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 get to pacing, you should know that classes at my school meet for 65 minutes and we are on a 7-period rotating schedule. Sometimes a class meets 3 times a week, sometimes 4; it depends on the week.

You might also be interested in what I teach in Algebra 2 or what I teach in my non-AP Calculus class.

Pacing Guides

I am including a pacing guide for both on-level Precalculus and Honors Precalculus.

The links will take you to resources that I have 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.

on-level Precalculus

Below is my pacing guide for on-level Precalculus. Scroll down to see the pacing guide for Honors Precalculus.

The textbook we use is Larson's Precalculus with Limits: A Graphing Approach, 7th edition.

session	section	ON LEVEL PRECALCULUS
1	1.1 to 1.3	Lines, Functions, Graphs day 1
2	1.1 to 1.3	Lines, Functions, Graphs day 2
3	1.4	Shifting, Reflecting, Stretching VIDEO: How to Teach Graphing Transformations
4	review	review ch1 functions
5	quiz	quiz ch1 functions
6	1.5	Combinations of Functions
7	1.6	Inverse Functions Worksheet or this Inverse Functions Circuit
8	1.7	Linear Models and Scatterplots
9	review	review ch1 functions
10	test	test ch1 functions
11	2.1	Quadratic Functions
12	2.2	Polynomial Functions of Higher Degree (leading coefficient test, intermediate value theorem)
13	2.3	Real Zeros of Polynomial Functions (Remainder and Factor Theorem, Rational Zero Test)
14	2.4	Complex Numbers
15	review	review ch2 quadratic and polynomial functions
16	quiz	quiz ch2 quadratic and polynomial functions
17	2.5	Fundamental Theorem of Algebra or Find All Zeros Circuit
18	2.6	Rational Functions and Asymptotes
19	2.7	Graphs of Rational Functions
20	review	review ch2 polynomial and rational functions
21	review	review ch2 polynomial and rational functions again
22	test	test ch2 polynomial and rational functions
23	3.1	Exponential Functions and Their Graphs
24	3.2	Logarithmic Functions and Their Graphs, extra practice
25	3.3	Properties of Logarithms  or Properties of Logs Level 1
26	review	review ch3 exponential and log functions
27	quiz	quiz ch3 exponential and log functions
28	3.4	Solving Exponential and Logarithmic Equations  or Log Equations Level 1
29	3.5	Exponential and Logarithmic Models
30	review	review ch3 exponential and log functions and equations
31	test	test ch3 exponential and log functions and equations
32	8.1	Sequences and Series
33	8.2	Arithmetic Sequences and Partial Sums
34	8.3	Geometric Sequences and Series
35	review	review ch8 sequences and series
36	quiz	quiz ch8 sequences and series
37	8.5	Counting Principles
38	8.6	Probability
39	8.4	Binomial Theorem
40	review	review ch8 sequences, series, probability
41	test	test ch8 sequences, series, probability
42	review	review for exam
43	review	review for exam
		SEMESTER 2
1	4.3	Right Triangle Trig   also check out Notes for Unit 4
2	4.1	Degree and Radian Measure (do not cover linear and angular speed)
3	4.2	Trig Functions: The Unit Circle
4	4.4	Trig Functions of Any Angle
5	review	Unit circle quiz and review for ch 4 quiz
6	review	review ch4 trigonometric functions
7	quiz	quiz ch4 trigonometric functions
8	4.5	Graphs of Sine and Cosine Amplitude and Period WORKSHEET  and Graphing Sine and Cosine Circuit worksheet  VIDEO: How to Teach Graphing Sine and Cosine
9	practice	Graphs of Sine and Cosine practice WORKSHEET
10	4.6	Graphing Secant and Cosecant VIDEO: How to Teach Graphing Secant and Cosecant
11	4.6	Graphing Tangent and Cotangent  VIDEO: How to Teach Graphing Tangent and Cotangent
12	practice	graphing practice
13	4.7	Inverse Trig Functions
14	review	review ch4 trig functions and graphs of trig functions
15	test	test ch4 trig functions and graphs of trig functions
16	5.1	Using Fundamental Identities
17	5.2	Verifying Identities
18	5.3	Solving Trig Equations
19	review	review ch5 verifying identities and solving trig equations
20	quiz	quiz ch5 verifying identities and solving trig equations
21	5.4	Sum and Difference Identities
22	5.5	Double Angle Identities (no half-angle)
23	review	review trig identities and equations
24	test	test trig identities and equations
25	6.1	Law of Sines
26	6.1	Law of Sines Ambiguous Case
27	6.2	Law of Cosines
28	review	review ch6 Laws of Sine and Cosine
29	quiz	quiz ch6 Laws of Sine and Cosine
30	6.3	Vectors in the Plane
31	6.4	Vectors and Dot Products
32	review	review ch6 Laws of Sine and Cosine and vectors
33	test	test ch6 Laws of Sine and Cosine and vectors
34	9.1	Circles
35	9.1	Parabolas
36	9.2	Ellipses
37	9.3	Hyperbolas (do not cover eccentricity)
38	review	review ch9 conic sections
39	test	test ch9 conic sections
40	Project	students work with a partner to make a review activity for a previous unit
41	Project	project
42	Project	project
43	review	review for exam
44	review	review for exam
		*if time, do a 5 day unit on Limits (3 days of instruction, 1 day of review, 1 day for a quiz)

Honors Precalculus

Below is my pacing guide for Honors Precalculus.

