Precalculus curriculum

A function-centered precalculus path covering polynomial, rational, exponential, logarithmic, trigonometric, analytic geometry, vectors, sequences, and series.

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High school precalculus / calculus readiness

Precalculus curriculum

A function-centered precalculus path covering polynomial, rational, exponential, logarithmic, trigonometric, analytic geometry, vectors, sequences, and series.

Pacing

9 units, 24-34 weeks self-paced

Units

9 unit sequence

Practice

36 checked answers

Support

Self-paced or tutor-guided

Outcomes

Use function families fluently across symbolic, graphical, numeric, and verbal forms.
Build trigonometry and analytic geometry skills needed for calculus.
Enter calculus with modeling habits instead of memorized fragments.

Unit sequence

Built for independent progress first, then tutor support where the student gets stuck.

01
Function toolkit review
- Use domain, range, composition, inverse functions, and transformations.
- Compare functions from formulas, graphs, and tables.
Practice: Analyze three representations of the same function and explain which features each makes visible.
Unit work plan
1. 1
  Source study
  Start with Precalculus 2e and OpenStax Math. Take notes until you can explain: Use domain, range, composition, inverse functions, and transformations.
2. 2
  Worked attempt
  Produce the assignment artifact: Analyze three representations of the same function and explain which features each makes visible.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Compare functions from formulas, graphs, and tables.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Function toolkit review practice set has 12 questions. If 5 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Precalculus unit "Function toolkit review"?
Solve polynomial and rational equations with domain checks.Compare functions from formulas, graphs, and tables.Use zeros, multiplicity, end behavior, asymptotes, and factoring.Use domain, range, composition, inverse functions, and transformations.
Practice artifact
Which practice artifact should you produce for "Function toolkit review" before asking a tutor for help?
Skip the unit and start a new subject.Memorize vocabulary without checking any examples.Watch videos without writing or solving anything.Analyze three representations of the same function and explain which features each makes visible.
02
Polynomial and rational functions
- Use zeros, multiplicity, end behavior, asymptotes, and factoring.
- Solve polynomial and rational equations with domain checks.
Practice: Sketch a rational function from intercepts, asymptotes, and sign intervals.
Unit work plan
1. 1
  Source study
  Start with Precalculus 2e and OpenStax Math. Take notes until you can explain: Use zeros, multiplicity, end behavior, asymptotes, and factoring.
2. 2
  Worked attempt
  Produce the assignment artifact: Sketch a rational function from intercepts, asymptotes, and sign intervals.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Solve polynomial and rational equations with domain checks.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Polynomial and rational functions practice set has 13 questions. If 6 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Precalculus unit "Polynomial and rational functions"?
Use domain, range, composition, inverse functions, and transformations.Solve polynomial and rational equations with domain checks.Use zeros, multiplicity, end behavior, asymptotes, and factoring.Compare functions from formulas, graphs, and tables.
Practice artifact
Which practice artifact should you produce for "Polynomial and rational functions" before asking a tutor for help?
Memorize vocabulary without checking any examples.Watch videos without writing or solving anything.Skip the unit and start a new subject.Sketch a rational function from intercepts, asymptotes, and sign intervals.
03
Exponential and logarithmic functions
- Model growth, decay, compound interest, and logarithmic scales.
- Solve exponential and logarithmic equations.
Practice: Fit an exponential model and interpret its initial value, rate, and limitations.
Unit work plan
1. 1
  Source study
  Start with Precalculus 2e and OpenStax Math. Take notes until you can explain: Model growth, decay, compound interest, and logarithmic scales.
2. 2
  Worked attempt
  Produce the assignment artifact: Fit an exponential model and interpret its initial value, rate, and limitations.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Solve exponential and logarithmic equations.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Exponential and logarithmic functions practice set has 14 questions. If 7 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Precalculus unit "Exponential and logarithmic functions"?
Use zeros, multiplicity, end behavior, asymptotes, and factoring.Compare functions from formulas, graphs, and tables.Use domain, range, composition, inverse functions, and transformations.Model growth, decay, compound interest, and logarithmic scales.
Practice artifact
