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Core mathematics

Integrated Math 3 Honors

Polynomials, trigonometry, and polar and parametric curves, ending at the doorstep of calculus.

1 unit · 11 lessons · 245 practice items · 76 videos

Integrated Math 3 Honors finishes the honors integrated pathway. The opening unit studies polynomial functions: comparing growth rates, reading end behavior from formulas, graphs, and tables, adding and multiplying functions graphically, the fundamental theorem of algebra, binomial expansion, and the remainder theorem. The units that follow will take up rational functions, modeling with geometry, and trigonometry across the first semester, then modeling with functions, polar and parametric curves, and statistics, and the closing unit will introduce limits and the derivative, the step into calculus.

Much of the practice is drawn on axes: you sketch the polynomial yourself, and a sketch grades as correct only when it crosses the axis at odd-multiplicity roots, bounces at even ones, and carries the right end behavior. Alongside the sketches come expressions entered in math notation, functions ordered by growth rate, and values placed on graphs and tables, with short videos folded into the reading. As everywhere on the pathway, a skill closes after four correct answers in a row against its bank, and the unit test draws from the same pools.

Syllabus

Every published lesson in this course, by unit. Upcoming units fill in as their lessons publish.

1Polynomial functions11 lessons
  1. 1Comparing growth rates of linear, quadratic, and cubic functions
  2. 2Ordering functions from slowest to fastest growing as x approaches infinity
  3. 3Understanding and comparing end behavior across representations
  4. 4Adding, subtracting, and multiplying polynomials graphically
  5. 5The nature of roots and the Fundamental Theorem of Algebra
  6. 6Binomial expansion with Pascal's triangle
  7. 7Applying the Fundamental Theorem of Algebra; box-method division
  8. 8The Remainder Theorem: finding all linear factors and roots, part 1
  9. 9The Remainder Theorem part 2: conjugate pairs and least-degree polynomials
  10. 10Practicing all things polynomial: graphing and solving
  11. 11Unit 1 test
2Rational functionsUpcoming
3Modeling with geometryUpcoming
4Trigonometric functionsUpcoming
ExamSemester 1 finalUpcoming
5Modeling with functionsUpcoming
6Polar and parametric functionsUpcoming
7StatisticsUpcoming
8Limits and introduction to derivativesUpcoming
ExamSemester 2 finalUpcoming