# Pre-Calculus Interactive Notebook Activities and Guided Notes Bundle

^{th}- 12

^{th}, Homeschool

- Zip

### Description

*********** If you have purchased our Algebra 2 Bundle you already have a lot of the material contained in this packet.** We have a separate small bundle of the Pre-Calculus items that are not included in the Algebra 2 Bundle so that you can purchase the additional notes for Pre-Calc that are not included in the Algebra 2 bundle.********* You can find that bundle here: **Pre-Calculus Add On Bundle for Algebra 2**

This HUGE (over 500 pages) Pre-Calculus bundle contains a guided/scaffolded notes, interactive foldable activities, and quick checks for understanding (exit tickets) for 14 units of study, perfect for Pre-Calculus students. There are over 145 focused note activities that contain sample teacher answer keys. Example problems are solved on the sample teacher answer keys, but you can have your students use them over and over again with problems from your own curriculum. There are over 150 interactive notebook activities which include descriptions for use. We have not included specific examples for the interactive notebook activities. We like to give them to students for review so that they can show what they have learned and personalize their notes. This product also contains over 170 quick checks for understanding that can be used as exit tickets or mini-quizzes. This bundle is perfect to use with any textbook or e-book curriculum and great for engaging all types of learners.

This bundle also contains a description of how to use the materials included.

Bundle contains the following individual units:

**Linear Relations and Functions**

Includes:

Relations: Domain and Range

Multiple Representations of a Relation

What is a Function?:

What do functions look like?

Create a Mapping of a Relation

Is the equation a linear equation?

State the Domain of a Function

Evaluating Functions for a Given Value

Operations with Functions

Composition of Functions

Ways to Write Equations of Lines

Writing Linear Equations in Standard Form

Types of Slope

Finding Slope

Linear Functions

Using Intercepts to Graph Lines

Graph a Line in Slope-Intercept Form

Graph a Line Given a Point and Slope

Writing Linear Equations

Equations of Parallel, Coinciding, and Perpendicular Lines

Graphing Parallel Lines

Graphing Perpendicular Lines

Correlation

Some Special Piecewise Functions

Graphing Linear Inequalities

Plus 12 Interactive Notebook foldable activities and 14 Quick Checks for Understanding

**Solving Systems of Equations in Two and Three Variables**

Includes:

Characteristics of Systems of Equations

What is a System of Equations?

How do you solve a system of equations by graphing?

Classifying Systems of Equations by Graphing

How do you solve a system of equations using substitution?

How do you solve a system of equations using elimination?

Multiply, Then Use Elimination

Graphing Inequalities

What is a system of inequalities?

Solving a System of Inequalities by Graphing

Solving a System of Equations (Graphing, Substitution,

and Elimination)

Systems of Equations in Three Variables

14 Steps for Solving a System of Equations in Three Variables with Elimination

9 Steps for Solving a System of Equations in Three Variables with Substitution

Plus 10 Interactive Notebook foldable activities and 7 Quick Checks for Understanding.

Includes:

What is a Matrix?

What are Equal Matrices?

Adding and Subtracting Matrices

Steps for Multiplying Matrices

Multiplying Matrices

Name that Matrix

Matrices: Special Types

The Product of a Scalar and a Matrix

Modeling Motion with Matrices

What is a Vertex Matrix/Translation Matrix?

How do you Translate a Shape using Matrices?

Reflection Matrices

Rotation Matrices

How do you Complete a Reflection or Rotation of a Shape Using a Matrix?

How do you Dilate a Shape Using a Matrix?

Plus 11 Interactive Notebook foldable activities and 8 Quick Checks for Understanding.

**Determinants and Multiplicative Inverses of Matrices**

Includes:

What is a Determinant?

Formula for Finding the Determinant of a 2x2 Matrix

Steps for Finding the Determinant of a 3x3 Matrix

Finding the Determinant of a 3x3 Matrix

Steps for Finding the Determinant of a 3x3 Matrix Using Diagonals

Finding the Determinant of a 3x3 Matrix Using Diagonals

Cramer's Rule for Two Variables

Cramer's Rule for Three Variables

Multiplicative Inverse of a Matrix

Solving Systems of Equations Using Matrix Equations in 4 Steps

Plus 7 Interactive Notebook foldable activities and 7 Quick Checks for Understanding.

**Understanding Graphs – Math Journal Activities**

Includes:

Point Symmetry/Symmetry with Respect to the Origin/Example/Non-Example

Line Symmetry (x-axis, y-axis, y=x, and y=-x)

Parent Graph (Cut and Paste)

Changes to Parent Functions

Parent Function (Match)

Are the Ordered Pairs Solutions to the Inequality?

