AP Calculus AB

Pacing Guide: Precalculus Review

For the first few weeks, this class will be reviewing important (and sometimes obscure) precalculus/algebra/trigonometry concepts. These topics and dates we will be reviewing are:

-Introduction to AP Calculus: August 7

-Project (Find the Distance): August 10-11

-Composition of Functions: August 12-13

-Piecewise Defined Functions: August 14

-Graphing Exponential Functions: August 17

-Solving Exponential Functions: August 18

-Solving Exponential Functions with Logarithms: August 19

(MAP Testing - August 20)

-Properties of Logarithms: August 21

-Modeling with Exponential and Logarithmic Functions: August 24

-Graphing Logarithmic Functions: August 25

-Function Inverses: August 26

-Evaluating Six Trigonometric Functions: August 27

-Solving Trigonometric Equations: August 28

-Law of Sine, Law of Cosine: August 31

-Review: September 1

-Precalculus test: September 2 - 3 (two-day test)

All Assignments can be viewed in the Canvas portion of the class. (Two weeks are displayed.) 

For this week-and-a-day, we will be previewing concepts of calculus that are important for this year. We be completing a math-based project. We also will be starting our precalculus review. Here is the schedule:

Friday, August 7:

We will be: introducing ourselves, discussing the aspects of the class, introducing the syllabus, answering your questions, and will be introducing the small math project that will open the class.

Monday, August 10, and Tuesday, August 11:

We will be completing a project that will take two days. Your work on the project is due Wednesday, August 12, at the beginning of class.

The Project: You will determine a distance measurement in the planetarium. I will explain what you will exactly be measuring in the class.

The Rules:

1) You may complete this in pairs or individually. If you work in pairs, you will have to complete a little more work, but can turn in only one project submission (instead of both students turning in work).

2) You can use any measuring devices made available to you in class.

3) You can use any algebra, geometry, trigonometry, or precalculus concepts to complete this task.

4) You will have two class periods to complete this work. You are more than welcome to work on this outside of class too.

5) Those working individually need to list 10 steps they took to complete the task. Those working in pairs need to list 15 steps they took to complete the task but will only submit one project paper for both students.

6) You may not climb on the planetarium projector's base or chairs. 

7) All work is due as you enter class on Wednesday, August 12.

What To Submit for the Project and How This Will Be Graded:

Part 1: Your estimation of the distance. (Do not forget units.)

   Grading (20 total points): 

      Within 1.0 feet of true measurement... 20 points

      Between 1.01 feet and 3.0 feet off true measurement... 15 points

      Between 3.01 feet and 5.0 feet off true measurement... 10 points

      More than 5.0 feet off true measurement... 5 points

Part 2: All your relevant math work that shows how you computed the distance.

    Grading (40 total points): 

      Best Work: All relevant math is shown, makes sense and has a good flow or can be understood... 40 points

      Decent Work: 80% relevant math is shown, makes sense and has a good flow or can be mostly understood... 30 points

      Work That Needs Help: A bit of relevant math is shown, does not really makes sense and has flow or can not really be understood... 15 points

      No Work Shown... 0 points

Part 3: Your 10 steps (individual work) or 15 steps (group work) that led you to your answer. Your steps must be complete sentences.

   Grading (40 total points): 

      Best Work: All steps are shown, all steps make sense and have good flow and can be understood... 40 points

      Decent Work: 80%+ steps are shown, all steps make reasonable but not perfect sense and have a flow that can be understood... 30 points

      Work That Needs Help: 60%-79.9% of steps are shown, all steps make reasonable but not perfect sense and have a flow that can be somewhat understood... 15 points

      Any steps that are not complete sentences lose half of that step's credit.

      No Work Shown... 0 points

Accepted Assignment Submissions:

Students may submit their assignments in any of the following formats:

a. Word document emailed to the teacher at glaser_j@aps.edu by the beginning of class on Wednesday, August 12.

b. Typed and printed submission turned in at the beginning of class on Wednesday, August 12.

c. An electronic poster emailed to the teacher at glaser_j@aps.edu by the beginning of class on Wednesday, August 12.

d. A physical poster turned in at the beginning of class on Wednesday, August 12.

e. Any other acceptable electronic medium (like Powerpoint, etc.) emailed to the teacher at glaser_j@aps.edu or made available to the teacher by the beginning of class on Wednesday, August 12.

Wednesday, August 12: 

We will be reviewing the graphing of polynomials.

Today's references:

https://mathbitsnotebook.com/Algebra2/Polynomials/POGraphing.html

Links to an external site.

https://warriorweb.dinecollege.edu/ICS/icsfs/GS_MTH110_SumDifferenceCubes.pdf?target=ffd89e37-ec64-4a70-9419-9146a3a3a0b5

Links to an external site.

Homework:

Complete #1 - #4 of the worksheet given in class.

(This work will be submitted for grading on Monday, August 17.)

Thursday, August 13: 

We will be reviewing the graphing of polynomials.

Today's references:

https://mathbitsnotebook.com/Algebra2/Polynomials/POGraphing.html

Links to an external site.

https://warriorweb.dinecollege.edu/ICS/icsfs/GS_MTH110_SumDifferenceCubes.pdf?target=ffd89e37-ec64-4a70-9419-9146a3a3a0b5

Links to an external site.

Homework:

Complete #1 - #8 of the worksheet given in class (#5 - #8 is new for today's work).

(This work will be submitted for grading on Monday, August 17.)

Friday, August 14: 

We will be reviewing piecewise functions.

Today's resource:

https://www.mathsisfun.com/sets/functions-piecewise.html

Links to an external site.

Homework:

Complete #1 - #10 of the worksheet given in class.

(This work will be submitted for grading on Monday, August 17.)

This week, we will be continuing a precalculus review. 

Regular homework will be assigned in the classroom. The homework will also be provided in the Canvas class. All this week's homework will be due on the first school day of the next week.

Remember, this is a senior-level ECA class. No late work will be accepted. 

Monday, August 17: 

We will be reviewing graphing exponential functions.

Today's resource:

https://www.varsitytutors.com/hotmath/hotmath_help/topics/graphing-exponential-functionsLinks to an external site.

Homework:

Complete #1 - #8 of the worksheet handed out in class. Students need to make a T-Chart calculating 6 points for each graph.

(This work will be submitted for grading on Monday, August 24.)

Tuesday, August 18: 

We will be reviewing solving exponential equations.

Homework:

Complete #1 - #12 of the worksheet handed out in class.

(This work will be due with the other work of the week on Monday, August 24.)

Wednesday, August 19: 

We will be solving exponential equations using logarithms.

https://www.mathsisfun.com/algebra/exponents-logarithms.html

Homework:

Complete #1 - #12 of the worksheet handed out in class.

(This work will be due with the other work of the week on Monday, August 24.)

Thursday, August 20: 

Students will be completing the BOY MAP Testing today. We will not have calculus class.

Friday, August 21: 

We will be reviewing properties of logarithms.

Homework:

Complete #1 - #26 of the worksheet handed out in class. 

(This work will be due with the other work of the week on Monday, August 24.)

Signup and paying for the AP Calculus AB test in May must be completed by October 30, 2026. To sign up for the class, students must access my College Board personal class/website. The instructional are below. Mr. Glaser's College Board AP classroom is: YWL2YD (for 2026-27).

STEP 1: Use the class-specific JOIN CODE to join your AP teacher’s classroom on

the MyAP website (http://myap.collegeboard.org) and set your exam decision to

“YES” no later than October 30, 2026.

STEP 2: Starting August 13, 2026, submit payment of $99 for the AP exam that you

are choosing to take at ECA/CEC’s payment website (http://aptsusa.com/eca-cec).

Payment must be received no later than October 30. 2026. (College Board charges

cancellation/unused exam fees; if a student cancels after a certain date, or fails to take the

exam in May, $40 will be forfeited to pay this charge.)

BOTH Steps 1 & 2 MUST be completed by October 30, 2026 to complete an AP

exam order activation. Orders activated after this will incur an additional

LATE FEE of $40 per exam. (LATE FEE is required by College Board.)

(Students eligible for free/reduced lunch should contact Counselor Alicia Faulds

(alicia.faulds@aps.edu) to obtain the fee reduction code. A $40 deposit will be collected, but $35 of

that fee will be refunded once the exam is completed, resulting in a final fee of $5 per exam.)

ECA/CEC AP Exam Ordering Deadline:

Exam Activation Deadline:  October 30, 2026

Full Exam Payment Deadline:  October 30, 2026

For more information and details as well as assistance and support visit http://aptsusa.com/eca-cec OR contact Ms. Vierra, ECA/CEC Testing Coordinator, at: jessica.vierra@aps.edu. 

AP® Honors Calculus AB

2026-27 School Year

Instructor: John Glaser

Email: glaser_j@aps.edu

Class Synopsis

This class is equivalent to the first semester college calculus class students receive at U.S. colleges and universities. The course is structured around the enduring understandings within integrals and the fundamental theorem of calculus.

This class’ purpose is to prepare high school students to pass the Calculus AB Advanced Placement Exam that will be given in May 2026.

Daily attendance to the class is imperative. New concepts and vital AP® review will happen every class and missed material may vitally impact future learning in the class. Homework can be expected every day. For the first semester, 30-60 minutes of homework will be typical. For the second semester, until the AP® exam, 45-90 minutes of homework will be typical.

Students are expected to keep a binder in which all notes, classwork, and homework will be kept. Since this class is a college-preparatory class, the homework will be given daily, but graded after the tests are taken. Students are expected to turn in the homework from the chapter the same class period they are taking that chapter’s test. Late homework will not be accepted.

Mr. Glaser is available by appointment for extra assistance in the class.

Class Textbook – Class sets and student whole-year check-out book available

Larson, Hostetler, Edwards. Calculus 8th ed. Houghton Mifflin, 2006. [CR4]

Student Supplies Needed For Calculus

-       Three-ring binder

-       Notebook paper

-       Graphing paper

-       Pencils

-       Graphing calculator (graphing calculators are available in the classroom) [CR3a]

Class Grade Breakdown

Tests and quizzes – 70% of overall average

Homework – 20% of overall average

Final exam – 10% of overall average

Curricular Requirements

CR1a  - The course is structured around the enduring understandings within Big Idea 1: Limits.

• See page 3, 4

CR1b - The course is structured around the enduring understandings within Big Idea 2: Derivatives.

• See page 4

CR1c - The course is structured around the enduring understandings within Big Idea 3: Integrals and the Fundamental Theorem of Calculus.

• See page 4, 5

CR2a - The course provides opportunities for students to reason with

definitions and theorems.

• See page 4, 6

CR2b - The course provides opportunities for students to connect concepts and processes.

• See page 6

CR2c - The course provides opportunities for students to implement algebraic/computational processes.

• See page 3, 4, 6

CR2d - The course provides opportunities for students to engage with graphical, numerical, analytical, and verbal representations and demonstrate connections among them.

• See pages 3, 4, 6

CR2e - The course provides opportunities for students to build notational fluency.

• See page 4, 5, 6

CR2f - The course provides opportunities for students to communicate mathematical ideas in words, both orally and in writing.

• See pages 4, 6

CR3a - Students have access to graphing calculators.

• See page 1, 3

CR3b - Students have opportunities to use calculators to solve problems.

• See page 3

CR3c - Students have opportunities to use a graphing calculator to explore and interpret calculus concepts.

• See page 3, 6

CR4 - Students and teachers have access to a college-level calculus textbook.

• See page 1

Other ECA/CEC Policies

Cell phone policy: At ECA/CEC, cell phone usage is not allowed in the classroom.  If Mr. Glaser sees or hears a cell phone, he will confiscate the phone and turn it in to the administration. The school’s policy on cell phone retrieval will then need to be followed by the student or the parent to have the phone returned.  At certain class times, the students’ cell phones can be used for mathematical applications. Mr. Glaser will inform the students of those applicable times.

Tardy policy: Students are expected to be on time to their classes. Tardy students will not be allowed to enter the class. They will be sent to the administrative offices, per ECA/CEC policy.

Teaching Strategies

This calculus curriculum assumes that all enrolled students have successfully completed the material in the pre-calculus course, such as linear and polynomial functions, inverse functions, exponential functions, logarithmic functions, trigonometric functions and inverses.

A variety of teaching techniques will be implemented for this class. Among the strategies will be: daily warm-up routines, classroom notes, classroom discussions, student collaboration, implementing algebraic/computational processes and problem solving, and AP® practice problems. Students will have numerous opportunities for students to reason with definitions and theorems. Students will also be practicing notational fluency in limits, derivation and integration processes. Students will have occasional activities to connect concepts and processes. Opportunities for students to communicate mathematical ideas in words, both orally and in writing, will occur daily. Due to the class being approximately one hour each day, homework and home review of lessons will be critical for good performance in the class and on the AP® exam at the end of the school year. In the classroom, graphing calculators will be available for students who do not own a calculator. The students can expect to use these calculators daily to explore and interpret calculus concepts. [CR3a] [CR3b] [CR3c]

 In addition to the ongoing, cumulative reviews to be conducted throughout the school year, students will be given an intense review and preparation unit several weeks prior to the AP® exam. During this time, practice problems will be given and scored, strategies will be reviewed, cumulative memorization quizzes will be given, notation will be emphasized, justification and verbal explanations will be refined, and appropriate calculator usage will be clarified.

Topic Sections

I. Limits

Limits will be introduced graphically and qualitatively first. Numerous graphs and functions will be used to explore limits. I will discuss the applications, use and interpretation of limits before technique. Qualitative discussion will include function continuity (and its consequences), behavior at infinity (including asymptotes), and the connection of limits to derivatives and integrals. Techniques will include mainly algebraic evaluation and resolving indeterminate forms. I will also discuss various topics related to infinite quantities. Derivative techniques (e.g. L'Hopital) will be introduced but not discussed in depth yet. Generally, implementation of many algebraic processes will be explored. [CR1a]

Sample Activity (Part I): Students explore limits at discontinuities in four ways: first, using the table feature on their calculators with decreasing increments; second, using algebraic techniques to “simplify” the expressions given as formulas; third, using the graph trace feature on their calculators; and fourth, using verbal descriptions of functions written in words to create graphs that match the verbal descriptions. Student work for the activity includes a written summary, using complete sentences, of their findings that compares and contrasts jump, removable, and asymptotic discontinuities. Student have an oral discussion on how the different representations reveal the discontinuities in different ways. [CR2b] [CR2c] [CR2d] [CR2e] [CR2f] [CR3c]

Relevant Text Sections: 1.1 - 1.5, 2.1

II. Interpreting Derivatives part.1

First, the importance of derivatives will be established by discussing practical applications (e.g. science, engineering, business). Students will learn how limits and derivations are linked. Qualitative discussion will follow on the many ways to interpret derivatives as rates of change and the importance of different notations (e.g. Leibniz, Lagrange). I will also discuss conditions for derivation and the relation to continuity. [CR1b]

Relevant Text Sections: 2.1, 3.1 - 3.6

III. Derivation Technique

Derivation rules (power, product, chain, quotient) will be introduced with polynomials and rational functions. Graphical interpretations of these rules will be discussed after all have been introduced analytically. Support algebraic topics, such as nested functions, will be discussed as needed. [CR1b]

Relevant Text Sections: 2.2, 2.3, 2.4

IV. Interpreting Derivatives part.2

Derivative interpretation for basic motion (position, velocity and acceleration) will be covered in depth. I will also discuss parametric equations, 2d vectors and motion in 2 dimensions. I will introduce implicit differentiation and discuss its importance for time-related application (related rates) and integration. [CR1b]

Relevant Text Sections: 2.2, 2.5, 2.6

Sample Activity (Parts II through IV): Students use a worksheet to explore the derivative function using the limit definition of the derivative at a point. For several points, students compute the difference quotient algebraically using the definition and use a table and/or graph on their calculators to evaluate the limits and interpret their results in terms of the definition to decide if the derivative does or does not exist at each point. The original function and its derivative values are plotted on two graphs with the same horizontal axes. Students trade papers and validate each other’s answers. [CR2a]

V. Interpreting Integrals part I. [CR1c]

In order to focus properly on the concept of integration, we will begin working with only polynomials. I introduce indefinite integrals by defining them as antiderivatives (and foreshadow differential equations). We begin application with areas and volumes, and briefly discuss the numerous applications to science and engineering. Relevant Text Sections: 4.1, 4.2

VI. Fundamental Theorem of Calculus

The Riemann sum is introduced, along with summation notation (and other integral approximation techniques). The definite integral will now be introduced as the zero width limit of the Riemann sum. The First Fundamental Theorem of Calculus is introduced and explored. [CR1c] The Second Fundamental Theorem of Calculus is introduced and explored. [CR1c] We will discuss how the Fundamental Theorems of Calculus (FToC) bridges the concepts of definite integrals, indefinite integrals and derivatives.

Relevant Text Sections: 4.3, 4.4

VII. Integration Technique part I.

The basic techniques for integration will be presented in terms of 'inversions' of the derivation rules. [CR1c] The two most significant techniques will be substitution, and integration by parts.

Relevant Text Sections: 4.5

VII. Interpreting Integrals part2

We will continue working with integrals focusing at first on changes to integration limits, functional integration limits (including substitutions) and geometric interpretation. We will also discuss area and volume calculations with both conceptual and analytical emphasis. [CR1c]

Relevant Text Sections:

7.1 – 7.3

Sample Activity (Parts V through VI): Students write an expression for an approximation of the area between the horizontal axis and the graph of

f(x) for a particular function given as a formula on a specified interval as a left, right, and midpoint Riemann sum using n subdivisions. They then use a Desmos graph with slider to explore sums. The file superimposes rectangular areas on the graph of f(x) showing the sum value. The software allows for left, right, and midpoint sums. The slider increases the number of partitions to explore precision. Finally, students write limits of their Riemann suns as n goes to infinity, then identify each as a definite integral, and use the Fundamental Theorem of Calculus to evaluate the integral. [CR2e]

IX. First Order Ordinary Differential Equations

First order ordinary differential equations will be introduced by discussing their wide use in science including population growth and decay.  Geometric interpretations including slope fields will be then be included along with numerical methods.

Relevant Text Sections: 6.1 - 6.2

Sample Activities Summary

Sample Activity (Part I): Students explore limits at discontinuities in four ways: first, using the table feature on their calculators with decreasing increments; second, using algebraic techniques to “simplify” the expressions given as formulas; third, using the graph trace feature on their calculators; and fourth, using verbal descriptions of functions written in words to create graphs that match the verbal descriptions. Student work for the activity includes a written summary, using complete sentences, of their findings that compares and contrasts jump, removable, and asymptotic discontinuities. Student have an oral discussion on how the different representations reveal the discontinuities in different ways. [CR2b] [CR2c] [CR2d] [CR2e] [CR2f] [CR3c]

Sample Activity (Parts II through IV): Students use a worksheet to explore the derivative function using the limit definition of the derivative at a point. For several points, students compute the difference quotient algebraically using the definition and use a table and/or graph on their calculators to evaluate the limits and interpret their results in terms of the definition to decide if the derivative does or does not exist at each point. The original function and its derivative values are plotted on two graphs with the same horizontal axes. Students trade papers and validate each other’s answers. [CR2a] [CR2b]

