Izydorczak 2014

Terminology

Algebra 1A

Module 1

Izydorczak 2014Module 1 Lesson 1

Linear FunctionThe graph of a line

Picture/Examples UsesConstant Change

Constant rate of change

Rise Slope Run

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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

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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

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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

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Polynomial

Module 1 Lesson 6

A expression containing one or more monomials (or terms)

5x3

6x2 – 5x + 1

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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

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Binomial

Module 1 Lesson 6

The sum or difference of two monomials

4n2 - 6nThere is adding or subtracting

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Trinomial

Module 1 Lesson 6

The sum or difference of three monomials

15a8 – 10a3 - 1

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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

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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

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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

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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

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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

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Algebraic Equation

Module 1 Lesson 9

A statement of equality between two expressions

Picture/Examples

5x – 7 = 2x + 9

Equal Sign

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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

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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

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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)

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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

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Numerical Symbol

A symbol that represents a specific number.

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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.

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Numerical Expression

an algebraic expression that contains onlynumerical symbols (no variable symbols) and which evaluates to a single number.)