Mathematics · Suggested grades 11–12

Precalculus and Trigonometry
Course map.

Investigate functions, polynomial and rational relationships, exponential/logarithmic models, trigonometry and sequences.

Grade ranges and the sequence below are suggestions, not graduation requirements. Choose by readiness and your school’s course plan.

Before this course

Algebra II function and equation skills.
Geometry, right-triangle relationships and comfort with graphs.

Where it can lead

Builds advanced algebraic and trigonometric reasoning for later mathematics and applied science. Some chosen standards carry the official (+) advanced-preparation marker.

A suggested progression

Function structure and composition
Exponential, logarithmic and rational models
Trigonometry and sequences

Six starter mini-lessons sample selected skills. This is not a full year of daily instruction, complete standards coverage, an accredited course or graduation credit. Grade placement and unit order are planning guidance, not requirements.

Unit → Lesson

Your learning path

3 units · 6 starter lessons

Unit 1: Functions, transformations and rational graphs

Predict graph features from algebraic structure.

Before this unit: Algebra II Domain and factoring

Transformations of a Function35 minutes · HSF.BF.B.3
Polynomial Zeros and Rational Graph Boundaries40 minutes · HSF.IF.C.7.c · HSF.IF.C.7.d (+)

Browse this unit →

Unit 2: Exponential inverses and the unit circle

Connect inverse relationships to angles and cyclic quantities.

Before this unit: Exponential functions Right-triangle ratios

Logarithms as Exponential Inverses35 minutes · HSF.BF.B.5 (+)
The Unit Circle Beyond One Turn35 minutes · HSF.TF.A.2

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Unit 3: Periodic models and finite sequences

Build models of repetition and accumulate geometric terms.

Before this unit: Radian measure Geometric sequences

A Sinusoidal Wheel-Height Model35 minutes · HSF.TF.B.5
Finite Geometric Sums in a Design35 minutes · HSA.SSE.B.4

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A course map. A practical starting point.

These 138 original mini-lessons sample 23 courses for grades 9–12. They do not provide a full year of daily lessons, complete standards coverage, accredited courses or graduation credit. Suggested grade ranges, prerequisites and unit order are planning guidance; school pathways and elective availability vary. Calculus is excluded.

Subject-content contribution identifies a selected math, English, science or world-language skill. Common Core high school math uses conceptual categories, not universally assigned courses or grades. Mapping a skill to a course is an instructional choice. (+) Additional preparation identifies standards the official source marks for advanced study.

English uses the 9–10 and 11–12 bands; there are no separate Common Core English 9, 10, 11 or 12 codes. NGSS references identify the high school band and partial performance-expectation contributions.

Supporting Common Core literacy connection applies only to an actual reading, writing or communication activity. It does not establish science, social studies or elective subject-content alignment. Unverified subject-content mappings are labeled explicitly.

Spanish uses World-Readiness language standards, identified by their official names in the current summary. Common Core does not measure Spanish proficiency. Supported lesson practice is distinct from an independently assessed proficiency rating and from the course title.

Use North Carolina’s Standard Course of Study ↗ for local planning. No NC alignment is claimed without a verified crosswalk. Each mapping links to official wording, records its verification date and explains the part practiced.