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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) + c Example: (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.
Chapter 3 Notes: Solving Linear Equations
Some verbal expressions that suggest the equals sign:
Is is equal to is as much as
Equals is the same as is identical to
Ratio: is a comparison of two numbers by division. The ratio of x to y can be expressed:
x to y x: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 x = 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.
2 Ways to Determine if a Relation is a Function
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 / DescriptionSlope- 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.
Linear Correlation: STAT, CALC, 4, ENTER, the r is the linear coefficient.
If r is close to -1 then you have a negative correlation.
If r is close to 1 you have a positive correlation.
If r is close to 0 there is NO correlation.
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 draw a dashed line.
3. If the symbols are then draw a solid line.
4. < and mean shade LEFT.
5. > and mean shade to the RIGHT.
Less than: Shade LEFT Greater than: Shade RIGHT
< , > DASHED LINE SOLID LINE
FLIP THE SIGN: MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER
AND: INTERSECTION OR: DOES NOT INTERSECT
Chapter 7 Notes: Solving Systems of Equations
System of equations: two or more equations with the same variables.
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 ¹ 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.
FOIL Method: used to multiply two binomials.
F- multiply the First terms;
O- Outer terms,
I- Inner terms, and
L- Last terms.
F L
(x + 3)(x – 2) Product of first terms: (x)(x) + Product of Outer terms (-2)(x) + Product of
I inner terms (3)(x) + product of last terms (3)(-2)
O
The opposite of squaring something is to take the square root of it.
Range: (Maximum data entry) – (Minimum data entry)
Measure / Metric / CustomaryLength / 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: K H D D C M
Kill Her Dead (measure) Don’t Cry Milli
Created by Meike McDonald, www.meikemcdonald.com