What to Teach in Precalculus

You might work in a state or country where there are Precalculus standards that you have to cover, you might work in a state where the standards only cover up to Algebra 2, or you might work in a private school where you have more autonomy about what to teach in Precalculus.

If you are one of the latter two cases, then you might be interested in the Precalculus pacing guide below.

Before we discuss pacing, it's essential to note that classes at my school meet for 65 minutes and we follow a 7-period rotating schedule. Sometimes a class meets 3 times a week, sometimes 4; it depends on the week.

You may also be interested in the topics I cover in Algebra 2 or my non-AP Calculus class.

Pacing Guides

The links will direct you to resources available in my TeachersPayTeachers store. You can get all of my current and future Precalculus products here: bit.ly/precalculusbundle.

If you want a FREE Google Sheets version of these pacing guides, scroll down to the bottom of this page.

session	Lesson	Topic	Homework
Buy the entire course here (coming soon)
		FUNCTIONS AND THEIR GRAPHS	Buy Unit 1 Lessons and Notes here
1	1.1	Slopes and Equations of Lines	Slopes and Equations of Lines worksheet
2	1.2	Non-Linear Inequalities	Non-Linear Inequalities WORKSHEET
3	1.3	Functions (relation vs. function, domain, range, piecewise)	Functions CIRCUIT worksheet
4	1.4	Graphs of Functions (vertical line test, relative extrema, even, odd)	Graphs of Functions worksheet
5	review	review functions
6	QUIZ	quiz unit 1 functions
7	1.5	Transformations of Functions	Transformations of Functions WORKSHEET
8	practice		Transformations of Functions CARD SORT
9	1.6	Operations with Functions (operations, composition)	Operations with Functions Worksheet
10	1.7	Inverse Functions	Inverse Functions WORKSHEET
11	review	review functions
12	TEST	test unit 1 functions
		POLYNOMIAL AND RATIONAL FUNCTIONS	Buy Unit 2 Lessons and Notes here
13	2.1	Quadratic Functions	Quadratic Functions TRASHKETBALL GAME Quadratic Functions Worksheet for Precalculus
14	2.2	Graphs of Polynomial Functions (leading coefficient test, zeros with multiplicity)	Graphs of Polynomial Functions Worksheet
15	2.3	Zeros of Polynomial Functions (find zeros by factoring, given zeros, write the equation, intermediate value theorem)	Zeros of Polynomial Functions Worksheet
16	2.4	Dividing Polynomials (remainder and factor theorems, rational zero test)	Polynomial Division CARD SORT activity with Long Division and Synthetic Division Dividing Polynomials Worksheet
17	2.5	Complex Numbers	Complex Numbers CIRCUIT worksheet
18	2.6	Fundamental Theorem of Algebra	All Zeros of Polynomial Functions CIRCUIT worksheet Fundamental Theorem of Algebra WORKSHEET
19	review	review quadratic and polynomial functions	Polynomial Functions CARD SORT Fundamental Theorem of Algebra
20	QUIZ	quiz unit 2 quadratic and polynomial functions
21	2.7	Rational Functions and Asymptotes	Rational Functions WORKSHEET
22	2.8	Graphs of Rational Functions	Graphs of Rational Functions worksheet
23	practice	Graphs of Rational Functions practice	Rational Functions CARD SORT
24	review	review polynomial/rational functions, variation
25	TEST	test unit 2 polynomial/rational functions, variation
		EXPONENTIAL AND LOGARITHMIC FUNCTIONS	Buy Unit 3 here (coming soon)
26	3.1	Exponential Functions and Their Graphs	Exponential Functions and Graphs CIRCUIT worksheet
27	3.2	Logarithmic Functions and Their Graphs	Logarithmic Functions and Their Graphs WORKSHEET
28	practice	Practice Exponential and Log Functions	Exponential and Log Functions and Graphs Practice WORKSHEET
29	3.3	Properties of Logarithms	Properties of Logarithms CIRCUIT worksheet Level 2
30	review	review exponential and log functions
31	QUIZ	quiz unit 3 exponential and log functions
32	3.4	Solving Exponential and Logarithmic Equations	Solving Exponential and Logarithmic Equations CIRCUIT worksheet
33	3.4	Solving Exponential and Logarithmic Equations again	Solving Exponential and Logarithmic Equations CARD SORT
34	3.5	Exponential and Logarithmic Models	Exponential Functions Growth and Decay Applications CIRCUIT worksheet
35	review	review exponential and log functions and equations	Exponents and Logarithms Unit Review Game TRASHKETBALL
36	TEST	test unit 3 exponential and log functions and equations
		TRIGONOMETRIC FUNCTIONS	Buy Unit 4 Notes and Lessons here
