12th Grade Precalculus Worksheets

Practice using function notation with numerical values and algebraic expressions

Worked solutions are included

If you are looking for your students to practice simplifying rational expressions using greatest common factor (GCF) and trinomial factoring, this is the product for you! With 18 different questions included as well as 3 guided examples at the top of the page for your students reference, this product is the perfect worksheet to really get them to understand how to simplify rational expressions before a quiz, test or to even use as a classwork assessment since it comes with an answer key!

INCLUDED:

- 2 Page Worksheet

- 18 simplifying rational expressions practice

- 3 guided examples

- Answer Key

LINKED PRODUCT HIGHLIGHT

If you want a more involved lesson that is completely done for you from warm up to assessment, differentiated and NO PREP REQUIRED on simplifying rational expressions, check out this resource in my store:

ALGEBRA 2 DIFFERENTIATED LESSON PLAN (SIMPLIFYING RATIONAL EXPRESSIONS)

A mixture of problem solving questions on Arithmetic and Geometric Series.

A useful task to assess understanding of both types of series. Could also be used as a homework task or a class assessment.

Worked solutions are included.

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.

Worksheet and worked solutions for introducing the absolute value function.

Students will sketch transformations of the absolute value of x.

Students also be able to write inequalities using the absolute value function

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.

First lesson on splitting rational expressions into partial fractions.

PowerPoint with warm up questions on adding and subtracting rational expressions. There are three worked examples for the teacher, with a matching one for students to try.

Worksheet with 3 differentiated sections:

1. denominators factored
2. denominators require factoring first
3. Extension questions

Worked solutions are included

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.

No prep lesson for discovering the double angle formulae.

This follows on from Trigonometry - Compound Angles no prep lesson

• A PowerPoint using compound angles to deduce the double angle formulae with two examples of proving identities
• A two page worksheet with over 30 questions involving equations and identities
• 5 pages of worked solutions to accompany this.

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.

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.

A lesson on sketching reciprocal graphs.

• A PowerPoint reminding students of the shapes of y = a/x and y = a/x^2
• Use algebra to solve equations relating to the intersection of a line and a reciprocal
• Sketching more complex reciprocal functions of the form (ax + b)/(cx + d)
• Sketching functions of the form [Quadratic]/[Linear]
• Extension questions
• Worked solutions included
• B &W and color versions included
• Ideal for students preparing for University

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.

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.

Introduction to complex numbers and imaginary numbers no prep lesson.

• Power Point begins with introducing i as the square root of (-1), simplifying radicals of negative numbers, solving quadratics with complex roots and finally, adding and subtracting complex numbers
• Worksheet includes examples on all of the above
• Worked solutions are included to share with students should you wish

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.

Second no prep lesson on Partial Fractions. This one concerns the situation when the denominator consists of a linear factor and an irreducible non repeating quadratic factor.

• PowerPoint with a teacher example and a similar one for students to try
• Worksheet with differentiated questions - middle section of questions review factoring sums and differences of two cubes which are needed to the extension section (3 Bananas)
• Full worked solutions included

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Partial Fractions 1 - non repeating linear factors no prep lesson

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.

No prep lesson for solving equations and inequalities involving the absolute value function.

• PowerPoint with examples [x-a]=k and [x=a]>k,
• Extension examples with [ax+b]=[cx+d]
• Worksheet and 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.

No prep lesson for discovering the double angle formulae.

This follows on from Trigonometry - Compound Angles no prep lesson

• A PowerPoint using compound angles to deduce the double angle formulae with two examples of proving identities
• A two page worksheet with over 30 questions involving equations and identities
• 5 pages of worked solutions to accompany this.

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.

Activity involving stretches of sinx. Students to use graphing software to help plot transformations and describe them. Answer sheet included

Worksheet and solutions on applying the knowledge

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.

No Prep Lesson on finding the sum of an infinite geometric series (The Sum to Infinity)

• PowerPoint with introduction
• Worksheet
• Worked Solutions

This follows the previous lesson: Finding the sum of a geometric series.

Sum of a Geometric Series No Prep Lesson

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.

No prep lesson

• Activity to introduce and discover rules for translating functions. Use of graphing software is ideal. Answers included
• Worksheet on translating functions, sketching translated graphs and finding the algebraic equations of the new graphs
• Worked solutions included

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.

This resource provides students with a comprehensive introduction to parametric equations. It includes a PowerPoint presentation with clear explanations and two examples of drawing graphs in parametric form.

In addition to the PowerPoint, this resource includes a worksheet that guides students through an investigation of a number of equations using technology. The worksheet is designed to help students apply the knowledge they gained from the PowerPoint presentation to solve problems in a practical context. The questions are challenging and require students to use various tools, including graphing calculators and software, to explore the graphs of the given equations in parametric form.
Furthermore, the resource offers worked solutions to all the questions in the worksheet, enabling students to check their answers and understand the solution process in detail. The solutions provide step-by-step explanations of how to solve the problems using technology, making it easier for students to grasp the concepts involved.

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.

No prep lesson. PowerPoint begins with a definition of a radian and then convert between radians and degrees. Also includes the application of radians to find the arc length and sector area. Extension includes area of a segment.

Worksheet and worked solutions convert between radians and degrees and problem solving in finding arc lengths, areas of sectors and segments

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.

Third no prep lesson on Partial Fractions. This is where the denominator consists of a repeated linear factor.

• PowerPoint with example for teachers and a similar one for students to attempt
• Differentiated worksheet where second exercise require factoring cubics on the denominator

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Partial Fractions 1 -non repeating linear factor no prep lesson

Partial Fractions 2 - irreducible quadratic factor no prep lesson

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.

No prep lesson for finding composite functions

• PowerPoint with numerical and algebraic examples of composite functions. Also includes examples for solving equations where a composite function is required to be found first
• Worksheet with increasing difficulty and worked solutions included

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Functions - Function Notation

Functions - Domain and Range no prep lesson

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.