Steps for Graphing Non-Linear Inequalities

Solving Absolute Value Inequalities

Inverse Relations/Functions

Continuous vs. Discontinuous Functions

Discontinuous Functions (Infinite, Jump, Point, and Everywhere)

How do you test for continuity?

Using the Continuity Test

Continuity on an Interval

End Behavior of Polynomial Functions

When is a function monotonic on an interval?

Increasing, Decreasing, and Constant Functions

Examining the Intervals of a Given Function

Critical Points (Cut and Paste)

Extrema (Cut and Paste)

Defining Key Terms: Asymptotes

Find the Vertical and Horizontal Asymptotes for a Graph

Using Parent Graphs to Graph New Functions

Horizontal vs. Slant Asymptote

Find the Slant Asymptote and Vertical Asymptote for a Graph

Rational Functions with a Common Factor in the Numerator and Denominator

Plus 14 Interactive Notebook foldable activities and 18 Quick Checks for Understanding.

**Polynomial and Rational Functions**

Includes:

Review: Finding the Degree and Leading Coefficient of a Polynomial in One Variable

Evaluating a Polynomial Function for a Given Value

Evaluating a Polynomial Function for a Variable or Algebraic Expression

Graphs of Polynomial Functions (Handout)

Graphs of Polynomial Functions Reflection

End Behavior of Polynomial Functions

Graphs of Polynomial Functions

The Fundamental Theorem of Algebra

Write a polynomial equation with the given roots.

Find the roots of a function and graph.

Locate the zeros of a function by graphing.

Finding the relative maximum and minimum by graphing.

The Location Principle

Reviewing Polynomial Factoring Techniques

Factoring Polynomials

Solving Polynomial Functions Using Quadratic Techniques

What can the discriminant of the quadratic formula tell you about the roots of the equation?

Writing Polynomial Equations in Quadratic Form

Solve a Quadratic Equation by Completing the Square

Solve a Quadratic Equation Using the Quadratic Formula

The Remainder and Factor Theorems

Using Synthetic Division to Divide a Polynomial by a Binomial

Rational Root Theorem and Descartes’ Rule of Signs

Use Descartes’ Rule of Signs and the Rational Root Theorem to Determine the Zeros of a Function

The Rational Root Theorem and Integral Zero Theorem

Use Descartes’ Rule of Signs and the Rational Root Theorem to Determine the Zeros of a Function (Leading Coefficient Does Not Equal 1)

Solving Rational Equations

Decomposing a Rational Expression into Partial Fractions

Solving Radical Equations

Solving Radical Equations with More than One Radical

Graphing a Radical Equation

Plus 23 Interactive Notebook foldable activities and 14 Quick Checks for Understanding.

**Vectors and Parametric Equations**

Includes:

What is a Vector? (with Sample Teacher Key)

Vector Terms (Matching) (with Teacher Key)

Types of Vectors (Define/Draw) (with Sample Teacher Key)

Methods for Adding Vectors (with Sample Teacher Key)

What is a Scalar Quantity? (with Sample Teacher Key)

Representing a Vector as an Ordered Pair (with Sample Teacher Key)

Introduction to Unit Vectors (with Sample Teacher Key)

Vector Operations in Two Dimensions (with Sample Teacher Key)

Handout: Graphing Ordered Triples in 8 Steps

Vector and Magnitude for Two Ordered Triples (with Sample Teacher Key)

Vector Operations in Three Dimensions (with Sample Teacher Key)

Inner Product-Dot Product in Two Dimensions (with Sample Teacher Key)

Inner Product-Dot Product in Three Dimensions (with Sample Teacher Key)

Using the Determinant of a 3x3 Matrix to Find the Cross Product of Vectors in Space (with Sample Teacher Key)

Using Vectors to Represent Force (with Sample Teacher Key)

More Vector Terms (Match) (with Teacher Key)

Vector Equations and Parametric Equations (with Sample Teacher Key)

Parametric Equations in Linear Forms (with Sample Teacher Key)

Projectile/Trajectory/Range (with Sample Teacher Key)

Intro: Using Parametric Equations to Find the Path of a Projectile (with Sample Teacher Key)

Writing Parametric Equations to Represent the Path of a Projectile (with Sample Teacher Key)

Representing a Point in Space as a Matrix (with Sample Teacher Key)

What is a Vertex Matrix? (with Sample Teacher Key)

What is a Translation Matrix? (with Sample Teacher Key)

Handout: How do you Translate a Three-Dimensional Shape Using Matrices?

Handout: Reflection Matrices

Handout: How do you Complete the Reflection of a Three-Dimensional Shape Using Matrices?

Handout: Review-Steps for Multiplying Matrices

Plus 13 Interactive Notebook foldable activities and 18 Quick Checks for Understanding.

