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What are absolute value functions?

Demonstrate an understanding of the absolute value of real numbers

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

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Solving absolute value equations

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

Solve problems involving operations on radicals and radical expressions with numerical and variable radicands

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Combining Like Radicals

Adding and Subtracting Radicals

Multiplying radicals

Multiplying Radicals

Operations with radicals

Operations with Radicals

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Solve problems involving radical equations limited to square roots

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Determine equivalent forms of rational expressions with numerators and denominators that are monomials, binomials or trinomials

Partial fraction decomposition

Simplifying rational expressions and restrictions

Simplifying complex fractions

Perform operations on rational expressions with numerators and denominators that are monomials, binomials or trinomials

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Solve problems involving rational equations with numerators and denominators that are monomials, binomials or trinomials

Solving rational equations

Applications of rational equations

Factor polynomial expressions of various forms

Factoring difference of cubes

Factoring sum of cubes

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Analyze geometric sequences and series to solve problems

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

Graph and analyze reciprocal functions limited to the reciprocal of linear and quadratic functions

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Analyze quadratic functions of the form y = a(x - p)² + q and determine characteristics of the corresponding graph

Characteristics of quadratic functions

Transformations of quadratic functions

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Completing the Square

Analyze quadratic functions of the form y = ax² + bx + c to identify characteristics of the corresponding graph

Introduction to quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Solve problems involving quadratic equations

Solving polynomial equations by iteration

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Solve algebraically and graphically problems involving systems of linear-quadratic and quadratic-quadratic equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

Solve problems involving linear and quadratic inequalities in two variables

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Solve problems involving quadratic inequalities in one variable

Solving quadratic inequalities

Analyze arithmetic sequences and series to solve problems

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Demonstrate an understanding of angles in standard position from 0° to 360°

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Solve problems using the three primary trigonometric ratios for angles from 0° to 360° in standard position

Unit circle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Solve problems using the cosine law and sine law, including the ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Parent Assignments

Challenge Zone

Foundation Review

Grade 11 Pre-Calculus Mathematics (30S)

Develop algebraic reasoning and number sense

Develop algebraic and graphical reasoning through the study of relations

Develop trigonometric reasoning

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Evaluating absolute value expressions with arithmetic and cube roots

Piecewise form of absolute value with a quadratic expression

Evaluating absolute value of positive, negative, and zero values

Expressing |5 - 4x| as a piecewise function

<a href='[[glossary.html|{"keyword":"Absolute Value","term":"Absolute Value"}]]'>Absolute value</a> is basically the distance between "number" and "zero" on a number line. We will look into this concept in this lesson. We will also learn how to express absolute value functions as piecewise functions.

Absolute value functions

What You'll Learn

Define absolute value as the distance between a number and zero on a number line

Evaluate absolute value expressions with positive, negative, and zero values

Express absolute value functions as piecewise functions using domain conditions

Determine breaking points by solving when the inside expression equals zero

Apply sign rules to convert negative outputs to positive using absolute value

What You'll Practice

Evaluating absolute values of integers, negatives, and nested expressions

Converting absolute value of linear expressions into two-piece piecewise functions

Converting absolute value of quadratic expressions into three-piece piecewise functions

Using test values to determine signs across different domain regions

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

4 Video lessons

Practice exercises

Skills

Absolute Value

Piecewise Functions

Number Line

Domain Analysis

Quadratic Expressions

Sign Rules

Function Notation