Which practice artifact should you produce for "Exponential and logarithmic functions" before asking a tutor for help?
Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.Fit an exponential model and interpret its initial value, rate, and limitations.Skip the unit and start a new subject.
04
Trigonometric foundations
- Use radians, the unit circle, right-triangle trig, and identities.
- Translate among angles, coordinates, and trig values.
Practice: Build a unit-circle reference sheet from symmetry, not memorized tables.
Unit work plan
1. 1
  Source study
  Start with Precalculus 2e and OpenStax Math. Take notes until you can explain: Use radians, the unit circle, right-triangle trig, and identities.
2. 2
  Worked attempt
  Produce the assignment artifact: Build a unit-circle reference sheet from symmetry, not memorized tables.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Translate among angles, coordinates, and trig values.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Trigonometric foundations practice set has 15 questions. If 8 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Precalculus unit "Trigonometric foundations"?
Use domain, range, composition, inverse functions, and transformations.Compare functions from formulas, graphs, and tables.Use zeros, multiplicity, end behavior, asymptotes, and factoring.Translate among angles, coordinates, and trig values.
Practice artifact
Which practice artifact should you produce for "Trigonometric foundations" before asking a tutor for help?
Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.Build a unit-circle reference sheet from symmetry, not memorized tables.Skip the unit and start a new subject.
05
Trigonometric graphs and equations
- Graph sine, cosine, tangent, and transformations.
- Solve trig equations over restricted intervals.
Practice: Model a periodic situation and identify amplitude, period, phase shift, and midline.
Unit work plan
1. 1
  Source study
  Start with Precalculus 2e and OpenStax Math. Take notes until you can explain: Graph sine, cosine, tangent, and transformations.
2. 2
  Worked attempt
  Produce the assignment artifact: Model a periodic situation and identify amplitude, period, phase shift, and midline.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Solve trig equations over restricted intervals.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Trigonometric graphs and equations practice set has 16 questions. If 9 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Precalculus unit "Trigonometric graphs and equations"?
Use zeros, multiplicity, end behavior, asymptotes, and factoring.Use domain, range, composition, inverse functions, and transformations.Graph sine, cosine, tangent, and transformations.Compare functions from formulas, graphs, and tables.
Practice artifact
Which practice artifact should you produce for "Trigonometric graphs and equations" before asking a tutor for help?
Memorize vocabulary without checking any examples.Skip the unit and start a new subject.Model a periodic situation and identify amplitude, period, phase shift, and midline.Watch videos without writing or solving anything.
06
Analytic geometry
- Use conics, distance, midpoint, and equations of curves.
- Connect geometric definitions to algebraic forms.
Practice: Classify and sketch a conic from its equation after completing the square.
Unit work plan
1. 1
  Source study
  Start with Precalculus 2e and OpenStax Math. Take notes until you can explain: Use conics, distance, midpoint, and equations of curves.
2. 2
  Worked attempt
  Produce the assignment artifact: Classify and sketch a conic from its equation after completing the square.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Connect geometric definitions to algebraic forms.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Analytic geometry practice set has 17 questions. If 10 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Precalculus unit "Analytic geometry"?
Use zeros, multiplicity, end behavior, asymptotes, and factoring.Compare functions from formulas, graphs, and tables.Use domain, range, composition, inverse functions, and transformations.Connect geometric definitions to algebraic forms.
Practice artifact
Which practice artifact should you produce for "Analytic geometry" before asking a tutor for help?
Skip the unit and start a new subject.Classify and sketch a conic from its equation after completing the square.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.
07
Vectors, parametric equations, and polar coordinates
- Represent magnitude, direction, motion, and polar graphs.
- Move between rectangular, parametric, and polar forms.
Practice: Describe a motion path with parametric equations and interpret the parameter.
Unit work plan
1. 1
  Source study
  Start with Precalculus 2e and OpenStax Math. Take notes until you can explain: Represent magnitude, direction, motion, and polar graphs.
2. 2
  Worked attempt
  Produce the assignment artifact: Describe a motion path with parametric equations and interpret the parameter.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Move between rectangular, parametric, and polar forms.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Vectors, parametric equations, and polar coordinates practice set has 18 questions. If 11 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Precalculus unit "Vectors, parametric equations, and polar coordinates"?
Use zeros, multiplicity, end behavior, asymptotes, and factoring.Use domain, range, composition, inverse functions, and transformations.Represent magnitude, direction, motion, and polar graphs.Compare functions from formulas, graphs, and tables.
Practice artifact
Which practice artifact should you produce for "Vectors, parametric equations, and polar coordinates" before asking a tutor for help?
Describe a motion path with parametric equations and interpret the parameter.Skip the unit and start a new subject.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.
08
Sequences, series, and induction preview
- Use arithmetic and geometric sequences and finite/infinite series.
- Recognize recursive definitions and convergence basics.
Practice: Compare explicit and recursive models for the same sequence.
Unit work plan
1. 1
  Source study
  Start with Precalculus 2e and OpenStax Math. Take notes until you can explain: Use arithmetic and geometric sequences and finite/infinite series.
2. 2
  Worked attempt
  Produce the assignment artifact: Compare explicit and recursive models for the same sequence.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Recognize recursive definitions and convergence basics.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Sequences, series, and induction preview practice set has 19 questions. If 12 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Precalculus unit "Sequences, series, and induction preview"?
Use zeros, multiplicity, end behavior, asymptotes, and factoring.Compare functions from formulas, graphs, and tables.Use domain, range, composition, inverse functions, and transformations.Recognize recursive definitions and convergence basics.
Practice artifact
Which practice artifact should you produce for "Sequences, series, and induction preview" before asking a tutor for help?
Watch videos without writing or solving anything.Skip the unit and start a new subject.Memorize vocabulary without checking any examples.Compare explicit and recursive models for the same sequence.
09
Calculus readiness
- Preview limits, rates of change, and accumulation.
- Diagnose remaining algebra and trig gaps.
Practice: Complete a mixed readiness audit and write a targeted repair plan before starting derivatives.
Unit work plan
1. 1
  Source study
  Start with Precalculus 2e and OpenStax Math. Take notes until you can explain: Preview limits, rates of change, and accumulation.
2. 2
  Worked attempt
  Produce the assignment artifact: Complete a mixed readiness audit and write a targeted repair plan before starting derivatives.
3. 3
  Checked answers
  Complete the PeerTutor checks below and correct misses before moving on.
4. 4
  Tutor handoff
  Bring your attempted work, the exact missed check, and one question about: Diagnose remaining algebra and trig gaps.
Original practice checks
Answer in PeerTutor, then use the explanation or bring the miss to a tutor.
4 checked answers
Quantitative warmup
A Calculus readiness practice set has 20 questions. If 13 are complete, how many remain?
Mathematical reasoning
Which habit best fits a serious math solution?
show steps and check the result in contextcopy only the final answerignore units and domainskip the hard cases
Unit readiness
Which target best matches the Precalculus unit "Calculus readiness"?
Use zeros, multiplicity, end behavior, asymptotes, and factoring.Use domain, range, composition, inverse functions, and transformations.Compare functions from formulas, graphs, and tables.Preview limits, rates of change, and accumulation.
Practice artifact
Which practice artifact should you produce for "Calculus readiness" before asking a tutor for help?
Complete a mixed readiness audit and write a targeted repair plan before starting derivatives.Watch videos without writing or solving anything.Memorize vocabulary without checking any examples.Skip the unit and start a new subject.

Source library

These are source links, not scraped course copies. Licenses differ, so the label tells students how each source is used.

View the full citation index

Precalculus 2e

OpenStax

Open textbook - CC BY-NC-SA 4.0

Functions, trigonometry, analytic geometry, sequences, series, and readiness for calculus.

OpenStax Math

OpenStax

Open textbook - CC BY-NC-SA 4.0

Free math textbooks including Algebra 1, Calculus, Statistics, and Principles of Data Science.

Introductory science and math courses

MIT OpenCourseWare

Open courseware - Creative Commons

College-level calculus, physics, chemistry, biology, and related introductory material.

FlexBook textbooks and concepts

CK-12 Foundation

Free educational link-out - CK-12 terms

STEM FlexBooks, bite-size concepts, practice, and standards-aligned textbook paths; linked rather than republished.

Precalculus curriculum