Less than $5 11th Grade Algebra PowerPoint Presentations (by price, high to low)

Are you teaching your High School students about Functions Limit - continuity- derivative? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 20 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ Limit

✦ Continuity:

• ✦ Continuity at a point
• ✦ Continuous Function on an Interval

✦ Composite of two functions

✦ Derivative

✦ Asymptotes

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

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Other Resources:

⤞ Integration | Definite & Indefinite integral| High School Math PowerPoint Lesson

⤞ Trigonometric Formulas | High School Math PowerPoint Lesson Slides

⤞ Trigonometry Trigonometric Equations | High School Math PowerPoint Lesson Slides

⤞ Sign of The 2nd Degree Polynomials | High School Math PowerPoint Lesson Slides

⤞ Orthogonality In Space | High School Math PowerPoint Lesson Slides

Are you teaching your High School students about Equations of Parallel and Perpendicular Lines? This resource is great for you! Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 43 total slides

✦ Title slide

✦ 27 slides for notes and examples.

✦ 15 slides for application.

✦ All steps are animated to allow the teacher to explain them gradually.

At the end of the lesson, students will be able to

✦ Understand a form of the equation of a line

✦ Recognize the properties of parallel lines

✦ Derive equations of parallel lines

✦ Understand the properties of perpendicular lines

✦ Derive equations of perpendicular lines

✦ Solve problems involving parallel and perpendicular lines

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

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Other Resources:

⤞ Angles in Circles using Tangents | PowerPoint Presentation Lesson | High School

⤞ Polynomials of One Variable | PowerPoint Presentation Math Lesson | High School

⤞ Square Roots part 2 | PowerPoint Presentation Math Lesson High School Radical

⤞ Rational & Irrational Numbers | PowerPoint Presentation Math Lesson High School

⤞ Fractional Expressions | PowerPoint Presentation Lesson High School Math Algebra

Are you teaching your High School students about Square Roots? This resource is great for you! Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 24 total slides

✦ 18 slides for notes and examples.

✦ 5 slides for application.

✦ All steps are animated to allow the teacher to explain them gradually.

At the end of the lesson, students will be able to

✦ Define and explain what a square root is.

✦ Recognize the square root symbol (√) and understand its significance.

✦ Explain some square root properties.

✦ Understand Rules of Calculations.

✦ Expand & Reduce an Expression.

✦ Make comparison of Two Radicals.

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

To check out Square Roots (part 1) click here

-Follow us on TeachShare to be informed with new products and updates.

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Other Resources:

⤞ Powers and Radicals | High School Math PowerPoint Lesson Slides

⤞ Polynomials | High School Math PowerPoint Lesson Slides

⤞ First Degree of Equations and Inequalities | High School Math PowerPoint Lesson

⤞ Rational & Irrational Numbers | PowerPoint Presentation Math Lesson High School

⤞ Fractional Expressions | PowerPoint Presentation Lesson High School Math Algebra

This MID-YEAR Back to School Algebra 2 Review Activity Packet is the perfect way to review the first half of the year with your students in a fun & engaging way! This pack includes 10 different topics and 10 activity worksheets that can be used as classwork, homework, warm ups or exit slips. It can also be used to promote groupwork!

There is space on each activity to show work, directions and can be completely independent.

Use these activities all at once or save them to have an activity on 10 different days!

Ways to use these worksheets:

• stations
• review booklet
• 10 days of homework
• sub plans
• practice worksheets

This activity pack includea:

1)Remainder Theorem Matching Activity

2)Multiplying Polynomials True or False

3)Factoring Completely Maze

4)End Behavior Coloring Activity

5)Solving Polynomial Equations Escape Room

6)Complex Numbers Matching Activity

7)Solving Radical Equations Matching Activity

8)Quadratic Formula Word Unscramble

9)Rational Equations Coloring Activity

10)3-Variable System of Equations Coloring Activity/Matching

11)Answer Keys for all activities

12)The powerpoint for you to project and write on

If you like this review and are looking for other review activities for Algebra 1 and Algebra 2, check out the following:

Algebra 2 Review Pixel Art

Algebra 1 Review Activity Pack

Algebra 1 Escape Room (Digital and Paper)

You might also like:

More Algebra 2 Resources

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Are you teaching your High School students about Equation of a circle? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 15 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ Definition of a circle.

