Honors
Pre-calculus · Honors · High school · Math
Topics typically covered in Pre-calculus · Honors, grouped by unit. Click a topic for the full text and study materials — the same components as K–12 standards pages.
Standards
Click a standard for the full text and study materials.
Functions
- 1.1 — Use function notation. Evaluate and interpret functions using function notation in algebraic and contextual settings.
- 1.2 — Interpret functions. Interpret function notation and relate inputs and outputs in context.
- 1.3 — Domain and range. Determine domain and range from formulas, graphs, and contexts.
- 1.4 — Analyze average rates of change. Calculate and interpret average rates of change over specified intervals.
- 1.5 — Features of graphs. Identify intercepts, extrema, intervals, symmetry, and end behavior from function graphs.
- 1.6 — Composition, transformations, and inverses. Compose functions, transform their graphs, and determine inverse functions.
- 1.7 — Advanced function analysis. Compare rates of change across function families; analyze piecewise domains carefully.
Linear, polynomial, and rational functions
- 2.1 — Linear functions and modeling. Build and interpret linear models.
- 2.2 — Complex numbers and quadratics. Operate with complex numbers; analyze quadratic functions.
- 2.3 — Analyze power functions. Analyze the graphs, domains, ranges, and end behavior of power functions.
- 2.4 — Polynomial functions. Analyze polynomial functions using their degree, zeros, extrema, and end behavior.
- 2.5 — Rational and radical functions. Graph rational functions; work with inverses and radicals; model with variation.
- 2.6 — Connect complex zeros and factorizations. Connect the complex zeros of a polynomial to its linear and quadratic factors.
- 2.7 — Polynomial degree. Determine a polynomial's degree and connect it to possible zeros and end behavior.
Exponential and logarithmic functions
- 3.1 — Exponential functions and graphs. Define and graph exponential functions.
- 3.2 — Logarithmic functions and properties. Define logs; use logarithmic properties.
- 3.3 — Solve exponential and logarithmic equations. Solve exponential and logarithmic equations using inverse relationships and logarithm properties.
- 3.4 — Logarithmic models to data. Fit logarithmic models to data and interpret their parameters in context.
Trigonometry
- 4.1 — Angles and the unit circle. Work in degrees and radians; evaluate trig functions on the unit circle.
- 4.2 — Solve right triangles. Use trigonometric ratios and the Pythagorean theorem to find unknown sides and angles.
- 4.3 — Applications of right-triangle trigonometry. Use right-triangle trigonometry to solve contextual problems involving lengths and angles.
- 4.4 — Graph sinusoidal functions. Graph sine and cosine functions using amplitude, period, phase shift, and vertical shift.
- 4.5 — Other trig functions with transformations. Graph transformations of tangent, cotangent, secant, and cosecant functions.
- 4.6 — Identities and trig equations. Verify identities; solve trigonometric equations.
- 4.7 — Further applications. Apply laws of sines and cosines; introduce polar form and vectors as needed.
- 4.8 — Graph polar equations. Graph polar equations and analyze their symmetry and key features.
- 4.9 — Parametric curves beyond the basics. Analyze parametric curves, their orientation, and their relationships to rectangular equations.
Systems, matrices, and analytic geometry
- 5.1 — Systems of equations and inequalities. Solve linear and nonlinear systems; introduce matrices.
- 5.2 — Conic sections. Analyze ellipses, hyperbolas, and parabolas algebraically and graphically.
- 5.3 — Vectors and matrices (intro). Perform vector operations and basic matrix work for systems.
- 5.4 — Matrix methods for systems. Solve systems with matrices, including inverses and Gaussian elimination (intro).
Sequences, probability, and counting
- 6.1 — Sequences and series. Work with arithmetic and geometric sequences and series.
- 6.2 — Mathematical induction (intro). Use a base case and inductive step to prove simple statements about positive integers.
- 6.3 — Use permutations and combinations. Choose and apply permutations or combinations to solve counting problems.
- 6.4 — Basic probability models. Build and use basic probability models for chance experiments.
Introduction to calculus
- 7.1 — Estimate limits from tables. Estimate one-sided and two-sided limits using tables of function values.
- 7.2 — Graphs of sequences. Represent sequences graphically and connect graphs to recursive and explicit forms.
- 7.3 — Limit properties and continuity. Apply limit laws; determine continuity at a point.
- 7.4 — Interpret the derivative as an instantaneous rate of change. Interpret the derivative as an instantaneous rate of change and a tangent-line slope.
- 7.5 — Slope of a tangent line. Estimate or calculate the slope of a tangent line as an instantaneous rate of change.
- 7.6 — Use precise language for one-sided limits. Use precise notation and language to describe left-hand and right-hand limits.
- 7.7 — Continuity conditions. Determine whether a function is continuous at a point or over an interval.
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