37	4.1	Right Triangle Trig	Right Triangle Trigonometry CIRCUIT worksheet
38	4.2	Degree and Radian Measure: unit circle (paper plate activity)	Radian and Degree Measure CIRCUIT worksheet
39	4.3	Linear and Angular speed	Linear and Angular Speed CIRCUIT worksheet
40	4.4	Trig Functions: The Unit Circle	Unit Circle CIRCUIT worksheet
41	4.5	Trig Functions of Any Angle	Trigonometric Functions of Any Angle CIRCUIT worksheet
42	review	review trigonometric functions	Unit Circle REVIEW GAME
43	QUIZ	quiz unit 4 trigonometric functions
44	4.6	Graphing Sine and Cosine	Graphs of Sine and Cosine CIRCUIT worksheet
45	4.7	Modeling with sine/cosine graphs	Modeling with Sine and Cosine WORKSHEET
46	4.8	Graphs of Other Trig Functions	Graphs of Other Trig Functions CIRCUIT worksheet
47	4.9	Inverse Trig Functions	Inverse Trigonometric Functions CIRCUIT worksheet
48	review	review 4 trig functions and graphs of trig functions
49	TEST	test unit 4 trig functions and graphs of trig functions
50		review for exam
51		review for exam
52		Final Exam
		Semester 2
		EXPONENTIAL AND LOGARITHMIC FUNCTIONS	Buy Unit 5 Notes and Lessons here
1	5.1	Using Fundamental Identities	Simplifying Trig Identities CIRCUIT worksheet with worked solutions
2	5.2	Verifying Identities	Verifying Trigonometric Identities Practice Self Check
3	5.3	Solving Trig Equations	Solving Trigonometric Equations CIRCUIT worksheet
4	review	review verifying identities and solving trig equations
5	QUIZ	quiz unit 5 verifying identities and solving trig equations
6	5.4	Sum and Difference Identities	Sum and Difference Identities CIRCUIT worksheet
7	5.5	Double Angle & Half Angle Identities	Double Angle Identities CIRCUIT worksheet
8	review	review trig identities and equations
9	TEST	test unit 5 trig identities and equations
		LAW OF SINES, LAW OF COSINES, VECTORS	Buy Unit 6 Notes and Lessons here
10	6.1	Law of Sines	Law of Sines Side by Side Partner worksheet
11	6.2	Law of Cosines	Law of Cosines Side by Side Partner worksheet
12	6.3	Intro to Vectors	Intro to Vectors Circuit
13	6.4	Vectors in a Plane	Vectors in a Plane Circuit worksheet
14	6.5	Dot Product & Angle Between Vectors	Dot Product and Angle Between Vectors WORKSHEET
15	review	review Laws of Sine and Cosine and vectors
16	TEST	test unit 6 Laws of Sine and Cosine and vectors
		CONICS AND POLAR	Buy Unit 7 Notes and Lessons here
17	7.1	Circles & Parabolas	Conics Circles and Parabolas CIRCUIT worksheet
18	7.2	Ellipses	Conics Ellipses WORKSHEET
19	7.3	Hyperbolas (includes eccentricity)	Conics Hyperbolas WORKSHEET
20	practice	practice Conics	Conic Sections CARD SORT
21	review	review conic sections	Conic Sections Review Game Sticky Points
22	QUIZ	quiz unit 7 conic sections
23	7.4	Parametric Equations	Parametric Equations CIRCUIT worksheet with worked solutions
24	7.5	Polar Coordinates (and Equations)	Polar Coordinates and Equations CIRCUIT worksheet with worked solutions DIGITAL & PRINT
25	7.6	Polar Graphs
26	review	review Conics and Polar
27	TEST	test unit 7 Conics and Polar
		SEQUENCES, SERIES, PROBABILITY	Buy Unit 8 here (coming soon)
28	8.1	Sequences and Series	Introduction to Sequences CIRCUIT worksheet
29	8.2	Arithmetic Sequences and Series	Arithmetic Sequences and Series CIRCUIT worksheet
30	8.3	Geometric Sequences and Series	Geometric Sequences and Series CIRCUIT
31	8.4	Binomial Theorem	Binomial Theorem CIRCUIT worksheet
32	review	review sequences, series, binomial theorem	Sequences and Series Review Game TRASHKETBALL
33	QUIZ	quiz unit 8 sequences, series, binomial theorem
34	8.5	Counting Principles	Counting Principles CIRCUIT worksheet
35	8.6	Probability	Probability CIRCUIT worksheet
36	review	review sequences, series, binomial theorem, probability
37	TEST	test unit 8 sequences, series, binomial, theorem, probability
38	review	review for exam
39	review	review for exam
40		Final Exam

Other topics that are often taught in Precalculus:

• Systems of 2 Linear Equations
• Systems of 3 Linear Equations
• Systems of Non-Linear Equations
• Systems of Linear Inequalities
• Systems of Non-Linear Inequalities
• Matrix Operations
• Inverse and Determinant of Matrices
• Solving Systems Using Matrices
• Matrices Review
• Complex Numbers in Polar Form
• Operating with Complex Numbers in Polar Form | De Moivre's Theorem
• Multiplying and Dividing Complex Numbers in Polar Form

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Questions? rebecca@hoffmath.com