✦ Equation of a circle determined by its center and radius.

✦ Equation of a circle determined by the ends of its diameter.

✦ Determine the center and radius of a circle from its equation.

✦ Position of a line and a circle.

✦ Intersection between a circle and a line.

✦ Position of a point with respect to a circle.

✦ Equation of the tangent to a circle.

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

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Other Resources:

⤞ Order on R-Framing and approximation | High School Math PowerPoint Lesson Slides

⤞ Generalities of Functions (part 1) | High School Math PowerPoint Lesson Slides

⤞ Coordinate System | High School Math PowerPoint Lesson Slides

⤞ Parallel Lines and Planes | High School Math PowerPoint Lesson Slides

⤞ Scalar Product of Vectors | High School Math PowerPoint Lesson Slides

Are you teaching your High School students about Polynomials? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 20 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ polynomial Definition, Null polynomial, Equal Polynomials

✦ Numerical value of a polynomial

✦ Identification method, Euclidean division method

✦ Remainder of the division of p(x) by (x-∝)

✦ Factorizing a polynomial using its constant term in the case where it is an integer

✦ Factoring and division by ( − )

✦ Factorization of the polynomial of the third degree knowing a root

✦ Simplification of rational fractions

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵

Other Resources:

⤞ First Degree of Equations and Inequalities | High School Math PowerPoint Lesson

⤞ Linear System | High School Math PowerPoint Lesson Slides

⤞ Equation of Straight Lines | High School Math PowerPoint Lesson Slides

⤞ Permutations, Combinations, and Counting Principle | High School Math PowerPoint

⤞ Absolute value and intervals | High School Math PowerPoint Lesson Slides

Are you teaching your High School students about Sets and Cartesian product? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 21 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ Definition of Sets and Elements

✦ Representation of a set (In extension, By comprehension, Venn Diagram )

✦ Types of sets (Empty set , A singleton, A pair )

✦ Subset of a set and its notation

✦ Complement of a set

✦ Intersection and union of two Sets

✦ Sets of numbers (Set of Natural Numbers, Set of integers, The rational numbers, The real numbers)

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵

Other Resources:

⤞ Complex Numbers | High School Math PowerPoint Lesson Slides

⤞ Equation of a circle tangent | High School Math PowerPoint Lesson Slides

⤞ Order on R-Framing and approximation | High School Math PowerPoint Lesson Slides

⤞ Generalities of Functions (part 1) | High School Math PowerPoint Lesson Slides

⤞ Coordinate System | High School Math PowerPoint Lesson Slides

Are you teaching your High School students about Numerical Sequence? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 19 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ General Definition of a numerical sequence

✦ Determination of a sequence

✦ Increasing and decreasing sequences

✦ Methods to study the sense of variation of a sequence

✦ Principle of reasoning by recurrence

✦ Particular Sequences

✦ Arithmetic Sequence

✦ Sum of the first n terms

✦ Geometric Sequence

✦ Calculation of the general term

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵

Other Resources:

⤞ Right Triangle Trigonometry | High School Math PowerPoint Lesson Slides

⤞ Lines and Planes In Space | High School Math PowerPoint Lesson Slides

⤞ Generalities of Functions (part 2) | High School Math PowerPoint Lesson Slides

⤞ Primitives Anti-Derivative | High School Math PowerPoint Lesson Slides

⤞ Derivative of Functions | High School Math PowerPoint Lesson Slides

Are you teaching your High School students about Powers and Radicals? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 21 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ Powers Definition