The textbook we use is Larson's Precalculus with Limits: A Graphing Approach, 7th edition.

The links will take you to resources that I have available in my TeachersPayTeachers store. You can buy 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	section	Honors Precalculus version 2
1	supplement	absolute value inequalities, quadratic inequalities, rational inequalities
2	1.3	Graphs of Functions (vertical line test, relative extrema, even, odd)
3	1.4	Shifting, Reflecting, Stretching VIDEO: How to Teach Graphing Transformations
4	1.4	transformations practice
5	1.6	Inverse Functions Worksheet or this Inverse Functions Circuit
6	review	review ch1 functions
7	quiz	quiz ch1 functions
8	2.2	Polynomial Functions of Higher Degree (leading coefficient test, intermediate value theorem)
9	2.2	Polynomial Functions of Higher Degree continued
10	2.3	Real Zeros of Polynomial Functions (Remainder and Factor Theorem, Rational Zero Test)
11	2.5	Fundamental Theorem of Algebra, or Find All Zeros Circuit
1 2	review	review ch2 quadratic and polynomial functions
13	quiz	quiz ch2 quadratic and polynomial functions
14	2.6	Rational Functions and Asymptotes
15	2.7	Graphs of Rational Functions
16	practice	Graphs of Rational Functions practice
17	supplement	Variation (direct, inverse, joint)
18	review	review ch2 polynomial/rational functions, variation
19	test	test ch2 polynomial/rational functions, variation
20	3.1	Exponential Functions and Their Graphs
21	3.2	Logarithmic Functions and Their Graphs
22	practice	practice Exponential and Log Functions
23	3.3	Properties of Logarithms
24	review	review ch3 exponential and log functions
25	quiz	quiz ch3 exponential and log functions
26	3.4	Solving Exponential and Logarithmic Equations
27	3.4	Solving Exponential and Logarithmic Equations again
28	3.5	Exponential and Logarithmic Models
29	review	review ch3 exponential and log functions and equations
30	test	test ch3 exponential and log functions and equations
31	8.1	Sequences and Series
32	8.2	Arithmetic Sequences and Partial Sums
33	8.3	Geometric Sequences and Series
34	8.4	Binomial Theorem
35	review	review ch8 sequences, series, binomial theorem
36	quiz	quiz ch8 sequences, series, binomial theorem
37	8.5	Counting Principles
38	8.6	Probability
39	practice	practice probability
40	review	review ch8 sequences, series, binomial theorem, probability
41	test	test ch8 sequences, series, binomial, theorem, probability
42	4.3	Right Triangle Trig       also check out Notes for Unit 4
43	4.1	Degree and Radian Measure: unit circle (paper plate activity)
44	4.1	Degree and Radian Measure: linear and angular speed
45	4.2	Trig Functions: The Unit Circle
46	4.4	Trig Functions of Any Angle
47	review	review ch4 trigonometric functions
48	quiz	quiz ch4 trigonometric functions
49	review	review for exam
50	review	review for exam
		Semester 2
1	4.5	Graphing Sine and Cosine VIDEO: How to Teach Graphing Sine and Cosine
2	practice	practice graphing sine and cosine
3	supplement	Modeling with sine/cosine graphs |  Trig Graphs Project
4	4.6	Graphs of Other Trig Functions  or Graphs of Tangent and Cotangent Circuit VIDEO: How to Teach Graphing Tangent and Cotangent VIDEO: How to Teach Graphing Secant and Cosecant
5	4.7	Inverse Trig Functions
6	4.8	Applications and Models
7	review	review ch4 trig functions and graphs of trig functions
8	test	test ch4 trig functions and graphs of trig functions
9	5.1	Using Fundamental Identities
10	5.2	Verifying Identities
11	5.3	Solving Trig Equations
12	review	review ch5 verifying identities and solving trig equations
13	quiz	quiz ch5 verifying identities and solving trig equations
14	5.4	Sum and Difference Identities
15	5.5	Double Angle Identities (no half-angle)
16	review	review ch5 trig identities and equations
17	test	test ch5 trig identities and equations
18	6.1	Law of Sines
19	6.2	Law of Cosines
20	6.3	Vectors in the Plane
21	6.3	6.3 again: Direction Angles
22	6.4	Vectors and Dot Products
23	review	review ch6 Laws of Sine and Cosine and vectors
24	test	test ch6 Laws of Sine and Cosine and vectors
25	9.1	Circles & Parabolas
26	9.2	Ellipses
27	9.3	Hyperbolas (includes eccentricity)
28	practice	practice Conics
29	review	review ch9 conic sections
30	quiz	quiz ch9 conic sections
31	9.4	Parametric Equations
32	9.5	Polar Coordinates (and Equations)
33	9.6	Polar Graphs
34	practice	practice Polar
35	review	review ch9 Conics and Polar
36	test	test ch9 Conics and Polar
37	11.1	Introduction to Limits
38	11.2	Techniques for Evaluating Limits
39	11.4	Limits at Infinity
40	11.3	The Tangent Line Problem
41	supplement	Lesson 5: Power Rule
42	supplement	Lesson 6: Product and Quotient Rules
43	review	review ch11 limits and derivatives
44	quiz	quiz ch 11 limits and derivatives
45	review	review for exam
46	review	review for 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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