AP Precalculus · COVERAGE & GAPS

AP Precalculus: Coverage Map & Learning Gaps

Foundation pilot for AP Precalculus assessed Units 1–3; Unit 4 explicitly listed outside scope

A partial map, not a completion score.

Topic codes/titles verified against official Course at a Glance PDF pp1–2; topic-level mapping, not an assertion that every CED learning objective is covered. No coverage percentage inferred from counts.

Mapping describes the available practice, not your mastery or readiness for the exam. Reviewed 2026-10-26.

58Objectives in this map

43Have partial practice

15Have no mapped practice

AP Precalculus course and syllabus AP Precalculus Course at a Glance

Official reference 1.1

Change in Tandem

Partial practice

2 linked question families · 10 variants. Variants are not separate syllabus objectives.

What still needs work

Only discrete evaluation and transformed points; covariation explanations need broader contexts.

Function change and transformations

AP Precalculus Course at a Glance

Official reference 1.2

Rates of Change

Partial practice

1 linked question families · 5 variants. Variants are not separate syllabus objectives.

What still needs work

Secant rates on selected intervals only; qualitative rate comparisons remain limited.

Function change and transformations

AP Precalculus Course at a Glance

Official reference 1.3

Rates of Change in Linear and Quadratic Functions

Partial practice

3 linked question families · 14 variants. Variants are not separate syllabus objectives.

What still needs work

No complete rate-graph interpretation or unknown quadratic model construction.

Function change and transformations Select and interpret a model

AP Precalculus Course at a Glance

Official reference 1.4

Polynomial Functions and Rates of Change

Partial practice

6 linked question families · 30 variants. Variants are not separate syllabus objectives.

What still needs work

Added sign intervals and multiplicity reasoning. Higher-order differences, comparisons of polynomial rates, and qualitative rate-graph arguments remain missing.

Polynomial structure and end behavior Use multiplicity and signs without expanding

AP Precalculus Course at a Glance

Official reference 1.5

Polynomial Functions and Complex Zeros

Partial practice

9 linked question families · 41 variants. Variants are not separate syllabus objectives.

What still needs work

Added conjugate pairing, minimum-degree reasoning and coefficient reconstruction. General complex-root solving beyond selected quadratic patterns and complete polynomial solving remain missing.

Zeros, factors and remainders Reconstruct real polynomials from complex zeros Use multiplicity and signs without expanding

AP Precalculus Course at a Glance

Official reference 1.6

Polynomial Functions and End Behavior

Partial practice

3 linked question families · 15 variants. Variants are not separate syllabus objectives.

What still needs work

Added leading-term ratio and odd/even multiplicity behavior. Both-tail descriptions across varied degrees and graph-to-rule reconstruction remain incomplete.

Polynomial structure and end behavior Use multiplicity and signs without expanding

AP Precalculus Course at a Glance

Official reference 1.7

Rational Functions and End Behavior

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Added polynomial-division slant intercepts. General unequal-degree rational behavior, nonlinear polynomial asymptotes and graph justification remain missing.

Rational functions and restrictions Separate holes from vertical and slant asymptotes

AP Precalculus Course at a Glance

Official reference 1.8

Rational Functions and Zeros

Partial practice

4 linked question families · 16 variants. Variants are not separate syllabus objectives.

What still needs work

Added rational-equation domain rejection and inequalities. Full zero multiplicity analysis, multiple exclusions and graph reconstruction remain incomplete.

Rational functions and restrictions Separate holes from vertical and slant asymptotes Solve rational equations with admissible inputs

AP Precalculus Course at a Glance

Official reference 1.9

Rational Functions and Vertical Asymptotes

Partial practice

1 linked question families · 4 variants. Variants are not separate syllabus objectives.

What still needs work

Added vertical-asymptote identification after one common-factor cancellation. One-sided behavior, repeated poles and multiple-asymptote graphs remain missing.

Separate holes from vertical and slant asymptotes

AP Precalculus Course at a Glance

Official reference 1.10

Rational Functions and Holes

Partial practice

3 linked question families · 12 variants. Variants are not separate syllabus objectives.

What still needs work

Added hole-height calculation with one canceled factor. Multiple holes, repeated-factor distinctions and reconstructing a rational rule from its graph remain missing.

Rational functions and restrictions Separate holes from vertical and slant asymptotes

AP Precalculus Course at a Glance

Official reference 1.11

Equivalent Representations of Polynomial and Rational Expressions

Partial practice

5 linked question families · 20 variants. Variants are not separate syllabus objectives.

What still needs work

Added rational simplification and domain-aware equations. Larger polynomial division, multiple-factor algebra and symbolic equivalence proofs remain incomplete.

Zeros, factors and remainders Rational functions and restrictions Solve rational equations with admissible inputs

AP Precalculus Course at a Glance

Official reference 1.12

Transformations of Functions

Partial practice

2 linked question families · 10 variants. Variants are not separate syllabus objectives.

What still needs work

Horizontal/vertical shifts and vertical stretches only; composition of general transformations incomplete.

Function change and transformations

AP Precalculus Course at a Glance

Official reference 1.13

Function Model Selection and Assumption Articulation

Partial practice

3 linked question families · 12 variants. Variants are not separate syllabus objectives.

What still needs work

Small tables and residual definitions only; assumption justification is mostly manual extension.

Select and interpret a model

AP Precalculus Course at a Glance

Official reference 1.14

Function Model Construction and Application

Partial practice

2 linked question families · 9 variants. Variants are not separate syllabus objectives.

What still needs work

Only simple linear reconstruction and output changes; realistic model construction incomplete.

Function change and transformations Select and interpret a model

AP Precalculus Course at a Glance

Official reference 2.1

Change in Arithmetic and Geometric Sequences

Partial practice

4 linked question families · 16 variants. Variants are not separate syllabus objectives.

What still needs work

Term and short sum calculations only; general recursive reasoning is absent.

Sequences as discrete models

AP Precalculus Course at a Glance

Official reference 2.2

Change in Linear and Exponential Functions

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Simple constant rates and ratios; comparative long-run analysis missing.

Select and interpret a model

AP Precalculus Course at a Glance

Official reference 2.3

Exponential Functions

Partial practice

4 linked question families · 16 variants. Variants are not separate syllabus objectives.

What still needs work

Growth/decay values and factor identification only; graphs and domains incomplete.

Exponential growth and decay

AP Precalculus Course at a Glance

Official reference 2.4

Exponential Function Manipulation

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Simple period conversion only; broad equivalent-base manipulation absent.

Exponential growth and decay

AP Precalculus Course at a Glance

Official reference 2.5

Exponential Function Context and Data Modeling

Partial practice

6 linked question families · 24 variants. Variants are not separate syllabus objectives.

What still needs work

Added fitting from non-unit intervals and strict target-time questions. No noisy-data regression, parameter uncertainty or empirical validation of realistic growth assumptions.

Exponential growth and decay Fit and compare exponential models from separated observations

AP Precalculus Course at a Glance

Official reference 2.6

Competing Function Model Validation

Partial practice

3 linked question families · 12 variants. Variants are not separate syllabus objectives.

What still needs work

Added linear versus exponential midpoint predictions. Broader residual-pattern analysis across several observations, fitted model comparison and contextual assumption justification remain incomplete.

Select and interpret a model Fit and compare exponential models from separated observations

AP Precalculus Course at a Glance

Official reference 2.7

Composition of Functions

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Two explicit rules at specified inputs; domains and graphical compositions incomplete.

Compose and reverse functions

AP Precalculus Course at a Glance

Official reference 2.8

Inverse Functions

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Affine inverses and restricted squares only; general one-to-one justification missing.

Compose and reverse functions

AP Precalculus Course at a Glance

Official reference 2.9

Logarithmic Expressions

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Integer powers and one product-rule sum only; irrational values and change of base missing.

Logarithms as inverse questions

AP Precalculus Course at a Glance

Official reference 2.10

Inverses of Exponential Functions

Partial practice

1 linked question families · 4 variants. Variants are not separate syllabus objectives.

