FAQ Coverage Gaps
Concepts from the learning graph not yet covered by any FAQ question, as of 2026-07-10. Coverage: 225/307 concepts (73.3%). Priority is based on in-degree centrality in the learning graph (how many other concepts depend on this one).
Critical Gaps (High Priority)
High-centrality concepts (in-degree ≥ 4) without FAQ coverage:
- Angle Definition (in-degree 5)
- Category: Trigonometry foundations
- Note: touched indirectly by the radian-measure and unit-circle questions, but has no dedicated question.
- Suggested question: "What is an angle in standard position?"
All other high-centrality concepts are covered.
Medium Priority Gaps
Medium-centrality concepts (in-degree 2–3) without FAQ coverage:
| Concept | Suggested Question |
|---|---|
| Factoring Polynomials | "How do I factor a polynomial?" |
| Exponential Equations | "How do I solve an exponential equation?" |
| Trig Function Evaluation | "How do I evaluate trig functions without a calculator?" |
| Tangent Graph | "What does the graph of the tangent function look like?" |
| Periodic Data Analysis | "How do I recognize periodic behavior in data?" |
| Slope Formula | Covered implicitly by "What is average rate of change?" |
| Positive and Negative Regions | "How do I find where a function is positive or negative?" |
| Variables and Expressions | Prerequisite review — low FAQ value |
| Number Line | Prerequisite review — low FAQ value |
| Order of Operations | Prerequisite review — low FAQ value |
| Independent Variable | Covered implicitly by function-definition questions |
| Reflection Over Y-Axis | Covered implicitly by transformation questions |
Low Priority Gaps
69 low-centrality concepts (in-degree ≤ 1) are uncovered. These are mostly leaf concepts — specific formulas, graph variants, and mechanical skills — that are well served by chapter content and glossary entries rather than FAQ answers. Grouped by theme:
- Polynomial arithmetic mechanics: Polynomial Addition, Polynomial Multiplication, Long Division of Polynomials, Synthetic Division, Remainder Theorem, Intermediate Value Theorem, Simplifying Rational Expr, Rational Inequalities
- Function behavior labels: Increasing Functions, Decreasing Functions, Constant Functions, Bounded Functions, Positive and Negative Regions, Local/Global Maximum and Minimum, Piecewise Functions, Change in Tandem, Linear Rate of Change, Rate of Change Units, Dependent Variable
- Transformation details: Vertical Compression, Writing Transformed Eqns, Exponential Transformations, Logarithmic Transformations, Graphing Trig Transformations, Vertical Shift of Trig
- Sequence details: Geometric Sequence Formula, Sequence Convergence, Sequence Divergence
- Exponential/log modeling details: Exponential Modeling, Logarithmic Modeling, Percent Rate of Change, Interpolation
- Identity formulas: Reciprocal Identities, Quotient Identities, Cofunction Identities, Even-Odd Identities, Sum and Difference Formulas, Double Angle Formulas
- Trig graph variants: Secant Graph, Cosecant Graph, Cotangent Graph, Period of Tangent, Asymptotes of Tangent, Quadrantal Angles, Inverse Trig Graphs, Composing Trig Inverses, Multiple Angle Equations, Trig Inequalities, Sector Area
- Sinusoidal model instances: Temperature Models, Daylight Hour Models, Sinusoidal Regression
- Polar/parametric details: Polar Function Definition, Circles in Polar Form, Polar Rate of Change, Polar Graph Intersections, Eliminating the Parameter, Velocity from Parametrics, Direction of Motion
- Vector/matrix details: Scalar Multiplication, Vector Subtraction, Dot Product, Vector Applications, Inverse of a Matrix, Matrix Applications
- Inverse function mechanics: Finding Inverses Algebraically, Decomposing Functions
Recommendations
- Add one question for the single critical gap (Angle Definition).
- Add questions for the 5–6 medium-priority gaps with genuine FAQ value (factoring, exponential equations, trig evaluation, tangent graph, positive/negative regions).
- Address identity-formula gaps with one consolidated "which identity do I use when?" question rather than one question per formula.
- Leave prerequisite-review and leaf-concept gaps to chapter content and the glossary; forcing FAQ questions for them would dilute quality.