBERS:
   A real number is any positive or negative number. This includes all integers and all rational and
   irrational numbers. Rational numbers may be expressed as a fraction (such as 7/8) and
   irrational numbers may be expressed by an infinite decimal representation (3.1415926535...).

Types of real numbers:

Practice:

B. ALGEBRAIC EXPRESSIONS:
A symbol or a combination of symbols used in algebra, containing one or more numbers, variables, and
arithmetic operations:

Simplifying Algebraic Expressions
I. Combining Like Terms                                 II. Distributive Property
Add/Subtract terms that are considered “like terms” –   Every term inside the parentheses is multiplied by the
have the same variable(s) with same exponent(s)         term outside of the parentheses.

Ex. 1                      Ex. 2

Practice: Simplify the following. Box your final answer

C. POLYNOMIAL EXPRESSIONS:
An expression of more than two algebraic terms, especially the sum/difference of several terms that contain
different powers of the same variable(s)

Multiplying Polynomials
The distributive property is used when you FOIL
want to multiply a single term by an
expression.

Practice: Multiply each expression

D. EQUATION:
A statement that asserts the equality of two expressions.

Solving Equations
Recall: To solve an equation, UNDO the order of operations. REMEMBER, addition is “undone” by subtraction
and vice versa. Multiplication is “undone” by division, and vice versa.

I. When solving equations with variables on both sides      II. In some equations, you will need to combine like
of the equal sign, be sure to get all terms with            terms and/or use the distributive property to simplify
variables on one side and all the terms without             each side of the equation, and then begin to solve it.
variables on the other side.

Practice: Solve each equation. Show all steps. Box your final answer

1. −(12 − 6x) = 6(x − 2)                                      2. 3m + 9m = 10(11+ 3m) − 9(6 + 2m)

   5 x−6                                                         2x     4x
     =                                                              +2=
3. 6   x +1    (HINT: CROSS MULTIPLY)                         4. 3      9

E.LITERAL EQUATION:

A literal equation is an equation where variables represent known values. Literal equations allow use to
represent things like distance, time, interest, and slope as variables in an equation.

Solving Literal Equations Solve for the indicated variable.

Sometimes you do not know values for the variable in a formula, so you cannot substitute. To solve a formula
or a literal equation for one of the variables in it, use properties of equality.

Practice: Solve each equation for the indicated variable. Show all steps. Box your final answer

                                                       1                              a−c
                                                  A=     h(b + b );b                        = m; x
1. ax + bx − 15 = 0; x                       2.        2 1 2 1                     3. x − a

4. A = P + Prt for t.                       5. 3x– 2a= 7a for x                   6. cx-d= a( x – y) for y

F. FUNCTION:
A special relationship where each input has a single output

Evaluating Functions
Evaluate the following functions.

• Substitute the value of x into the given function.
• Simplify the function.

Practice: Evaluate the function for the given value. Box your final answer.

1.   f (−4) =                                 2.   f (9a) =                   3. h(−7a) =

4. h(x + 1) =                                 5. g(0) =                       6. g(−6) =

G. RULES OF EXPONENTS:

Practice: Simplify each expression. Box your final answer:

H. RADICALS
To simplify a radical, we need to find the greatest perfect factor of the number under the radical sign (radicand)
and then take the square root of that number.

                                                  OR

Practice: Simplify the following radicals. Box your final answer.

I. FACTORING:
Factorization or factoring consists of writing a number or another mathematical expression as a product of
several factors, usually smaller or expressions.

Factoring. (GCF, Trinomial Factoring, Difference of Two Squares.)

Practice: Factor each expressions (Don’t forget if possible the GCF always goes first! )

J.GRAPHING LINEAR FUNCTIONS

The slope-intercept form is simply the way of writing the equation of a line so that the slope (steepness) and y-
intercept (where the line crosses the vertical y-axis) are immediately apparent. Often, this form is called
 y = mx + b form.

Graphing linear functions

Practice: Graph the following linear functions.

K.DOMAIN AND RANGE:
The domain of a function f(x) is the set of all x-values for which the function is defined, and the range of the
function is the set of all y-values that f takes. ... They may also have been called the input and output of the
function.)

How to find the Domain and the range graphically:

                                           DOMAIN: (-3,1]                    RANGE: [-4,0]

Practice: Find the domain and range of the given graphs: