Core mathematics
Integrated Math 3 Honors
Polynomials, trigonometry, and polar and parametric curves, ending at the doorstep of calculus.
2 units · 19 lessons · 391 practice items · 22 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 second unit turns to rational functions. The units that follow will take up 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
- 1Comparing growth rates of linear, quadratic, and cubic functions
- 2Ordering functions from slowest to fastest growing as x approaches infinity
- 3Understanding and comparing end behavior across representations
- 4Adding, subtracting, and multiplying polynomials graphically
- 5The nature of roots and the Fundamental Theorem of Algebra
- 6Binomial expansion with Pascal's triangle
- 7Applying the Fundamental Theorem of Algebra; box-method division
- 8The Remainder Theorem: finding all linear factors and roots, part 1
- 9The Remainder Theorem part 2: conjugate pairs and least-degree polynomials
- 10Practicing all things polynomial: graphing and solving
- 11Unit 1 test
2Rational functions8 lessons
- 1Rational expressions as rational numbers; operations
- 2Solving rational equations and inequalities graphically and algebraically
- 3Identifying features of rational functions
- 4Rewriting improper rational expressions in mixed form via division
- 5Even and odd functions; end behavior of rational functions
- 6Graphing rational functions using features and sign lines
- 7Graphing rational functions: holes, repeated factors, and slant asymptotes
- 8Unit 2 test