✦ Product of powers

✦ Division of powers

✦ Power of power

✦ Square Root Definition

✦ Solution of equations

✦ The n^th root of a real number

✦ Changing to rational exponent

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵

Other Resources:

⤞ Polynomials | High School Math PowerPoint Lesson Slides

⤞ First Degree of Equations and Inequalities | High School Math PowerPoint Lesson

⤞ Linear System | High School Math PowerPoint Lesson Slides

⤞ Equation of Straight Lines | High School Math PowerPoint Lesson Slides

⤞ Permutations, Combinations, and Counting Principle | High School Math PowerPoint

Using the Quadratic Formula to solve quadratic equations no prep lesson

• PowerPoint that begins with proving the quadratic formula by completing the square. Also includes worked examples for teaching how to use the formula
• Two worksheets with real-life applications as well as standard quadratic equations. There are enough questions to spread over two lessons or use one as a homework task.
• Worked solutions are included for both

You may also like

Quadratic Formula 1 Scavenger Hunt

Quadratic Formula 2 Scavenger Hunt

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

Are you teaching your High School students about Logarithm Functions? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 9 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ Definition

✦ Domain of definition

✦ Limits of ln⁡x

✦ Derivatives

✦ Graph of f(x)=ln⁡x

✦ Properties

✦ Base of logarithm

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

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Other Resources:

⤞ Functions Limit continuity derivative| High School Math PowerPoint Lesson Slides

⤞ Integration | Definite & Indefinite integral| High School Math PowerPoint Lesson

⤞ Trigonometric Formulas | High School Math PowerPoint Lesson Slides

⤞ Trigonometry Trigonometric Equations | High School Math PowerPoint Lesson Slides

⤞ Sign of The 2nd Degree Polynomials | High School Math PowerPoint Lesson Slides

Are you teaching your High School students about Equation of straight lines? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 18 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ Director vector of a straight line

✦ Parametric representation of a straight line

✦ Cartesian Equation of a straight line

✦ Relative Position between two Lines (Intersection Case)

✦ Parallelism of two Straight lines

✦ Condition of the orthogonality of two lines

✦ Straight line passing through a given point A and of given normal vector N ⃗

✦ Distance from a point to a Straight line

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵

Other Resources:

⤞ Permutations, Combinations, and Counting Principle | High School Math PowerPoint

⤞ Absolute value and intervals | High School Math PowerPoint Lesson Slides

⤞ Addition of Vectors | High School Math PowerPoint Lesson Slides

⤞ Thales' Theorem | PowerPoint Presentation Lesson slides High School Geometry

⤞ Linear Functions and Proportionality| PowerPoint Presentation Lesson High School

Are you teaching your High School students about Rational and Irrational Functions? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 22 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ Homographic Function

✦ Derivative and sense of variation

✦ Graph

✦ Oblique Asymptote

✦ Table of Variation

✦ Representative curve

✦ Center of Symmetry

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵

Other Resources:

⤞ Polynomial Functions | High School Math PowerPoint Lesson Slides

⤞ Scalar Product in Space | High School Math PowerPoint Lesson Slides | Cosine Law

⤞ Numerical Sequence | High School Math PowerPoint Lesson Slides

⤞ Generalities of Functions (part 2) | High School Math PowerPoint Lesson Slides

⤞ Primitives Anti-Derivative | High School Math PowerPoint Lesson Slides

Are you teaching your High School students about Scalar Product in Space? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 16 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ Definition of the scalar product

✦ Sign of the scalar product

✦ Calculating the scalar product

✦ Scalar product properties

✦ Cosine Law

✦ Analytical Form of The Scalar Product

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵

Other Resources:

⤞ Right Triangle Trigonometry | High School Math PowerPoint Lesson Slides

⤞ Numerical Sequence | High School Math PowerPoint Lesson Slides

⤞ Generalities of Functions (part 2) | High School Math PowerPoint Lesson Slides

⤞ Primitives Anti-Derivative | High School Math PowerPoint Lesson Slides

⤞ Derivative of Functions | High School Math PowerPoint Lesson Slides

Are you teaching your High School students about Functions limits and continuity? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 20 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ Boundary term