**Introduction to Graphing Polar Coordinates and Classical Curves**

Includes:

Label the Degree Measures on the Polar Coordinate System

Label the Radian Measures on the Polar Coordinate System

Polar Coordinate System Terms (Match)

Graph a Polar Coordinate in Radians

Graph a Polar Coordinate in Degrees

How do you Graph Polar Coordinates with a

Negative Angle Value?

Multiple Representations of a Polar Coordinate (Radians)

Multiple Representations of a Polar Coordinate (Degrees)

Graphing Basic Polar Equations

Distance Formula for the Polar Plane

How to use www.desmos.com to Graph Polar Equations

Graphs of Polar Equations

Graphs of Polar Equations (Classical Curves-Rose Curve)

Graphs of Polar Equations (Classical Curves-Lemniscate Curve)

Graphs of Polar Equations (Classical Curves-Limacon Curve)

Graphs of Polar Equations (Classical Curves-Cardiod Curve)

Graphs of Polar Equations (Classical Curves-Spiral of

Archimedes Curve)

Classical Curves Overview (Cut and Paste)

Plus 5 Interactive Notebook foldable activities and 5 Quick Checks for Understanding.

**Polar Coordinates and Complex Numbers**

Includes:

Review of Trigonometric Values

Forms of a Linear Equation (Standard/Rectangular, Normal Form, Polar Form)

Changing Polar Coordinates to Rectangular Coordinates

Changing Rectangular Coordinates to Polar Coordinates (x is positive)

Changing Rectangular Coordinates to Polar Coordinates (x is negative)

Example: Changing a Polar Equation to Rectangular Form

Example: Changing Rectangular Form to a Polar Equation

Polar Form of a Linear Equation

Example: Changing a Polar Equation in Linear Form to Rectangular Form

Operations with Complex Numbers

Powers of i

Graphing a Complex Number

Absolute Value of a Complex Number

Polar Form of a Complex Number

Changing a Complex Number to Polar Form in 4 Steps

Graphing a Complex Number in Polar Form

Changing a Number from Polar Form to Rectangular Form

Product of a Complex Number in Polar Form

Quotient of a Complex Number in Polar Form

De Moivre’s Theorem

Steps for Finding the Power of a Complex Number

Steps for Finding the Principle Root of a Complex Number

Plus 12 Interactive Notebook foldable activities and 17 Quick Checks for Understanding.

Includes:

What is the distance formula for two points?

What is the slope formula for two points?

What is the midpoint formula for two points?

How do you cut the cones to make the conic sections?

Steps for Determining Whether a Quadrilateral with Given Vertices is a Parallelogram (Worksheet)

Equations of Circles

Draw a picture of a circle that is tangent to the x-axis.

Draw a picture of a circle that is tangent to the y-axis.

Circles: Standard Form and Graphing

Use a system of equations to find the center and radius of a circle given three points on the circle.

Ellipse: Label the Diagram

Ellipse: Equations that you need to know.

Steps for writing the equation of an ellipse in standard form when given an equation in general form.

Hyperbola: Label the Diagram

Hyperbola: Equations that you need to know.

Steps for writing the equation of a hyperbola in standard form when given an equation in general form.

Parabola: Label the Diagram

Parabola: Equations that you need to know.

Steps for writing the equation of a parabola in standard form when given an equation in general form.

General Form of a Conic Section

Identify the conic section represented by each equation.

Steps for finding a rectangular equation given a parametric equation of a conic section.

Conic Section Review Sheet (2 pages)

Solving a System of Equations in Three Variables by Substitution (Review Sheets)

Plus 12 Interactive Notebook foldable activities and 12 Quick Checks for Understanding.

**Exponential and Logarithmic Functions**

Includes:

Review: Properties of Exponents

Simplifying Exponential Expressions

Evaluating Exponential Expressions

Radicals and Rational Exponents

Graph an Exponential Function

Graph an Exponential Inequality

Formulas: Population Growth/Decline and Value of Investments

What is e?

Formulas: Exponential Growth/Decay (e)/Continuously Compounded Interest (e)/Compound Interest

Logarithmic Functions

Converting between Logarithmic and Exponential Functions

Properties of Logarithms

Common Logarithms

Expanding Expressions with Common Logarithms

Change of Base Formula

Using Logarithms to Solve Exponential Equations

Natural Logarithms

Converting Logarithms to Natural Logarithms

The Inverse of Ln

Formula: Doubling Time of an Investment

Plus 13 Interactive Notebook foldable activities and 14 Quick Checks for Understanding.

