terminology algebra 1a module 1 izydorczak 2014. module 1 lesson 1 linear function the graph of a...
TRANSCRIPT
Izydorczak 2014Module 1 Lesson 1
Linear FunctionThe graph of a line
Picture/Examples UsesConstant Change
Constant rate of change
Rise Slope Run
Izydorczak 2014
Piecewise- Linear FunctionGiven 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.)
http://www.youtube.com/watch?v=PRtrGwdWTB0
Module 1 Lesson 1
Izydorczak 2014
Graphing Piecewise Defined Functions
http://www.youtube.com/watch?v=-ACJ8QJ6nN8
Module 1 Lesson 1
Izydorczak 2014Module 1 Lesson 2
Quadratic FunctionThe graph of a parabola
Picture/Examples UsesAny situation requiring squaring
Anything to do with gravity
Izydorczak 2014Module 1 Lesson 2
Exponential FunctionThe curved graph that changes rapidly
Picture/Examples UsesBacteria growth
Carbon Decay
Izydorczak 2014Module 1 Lesson 5
Commutative Property of Addition
If a and b are real numbers, then a + b = b +aorder changes
Picture/Examples
5 + 7 = 7 +5
Commutative Change
Uses
Simplifyingexpressions
Izydorczak 2014Module 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 + ( 10 + 4)
Uses
Simplifyingexpressions
Izydorczak 2014Module 1 Lesson 5
Commutative Property of Multiplication
If a and b are real numbers, then a b = b aorder changes
Picture/Examples
3 6 = 6 3
-12 9 = 9 -12
Uses
Simplifyingexpressions
Izydorczak 2014Module 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
Simplifyingexpressions
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/Examples
12X
10x – 6yNo Equal Sign
Izydorczak 2014
Polynomial
Module 1 Lesson 6
A expression containing one or more monomials (or terms)
5x3
6x2 – 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
3n
11x2yNo addition or subtraction
Izydorczak 2014
Binomial
Module 1 Lesson 6
The sum or difference of two monomials
4n2 - 6nThere is adding or subtracting
Izydorczak 2014
Trinomial
Module 1 Lesson 6
The sum or difference of three monomials
15a8 – 10a3 - 1
Izydorczak 2014
Degree of Monomial
Module 1 Lesson 6
The sum of the exponents of the variables that appear in the monomial
12x1y2z1
Degree: 43x5
Degree: 512xy2z
Izydorczak 2014
Degree of Polynomial
Module 1 Lesson 6
The degree of the monomial term with the highest degree
2x2y2 + 2x2 – 6y3 + 7
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
7x5+ 3x3 + 10x - 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.
7x5+ 3x3 + 10x – 13Leading term : 7x5
Leading coefficient : 7
Izydorczak 2014
Constant Term
Module 1 Lesson 6
A term with no variables
8Or
y= ax2 + bx + cy= 7x2 + 3x + 12
CONSTANT
Izydorczak 2014Module 1 Lesson 7
Distributive PropertyIf a,b and c are real numbers, then
a(b+c) = ab+ ac multiply inPicture/Examples
-5(x-2) = -5x + -5 -2 = -5x + 10
4(x+3) 4x + 12
UsesTo 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 X2 = 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
UsesTo 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 UsesTo 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 UsesTo find solutions to problems involving
restrictions/conditions
S
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.