✦ Limits at +∞ and -∞ of a function

✦ Limit of a function at one point x=a

✦ Asymptotes

✦ Indeterminate Forms

✦ Continuity of a function at one point x=a

✦ Theorem

✦ Sandwich Rule

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵

Other Resources:

⤞ Equations & polynomials of the 2nd degree | High School Math PowerPoint Lesson

⤞ Rational and Irrational Functions | High School Math PowerPoint Lesson Slides

⤞ Polynomial Functions | High School Math PowerPoint Lesson Slides

⤞ Scalar Product in Space | High School Math PowerPoint Lesson Slides | Cosine Law

⤞ Numerical Sequence | High School Math PowerPoint Lesson Slides

Are you teaching your High School students about Order on R- Framing and approximation? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 11 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ Order and Operations

(Addition and Subtraction, Multiplication, Division, Square and square root, Reciprocal )

✦ Comparing a positive number with its square , its square root , and its reciprocal

✦ Framing and Operations

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵

Other Resources:

⤞ Generalities of Functions (part 1) | High School Math PowerPoint Lesson Slides

⤞ Coordinate System | High School Math PowerPoint Lesson Slides

⤞ Parallel Lines and Planes | High School Math PowerPoint Lesson Slides

⤞ Scalar Product of Vectors | High School Math PowerPoint Lesson Slides

⤞ Statistics Part 2 | High School Math PowerPoint Lesson Slides

⤞ Statistics Part 1 | High School Math PowerPoint Lesson Slides

Multiplying complex numbers no prep lesson with

• A Power Point with examples of multiplying complex numbers and equating coefficients to find unknowns
• Worksheet with worked solutions

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

Are you teaching your High School students about polynomial functions? Plenty of examples and application exercises are included. You can also easily convert this to a Google Slides lesson by dragging it into your Google Drive.

What is included?

✦ 13 total slides for notes, examples and applications.

✦ All steps are animated to allow the teacher to explain them gradually.

Throughout the Lesson, students will be introduced to the following:
✦ Plan of the study of polynomial function

✦ The study of some polynomial function

✦ Intersection of two curves

✦ Graphic solution

✦ Graphic Comparison of two Functions

This resource is great for:

• In-Classroom Teaching (Displaying for the Whole Class)
• Online Learning
• Homeschooling
• Sharing on Google Classroom or Other Platforms as a Tool for Revision

-Follow us on TeachShare to be informed with new products and updates.

➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵

Other Resources:

⤞ Scalar Product in Space | High School Math PowerPoint Lesson Slides | Cosine Law

⤞ Numerical Sequence | High School Math PowerPoint Lesson Slides

⤞ Generalities of Functions (part 2) | High School Math PowerPoint Lesson Slides

⤞ Primitives Anti-Derivative | High School Math PowerPoint Lesson Slides

⤞ Derivative of Functions | High School Math PowerPoint Lesson Slides

Online lesson. You can send it to your students and they'll have everything they need. If you are online with them, you can project it and comment.

If you like an example of what can be done with this type of resources check:

https://www.youtube.com/watch?v=0\_sQPr4Ni50\&t=1s

Math inequalities

This PowerPoint presentation contains theory review about solving inequalities, examples and several exercises.

Printable

Suitable for IB MYP Middle Years Programme

Copyright © 2020 Matemaths

All rights reserved by author.

Permission to copy for single classroom use only.

Not for public display.

No prep lesson introducing the Factor Theorem

• PowerPoint showing the Factor Theorem and using it to factorise polynomials
• Worksheet with questions of increasing difficulty including solving cubic equations by factorisation
• B&W and color versions included
• Worked solutions to model answers

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.