Includes:

Parts of an Angle (Match)

Positive and Negative Angles

Standard Position

Quadrantal Angles

Measuring Angles in Degrees, Minutes, and Seconds

Expressing Decimal Degree Measures in Degrees, Minutes, and Seconds

Determine the Angle Measure of a Clockwise Rotation Around the Coordinate Plane

Determine the Angle Measure of a Counterclockwise Rotation Around the Coordinate Plane

Coterminal Angles and Reference Angles

Which Quadrant is your Angle in?

Using Quadrants to Figure out Reference Angles

Find the Measure of the Reference Angle

Review of the Pythagorean Theorem

Find the Six Trigonometric Ratios for Angle A

Trigonometric Ratios (Sine, Cosine, and Tangent)

Reciprocal Trigonometric Ratios (Cosecant, Secant, and Cotangent)

Special Right Triangle Relationships

Trigonometric Ratios for 30°, 45°, and 60°

Cofunctions

Unit Circle on a Coordinate Plane

The Six Trigonometric Functions on the Unit Circle

Using the Unit Circle to Find Values of Trigonometric Functions

Trigonometric Functions of an Angle in Standard Position

Find the Values of the Six Trigonometric Functions for an Angle in Standard Position Given a Point on its Terminal Side

Using Trigonometric Functions to Solve Problems Involving Right Triangles

Frequently Used Values from the Unit Circle

Inverses of Trigonometric Functions

Solve an Equation Using the Inverse of Trigonometric Functions

Evaluate an Expression with an Inverse Function Multiplied by a Function

Solve a Right Triangle Using Trigonometric Ratios and the Pythagorean Theorem

The Law of Sines

Formulas for Finding the Area of Triangles (Given Two Sides and an Angle Measure)

Formulas for Finding the Area of Triangles (Given Two Angles and a Side Measure)

The Law of Cosines

Hero’s Formula

Plus 13 Interactive Notebook foldable activities and 17 Quick Checks for Understanding.

**Graphing Trigonometric Functions**

Includes:

Radians

Radian Measures and Their Degree Equivalents

Length of an Arc

Area of a Circular Sector

Angular and Linear Velocity

Properties of the Graph y = sin x

Properties of the Graph y = cos x

Finding the Amplitude and Period of Sine and Cosine Functions

Phase Shifts

Midline

Vertical Shifts

Graphing Sine and Cosine Functions

Properties of the Graph of y = tan x

Properties of the Graph y = cot x

Properties of the Graph y = csc x

Properties of the Graph y = sec x

Period of Trigonometric Functions

Plus 7 Interactive Notebook foldable activities and 16 Quick Checks for Understanding.

**Basic Trigonometric Identities and Equations**

Includes:

Unit Circle Review

Review: Frequently Used Values from the Unit Circle

Use the Frequently Used Values from the Unit Circle Table to Find the Value of Each Expression

Basic Trigonometric Identities

Match the Basic Trigonometric Identity Pairs

Using Reciprocal Identities to Find the Value of Trigonometric Functions

Finding the Value of a Trigonometric Function

Sometimes You Need to Use More Than One Identity

Symmetry Identities

Using Substitution with the Symmetry Identities

Expressing Values as Trigonometric Functions of an Angle in Quadrant I

Opposite-Angle Identities

Using Opposite Angle Identities

Beginning: Use Trigonometric Identities to Simplify Trigonometric Expressions

Advanced: Use Trigonometric Identities to Simplify Trigonometric Expressions

Verifying Trigonometric Identities

Simplifying Trigonometric Equations

Plus 7 Interactive Notebook Foldable Activities and 7 Quick Checks for Understanding.

Please see individual units for full-length previews.

These units can be used for introducing topics or to reflect/review what you have covered in class discussion. The problems listed in this activity packet build nicely on each other if introduced in the order that they appear. Our students enjoy filling them out and organizing them in their math journals so that they can refer back to them throughout the year. These activities are a great way to promote writing in math.

**Related Products:**

****Full-year Curriculum Packs****

**Algebra 1 Curriculum Pack BUNDLE**

**Geometry Curriculum Pack BUNDLE**

**Algebra 2 Curriculum Pack BUNDLE**

**Scaffolded Notes/Interactive Notebook Bundles**

**Pre-Calculus Add on for Algebra 2 INB Bundle**

**High School Math Interactive Notebook Bundle (Algebra 1, Geometry, Algebra 2)**

**Student Practice Pages Bundles**

**Algebra 1 Student Practice Pages Bundle**

**Geometry Student Practice Pages Bundle**

**Algebra 2 Student Practice Pages Bundle**

**High School Math Student Practice Pages Bundle (Algebra 1, Geometry, Algebra 2)**

**Assessment Bundles**

**High School Math Assessment Bundle (Algebra 1, Geometry, Algebra 2)**

**If you like what you see, please click on the "Follow Me" star to learn about new products, sales, and more!