Integrated Math III
High school · Math
Available tracks
Topics typically covered
Click a topic for the full text and related unit practice.
Integrated Math III scope aligned to the Common Core integrated pathway (polynomial/rational functions, exponential and logarithmic functions, trigonometry, conics, and statistics), as used in California, Georgia, North Carolina, and similar state frameworks.
Polynomial and rational functions
- Polynomial graphs — Analyze end behavior, zeros, and multiplicities of polynomial functions
- Polynomial division — Use synthetic and long division; apply factor and remainder theorems
- Rational functions — Graph rational functions; identify asymptotes and holes
- Rational equations — Solve rational equations; check for extraneous solutions
Exponential and logarithmic functions
- Exponential models — Build and interpret exponential growth and decay models
- Logarithms — Convert between exponential and logarithmic form; evaluate logs
- Logarithm properties — Apply product, quotient, and power rules for logarithms
- Exponential and log equations — Solve exponential and logarithmic equations in one variable
Trigonometry
- The unit circle — Define trig functions on the unit circle; evaluate exact values
- Trigonometric graphs — Graph sine, cosine, and tangent; identify amplitude, period, and phase shift
- Trigonometric identities — Verify and apply Pythagorean and angle-sum identities
- Inverse trigonometric functions — Evaluate and graph inverse trig functions; solve basic trig equations
Conic sections
- Parabolas — Write equations of parabolas from focus-directrix definitions
- Circles and ellipses — Graph and write equations of circles and ellipses
- Hyperbolas — Graph hyperbolas; identify vertices, foci, and asymptotes
- Conic applications — Model orbits, optics, and design problems with conics
Statistics and modeling
- Normal distribution — Use mean and standard deviation to describe normal models; find z-scores
- Sampling distributions — Understand sample proportions and means; central limit idea (intro)
- Inference (intro) — Construct and interpret confidence intervals and simple hypothesis tests
- Model selection — Compare linear, exponential, and quadratic fits to data sets