What still needs work

Simple exponential/log conversion only; graphical inverse relationships missing.

Logarithms as inverse questions

AP Precalculus Course at a Glance

Official reference 2.11

Logarithmic Functions

Partial practice

1 linked question families · 4 variants. Variants are not separate syllabus objectives.

What still needs work

Shifted input evaluation only; domain/range and behavior analysis incomplete.

Logarithms as inverse questions

AP Precalculus Course at a Glance

Official reference 2.12

Logarithmic Function Manipulation

Partial practice

3 linked question families · 12 variants. Variants are not separate syllabus objectives.

What still needs work

Added log product/quotient equations with original domains. General variable-expression expansion/condensation and change-of-base applications remain missing.

Logarithms as inverse questions Solve logarithmic equations and inequalities with domains

AP Precalculus Course at a Glance

Official reference 2.13

Exponential and Logarithmic Equations and Inequalities

Partial practice

6 linked question families · 24 variants. Variants are not separate syllabus objectives.

What still needs work

Added positive-base exponential equations and base-two logarithmic inequalities with integer-domain counts. Bases between0and1, continuous solution-set notation, unequal-base numerical solving and nontrivial exponential inequalities remain missing.

Logarithms as inverse questions Solve logarithmic equations and inequalities with domains

AP Precalculus Course at a Glance

Official reference 2.14

Logarithmic Function Context and Data Modeling

Not yet covered

What still needs work

No dedicated logarithmic data-modeling family.

AP Precalculus Course at a Glance

Official reference 2.15

Semi-log Plots

Partial practice

4 linked question families · 16 variants. Variants are not separate syllabus objectives.

What still needs work

Added decoding straight lines on log-y axes and original-output interpolation. Constructing semi-log plots from noisy data, changing log bases and judging approximate linearity remain incomplete.

Read multiplicative change on a semi-log display

AP Precalculus Course at a Glance

Official reference 3.1

Periodic Phenomena

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Extrema and midline foundations only; contextual periodicity arguments incomplete.

Read a sinusoidal model

AP Precalculus Course at a Glance

Official reference 3.2

Sine, Cosine, and Tangent

Partial practice

4 linked question families · 16 variants. Variants are not separate syllabus objectives.

What still needs work

Basic angle conversion and special values only; full unit-circle reasoning incomplete.

Angles and the unit circle

AP Precalculus Course at a Glance

Official reference 3.3

Sine and Cosine Function Values

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Selected first-quadrant and half-turn values only; all-quadrant fluency incomplete.

Angles and the unit circle Read a sinusoidal model

AP Precalculus Course at a Glance

Official reference 3.4

Sine and Cosine Function Graphs

Partial practice

3 linked question families · 12 variants. Variants are not separate syllabus objectives.

What still needs work

One extrema graph and period computation; full graph transformation work missing.

Read a sinusoidal model

AP Precalculus Course at a Glance

Official reference 3.5

Sinusoidal Functions

Partial practice

4 linked question families · 16 variants. Variants are not separate syllabus objectives.

What still needs work

Read simple parameters; model selection and equation fitting incomplete.

Read a sinusoidal model

AP Precalculus Course at a Glance

Official reference 3.6

Sinusoidal Function Transformations

Partial practice

4 linked question families · 16 variants. Variants are not separate syllabus objectives.

What still needs work

Added phase anchoring and period recovery from peaks. Combined nonstandard transformations and graph-to-equation ambiguity remain incomplete.

Read a sinusoidal model Fit phase and frequency from observed peaks

AP Precalculus Course at a Glance

Official reference 3.7

Sinusoidal Function Context and Data Modeling

Partial practice

4 linked question families · 16 variants. Variants are not separate syllabus objectives.

What still needs work

Added sinusoid fitting from extrema and timing plus phase-dependent first midline crossings. No noisy periodic-data fit, model validity assessment or extended free-response context.

Read a sinusoidal model Fit phase and frequency from observed peaks

AP Precalculus Course at a Glance

Official reference 3.8

The Tangent Function

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Added counting tangent zeros on intervals. Tangent graph construction, asymptote locations and transformed tangent functions remain missing.

