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1 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 0 1 REMEMBER: x 1 , a a . 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: x , 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: Is is equal to is as much as Equals is the same as is identical to LESS THAN or MORE THAN - switch order 2 Ratio: is a comparison of two numbers by division. The ratio of x to y can be expressed: x x to y x:y y 4 8 Proportion: an equation stating that two ratios are equal. Example 2 4 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, semicircles. 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 ( x1 , y1 ) and ( x2 , y2 ) , look at the change in the y and x coordinates: ( y y1 ) m 2 , x1 x2 ( x2 x1 ) 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. 3 Form Slope- intercept Equation y = mx + b Point-slope y y1 m( x x1 ) Standard Ax + By = C Description m is the slope, and b is the y-intercept m is the slope and ( x1 , y1 ) is a given point. A and B are not both zero. Usually A is nonnegative and A, B, and C are integers whose greatest common factor is 1. slope(m) makes line steeper or flatter b (y intercept) moves line up and down 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 LEFT <,> Open circle/ dotted line , , Greater than: Shade RIGHT SOLID 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. 4 Product of Powers Property Power of a Power Property Power of a Product Property Negative Exponent Property Zero Exponent Property Quotient of Powers Property Power of a Quotient Property Chapter 8: Polynomials a m a n a m n (a m ) n a mn (ab) m a mb m 1 (a ) m m , a 0 (no zeros in the denominator) a 0 (a) 1 , a 0 (any # to zero power is 1) am a mn , a 0 n a a am ( ) m m , b 0 (m is distributed to everything) b b 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. (a b) 2 a 2 2ab b2 (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 Length Metric Kilometer (km) = 1000 meters (m) 1 meter = 100 centimeters (cm) 1 centimeter = 10 millimeters (mm) Customary 1 mile (mi) = 1760 yards (yd) 1 mile = 5280 feet (ft) 1 yard = 3 feet 1 foot = 12 inches (in) 1 yard = 36 inches Volume and Capacity 1 liter (L) = 1000 milliliters (L) 1 kiloliter (kL) = 1000 liters 1 gallon (gal) = 4 quarts (qts) 1 gallon = 128 fluid ounces (fl oz) 1 quart = 2 pints (pt) 1 pint = 2 cups (c) 1 cup = 8 fluid ounces Weight and Mass 1 kilogram (kg) = 1000 grams (g) 1 gram = 1000 milligrams (mg) 1 ton (T) = 2000 pounds (lb) 1 pound = 16 ounces (oz) 5 Metric Conversions: K H D Kill Her Dead (measure) Don’t Cry Milli D C M 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 Quadratic- ax2 + bx +c bigger the a is the thinner the parabola smaller the a is the wider the parabola negative a flips it upside down c moves the parabola up or down zeros or roots where parabola crosses the x axis 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