Terminology Algebra 1A Module 1 Izydorczak 2014

Module 1 Lesson 1 Linear Function The graph of a line Picture/Examples Uses Constant Change Constant rate of change Rise Slope Run Izydorczak 2014

Piecewise- Linear Function Given a finite number of non-overlapping intervals on the real number line, a (real) piecewise-linear function is function from the union of the intervals to the set of real numbers such that the function is defined by (possibly different) linear functions on each interval.) Module 1 Lesson 1 Izydorczak 2014

Graphing Piecewise Defined Functions Module 1 Lesson 1 Izydorczak 2014

Module 1 Lesson 2 Quadratic Function The graph of a parabola Picture/Examples Uses Any situation requiring squaring Anything to do with gravity Izydorczak 2014

Module 1 Lesson 2 Exponential Function The curved graph that changes rapidly Picture/Examples Uses Bacteria growth Carbon Decay Izydorczak 2014

Module 1 Lesson 5 Commutative Property of Addition If a and b are real numbers, then a + b = b +a order changes Picture/Examples = 7 +5 ommutative Commutative Change Change Uses Simplifying expressions Izydorczak 2014

Module 1 Lesson 5 Associative Property of Addition If a,b and c are real numbers, then (a + b) + c = a + (b + c) order DOES NOT changes Picture/Examples (1 + 2) + 4 = 1 + (2 + 4) (3 + 10) + 4 = 3 + ( ) Uses Simplifying expressions Izydorczak 2014

Module 1 Lesson 5 Commutative Property of Multiplication If a and b are real numbers, then a b = b a order changes Picture/Examples 3 6 = = Uses Simplifying expressions Izydorczak 2014

Module 1 Lesson 5 Associative Property of Multiplication If a,b and c are real numbers, then (ab)c = a(bc) Parentheses change place, ORDER DOES NOT Picture/Examples (2 3)8 = 2(3 8) Uses Simplifying expressions Izydorczak 2014

Algebraic Expression Module 1 Lesson 5 A number, a variable, or an arrangement of numbers and variables created by using the four operations (,,, ) No equal sign Picture/Examples12X 10x – 6y No Equal Sign Izydorczak 2014

Polynomial Module 1 Lesson 6 A expression containing one or more monomials (or terms) 5x 3 6x 2 – 5x + 1 Izydorczak 2014

Monomial Module 1 Lesson 6 A number or a variable or a product of number(s) and variable(s) (also called a term) Monomials do not contain addition or subtraction 3 n 11x 2 y No addition or subtraction Izydorczak 2014

Binomial Module 1 Lesson 6 The sum or difference of two monomials 4n 2 - 6n There is adding or subtracting Izydorczak 2014

Trinomial Module 1 Lesson 6 The sum or difference of three monomials 15a 8 – 10a Izydorczak 2014

Degree of Monomial Module 1 Lesson 6 The sum of the exponents of the variables that appear in the monomial 12x 1 y 2 z 1 Degree: 4 3x 5 Degree: 5 12xy 2 z Izydorczak 2014

Degree of Polynomial Module 1 Lesson 6 The degree of the monomial term with the highest degree 2x 2 y 2 + 2x 2 – 6y deg = 4 deg = 2 deg = 3 deg = 0 degree of polynomial: 4 Izydorczak 2014

Standard Form Module 1 Lesson 6 The terms of a polynomial are written in order from highest to lowest degree Alphabetical order 7x 5 + 3x x - 13 Izydorczak 2014

Leading Term & Leading Coefficient Module 1 Lesson 6 The leading term is the term of highest degree (the first term, if in standard form). The leading coefficient is the number in the leading term. 7x 5 + 3x x – 13 Leading term : 7x 5 Leading coefficient : 7 Izydorczak 2014

Constant Term Module 1 Lesson 6 A term with no variables 8 Or y= ax 2 + bx + c y= 7x 2 + 3x + 12 Izydorczak 2014

Module 1 Lesson 7 Distributive Property multiply in If a,b and c are real numbers, then a(b+c) = ab+ ac multiply in Picture/Examples -5(x-2) = -5x = -5x + 10 = -5x + 104(x+3) 4x x + 12 Uses To simplifying expressions To get rid of parentheses Izydorczak 2014

Algebraic Equation Module 1 Lesson 9 A statement of equality between two expressions Picture/Examples 5x – 7 = 2x + 9 Equal Sign Izydorczak 2014

Solution Set Module 1 Lesson 9 The set of all values that make an equation true; often written in curly braces The solution set of X 2 = 49 is 7, -7 Izydorczak 2014

Inequality Module 1 Lesson 9 A statement that one expression is >, <, ≤, ≥ or ≠ to another expression. Picture/Examples 9X- 14 > 28 Uses To make comparisons and solve problems Izydorczak 2014

System of Equations Module 1 Lesson 22 Two or more equations solved simultaneously (at the same time), resulting in the point of intersection of the graphs; can be solved graphically or algebraically Picture/Examples Uses To find intersection points and solve problems. (x,y) Izydorczak 2014

System of Inequalities Module 1 Lesson 22 Two or more inequalities solved simultaneously (at the same time), resulting in a region of points that are solutions (overlap of shaded regions) Picture/Examples Uses To find solutions to problems involving restrictions/conditions Izydorczak 2014

Numerical Symbol A symbol that represents a specific number. Izydorczak 2014

Variable Symbol A symbol that is a placeholder for a number. It is possible that a question may restrict the type of number that a placeholder might permit, maybe integers only or a positive real number, for instance. Izydorczak 2014

Numerical Expression an algebraic expression that contains only numerical symbols (no variable symbols) and which evaluates to a single number.) Izydorczak 2014