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Algebra I Study Guide for End of Course Test

The EOC test consists of 50 multiple choice questions. Answer ALL questions. A formula sheet will be given, a ruler, and a graphing calculator. Please review and study this material.

Chapter 1: The Language of Algebra

REMEMBER:, . Anything to the 0 power, is always 1.

Anything to the 1st power is always itself.

Commutative Property:communicate your order at the Sonic, therefore commutative is to change the order of the operation.

a + b = b + a Example: 1 + 2 = 2 + 1 (you still get the same answer)

Associative Property: You associate with your group of friends. The order does not change, only where the sets of parenthesis go.

a + (b + c) = (a + b) + cExample: (1 + 2) + 3 = 1 + (2 + 3) (the same answer)

Independent Variable: graphed on the horizontal axis, the thing you are changing or manipulating. (mnemonic MIX-manipulate, in dependent,x)

Dependent Variable: graphed on the vertical axis, what is depended upon.

(mnemonic DRY- dependent, responding, y)

Relation: set of ordered pairs.

Domain: set of the first numbers of the ordered pairs, containing all values of the independent variable. (x, y) – all x values

Range: set of second numbers of the ordered pairs, contains all values of the dependent variable. (x, y) – all y values

Chapter 2: Real Numbers

Absolute Value:, of a number is its distance from 0 on the number line. Since distance is nonnegative, the absolute value of a number is ALWAYS positive.

Irrational numbers non terminating and non repeating decimals π and the √ (square root) of a non perfect square

All other numbers are rational

Chapter 3 Notes: Solving Linear Equations

Some verbal expressions that suggest the equals sign:

Isis equal tois as much as

Equalsis the same asis identical to

LESS THAN or MORE THAN - switch order

Ratio: is a comparison of two numbers by division. The ratio of x to y can be expressed:

x to yx:y

Proportion: an equation stating that two ratios are equal. Example

X-intercept: the x-coordinate of the point at which it crosses the x-axis (where y = 0).

Y-intercept: the y-coordinate of the point at which the graph crosses the y-axis

(where y = 0).

Function: is a special type of relation in which each element of the domain is paired with exactly one element of the range. X DOES NOT REPEAT

2 Ways to Determine if a Relation is a Function ( x cannot repeat!)

1. Mapping: shows how each member of the domain is paired with each member of the range. A map that shows how each x value is paired with the y values.

2. Vertical Line test: determines whether a relation is a function.

If the vertical line does not intersect a graph in more than one point, the graph represents a function.

  • If the vertical line intersects the graph at two or more points, the graph does NOT represent a function.
  • Examples of graphs that are NOT functions: circles, hyperbolas, ellipses, semi-circles.
  • Therefore, the vertical line can only hit the graph ONCE to be a function!

Functional notation: f(x) = 2x + 1, the symbol f(x) is read “f of x,” the f is the name of the function, it not a variable that is multiplied by x.

Chapter 5: Analyzing Linear Equations

Slope: (rate of change) of a line is the ratio of change in y-coordinate to the corresponding change in x-coordinates. The slope measures how steep a line is. Suppose a line passes through and, look at the change in the y and x coordinates:

,

4 types of slope:

1. Positive slope goes up from left to right, m = a positive number.

2. Negative slope goes down from left to right, m = negative number.

3. NO slope are HOrizOntal lines have, y = some number.

4. Undefined slopes are vertical lines, you cannot ski down a vertical slope, x = some number.

Form / Equation / Description
Slope- intercept / y = mx + b / m is the slope, and b is the y-intercept
Point-slope / / m is the slope and (, ) is a given point.
Standard / Ax + By = C / A and B are not both zero. Usually A is nonnegative and A, B, and C are integers whose greatest common factor is 1.

Parallel lines: have the same slope.

Perpendicular lines: slopes are opposite reciprocals of each other. Vertical and horizontal lines are perpendicular. .

Algebra I Notes Chapter 6: Solving Linear Inequalities

If each side of an inequality is DIVIDED or MULTIPLIED by a negative number then CHANGE THE SYMBOL.

Graphing Inequalities:

  1. Always solve for y. If you multiply or divide by a negative number, flip the symbol.
  2. If the symbols are <, > then use open circle.
  3. If the symbols are then use solid dot.
  4. < and mean shade LEFT.
  5. > and mean shade to the RIGHT.

Less than: Shade LEFTGreater than: Shade RIGHT

< , > Open circle/ dotted lineSOLID DOT/ solid line

FLIP THE SIGN: MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER

Chapter 7 Notes: Solving Systems of Equations

System of equations: two or more equations with the same variables. SOLUTIONS

Graphing: solve both systems for y and type into y =, make sure you see the graph on the screen (may need to change the window), 2nd trace, 5, enter, enter, enter.

Chapter 8: Polynomials

Product of Powers Property

Power of a Power Property

Power of a Product Property

Negative Exponent Property(no zeros in the denominator)

Zero Exponent Property, a  0 (any # to zero power is 1)

Quotient of Powers Property

Power of a Quotient Property(m is distributed to everything)

Degree: of a monomial is the sum of the exponents of its variables. Degree of a polynomial is the greatest degree of any term. Look at the degree of each term.

Distribute: used to multiply two binomials.

(x + 3)(x – 2)Product of first terms: (x)(x) + Product of Outer terms (-2)(x) + Product of

inner terms (3)(x) + product of last terms (3)(-2)

The opposite of squaring something is to take the square root of it.

Factoring- Multiply choices to find answer. first terms make first of trinomial- last terms make last term of trinomial. Multiply inner and outer to make middle number.

Know special rules.

Measure / Metric / Customary
Length / Kilometer (km) = 1000 meters (m) / 1 mile (mi) = 1760 yards (yd)
1 meter = 100 centimeters (cm) / 1 mile = 5280 feet (ft)
1 centimeter = 10 millimeters (mm) / 1 yard = 3 feet
1 foot = 12 inches (in)
1 yard = 36 inches
Volume and / 1 liter (L) = 1000 milliliters (L) / 1 gallon (gal) = 4 quarts (qts)
Capacity / 1 kiloliter (kL) = 1000 liters / 1 gallon = 128 fluid ounces (fl oz)
1 quart = 2 pints (pt)
1 pint = 2 cups (c)
1 cup = 8 fluid ounces
Weight and / 1 kilogram (kg) = 1000 grams (g) / 1 ton (T) = 2000 pounds (lb)
Mass / 1 gram = 1000 milligrams (mg) / 1 pound = 16 ounces (oz)

Metric Conversions: KHDDCM

Kill Her Dead (measure) Don’t Cry Milli

Calculator- Reset -- blue 2nd – MEM which is add button –press 7—enter—press 2

Reset

NEED to fix table format press 2nd – TBLSET (window)—arrow down to Indpnt arrow

over to ask press enter—must enter numbers on table

Window standard -10 to10

Solve a quadratic

Factor

Complete the square

Quadratic Formula

RADICALS - Simplify do not leave anything under the radical sign that can be simplified.

Not simplified with a radical in denominator

Matrices - Adding/Subtacting and scalar multiplication

Arithmetic and Geometric sequences - know formulas

Exponential growth and decay