Angles and the unit circle Enumerate trigonometric solutions on a stated interval

AP Precalculus Course at a Glance

Official reference 3.9

Inverse Trigonometric Functions

Partial practice

4 linked question families · 16 variants. Variants are not separate syllabus objectives.

What still needs work

Added principal-value compositions and inverse evaluation. General inverse-trig graphs, transformed domains and applied angle recovery beyond special values remain incomplete.

Respect the principal range of an inverse trigonometric function

AP Precalculus Course at a Glance

Official reference 3.10

Trigonometric Equations and Inequalities

Partial practice

4 linked question families · 16 variants. Variants are not separate syllabus objectives.

What still needs work

Added interval-dependent sine/cosine/tangent solving and one sinusoidal midline inequality duration. General trigonometric inequalities, non-special-angle numerical roots and compound identities in solving remain missing.

Enumerate trigonometric solutions on a stated interval Fit phase and frequency from observed peaks

AP Precalculus Course at a Glance

Official reference 3.11

The Secant, Cosecant, and Cotangent Functions

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Added exact reciprocal-function values with signs. Secant/cosecant/cotangent graphs, their asymptotes and transformed domains remain missing.

Use reciprocal identities with quadrant signs

AP Precalculus Course at a Glance

Official reference 3.12

Equivalent Representations of Trigonometric Functions

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Added Pythagorean and reciprocal identities with quadrant choice. Symbolic identity proofs, broader equivalent forms and identities inside equations remain incomplete.

Use reciprocal identities with quadrant signs

AP Precalculus Course at a Glance

Official reference 3.13

Trigonometry and Polar Coordinates

Partial practice

5 linked question families · 20 variants. Variants are not separate syllabus objectives.

What still needs work

Added non-axis polar conversion and negative-radius equivalents. General-angle conversions, inverse coordinate recovery and multiple-equivalence descriptions remain incomplete.

Polar coordinates and equivalent points Connect polar curves, directed radii and rates

AP Precalculus Course at a Glance

Official reference 3.14

Polar Function Graphs

Partial practice

2 linked question families · 8 variants. Variants are not separate syllabus objectives.

What still needs work

Added constant-radius circle area and interpretation of r=a cosθ through Cartesian conversion. Full polar sketches, symmetry, negative radii on extended curves and general rose/limacon behavior remain missing.

Polar coordinates and equivalent points Connect polar curves, directed radii and rates

AP Precalculus Course at a Glance

Official reference 3.15

Rates of Change in Polar Functions

Partial practice

1 linked question families · 4 variants. Variants are not separate syllabus objectives.

What still needs work

Added average radial change on one angular interval. Comparing radial versus Cartesian rates across varied functions and graphical rate interpretation remain missing.

Connect polar curves, directed radii and rates

AP Precalculus Course at a Glance

Official reference 4.1

Parametric Functions

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.2

Parametric Functions Modeling Planar Motion

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.3

Parametric Functions and Rates of Change

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.4

Parametrically Defined Circles and Lines

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.5

Implicitly Defined Functions

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.6

Conic Sections

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.7

Parametrization of Implicitly Defined Functions

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.8

Vectors

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.9

Vector-Valued Functions

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.10

Matrices

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.11

The Inverse and Determinant of a Matrix

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.12

Linear Transformations and Matrices

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.13

Matrices as Functions

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Official reference 4.14

Matrices Modeling Contexts

Not yet covered

What still needs work

Unit 4 is part of the course framework but is not assessed on the AP exam; intentionally outside this pilot.

AP Precalculus Course at a Glance

Use the map with care.

All included objectives remain partial: a few families do not establish topic mastery.
96 parameterised families do not equal 400 independently designed tasks.
Written extensions are original self-assessment rubrics, not official AP scoring.

PLAN YOUR NEXT STEP

A clear route through the material

Compare the topics included in this foundation path with your exam requirements. Question variants are counted separately from task families; the map makes remaining gaps and review limitations visible.

Continue your preparation

Scope: Function reasoning foundations