Sample Activity (Parts V through VI): Students will take a function of a temperature trend on a 24-hour interval and will calculate the average temperature three ways: 1) using the Average Value Theorem, 2) Calculating the temperature every two hours, adding the sum of the temperatures dividing by the total number of samples taken, and 3) taking the high and the low of the day and dividing by two (actual National Weather Service method). The student will them compare the results and will discuss the accuracy of each method. Then the students, after deciding which method is most accurate, will debate whether the NWS adopting a new average temperature calculating methodology will invalidate climatology research trends with new methods of collecting samples. The students will use this exploration to connect the concepts of real-world average value theorem calculus with application of the average value theorem itself. [CR2b] [CR2e] [CR2f]

Sample Activity (Parts V through VI): Students write an expression for an approximation of the area between the horizontal axis and the graph of

f(x) for a particular function given as a formula on a specified interval as a left, right, and midpoint Riemann sum using n subdivisions. They then use a Desmos graph with slider to explore sums. The file superimposes rectangular areas on the graph of f(x) showing the sum value. The software allows for left, right, and midpoint sums. The slider increases the number of partitions to explore precision. Finally, students write limits of their Riemann suns as n goes to infinity, then identify each as a definite integral, and use the Fundamental Theorem of Calculus to evaluate the integral. [CR2e]

Approximate Course Timeline

Unit             Topic                                                          Number of Days

Preparation for Calculus and Precalculus/Trigonometry Review – 23 Days

Part 1          Introduction and Project                                      2

Part 2          Precalculus Review                                       18

Part 3          Overall Review and Test                                       3

Chapter 1: Limits and Their Properties – 15 Days

1.1               A Preview of Calculus                                           3

1.2               Finding Limits Graphically and Numerically      3

1.3               Evaluating Limits Analytically                             3

1.4               Continuity and One-Sided Limits                         3

1.5               Infinite Limits                                                        3

                     Review and Test

Chapter 2: Differentiation – 15 Days

2.1               The Derivative and the Tangent Line Problem  2

2.2               Basic Differentiation and Rates of Change          2

2.3               Product and Quotient Rules and H.O.D.              3

2.4               The Chain Rule                                                      3

2.5               Implicit Differentiation                                         3

2.6               Related Rates                                                         2

                     Review and Test

Chapter 3: Applications of Differentiation – 25 Days

3.1               Extrema on an Interval                                         3

3.2               Mean Value Theorem                                        4

3.3               First Derivative Test                                             3

3.4               Second Derivative Test                                         3

3.5               Limits at Infinity                                                    2

3.6               Summary of Curve Sketching                               2

3.7               Optimization Problems                                        2

3.8               Newton’s Method                                                  3

3.9               Differentials                                                           3

                     Review and Test

Chapter 4: Integration – 21 Days

4.1               Antiderivatives and Indefinite Integration         4

4.2               Area                                                                        3

4.3               Definite Integrals                                                  4

4.4               Fundamental Theorem of Calculus                     3

4.5               Integration by Substitution                                  4

4.6               Numerical Integration                                          3

                     Review and Test

Chapter 5: Logarithmic, Exponential, Transcendental Functions – 8 Days

5.1               Natural Log Functions: Differentiation               2

5.2               Natural Log Functions: Integration                 2

5.4               Exponential Functions                                          2

5.5               Bases other than e                                             2

                     Review and Test (with chapter 6)

Chapter 6: Differential Equations – 8 Days

6.1               Slope Fields                                                            4

6.2               Growth and Decay                                                 4

                     Review and Test (with chapter 5)

Chapter 7: Applications of Integration – 10 Days

7.1               Area of a Region Between Two Curves               4

7.2 and 7.3 Volumes                                                                 6

                     Review and Test

Review for AP® Exam                                                                   20