Lernziele:

1. Factor quadratics, finding their roots, relating their coefficents to their roots, utilize the discriminant, and apply completing the square to find vertices and roots. Solving quadratic inequalities and writing down the solution in the form of intervals. Solving a system of quadratic equations up to three variables simultaneously.

2. Graphing parabolas and finding their vertices and axes of sysmmetry both algebraically and geometrically. Converting a Parabola equation from the vertex form to the standard form and vice versa.

3. Graphing Circles, determining its center coordinates algebrically from the circle equation

4. Graphing ellipses, and hyperbolas using foci, directrices, axes, and asymptotes.

5. Derive standard equations for conics centered at (0,0) and translated to (h,k).

Module

Lernziele:

1. Execute long and synthetic division for various divisors.

2. Apply the Remainder and Factor Theorems to evaluate polynomials and verify roots.

3. State the Fundamental Theorem of Algebra.

Module

Lernziele:

1. Use the Rational Root Theorem and Descartes' Rule of Signs to identify root candidates.

2. Apply Radical Conjugate Root Theorems to identify irrational roots.

3. Calculate bounds on roots using synthetic division sign patterns.

4. Stating and proving the Complex Conjugate root theorem and how to utilize it in finding other roots of a given Polynomial.

Module

Lernziele:

1. Calculate elementary symmetric sums directly from polynomial coefficients for any degree.

2. Express higher-power sums and reciprocals of roots in terms of elementary symmetric polynomials.

3. Reconstruct or transform polynomials based on root data and transformations (e.g., y = x + k).

Module

Lernziele:

1. Apply the Method of Undetermined Coefficients to determine unknown polynomial parameters.

2. Factor multivariable polynomials using grouping, Simon's Favorite Factoring Trick, and nth power identities.

3. Identify common divisors and roots between polynomials through linear combinations and scaling.

Module

Lernziele:

1. Derive closed forms for arithmetic, geometric, and periodic recursive sequences.

2. Evaluate finite and infinite geometric series and simplify telescoping sums using partial fractions.

Module

Lernziele:

1. Formulate base cases and inductive steps to prove integer-based identities and inequalities.

2. Expand binomial expressions using the Binomial Theorem and Pascal's Identity.

3. Apply binomial coefficients to solve coefficient-finding problems.

Module

Lernziele:

1. Utilize the AM-GM Inequality and Cauchy-Schwarz Inequality for multivariable algebraic proofs.

2. Finding Minima-Maxima of some algebraic expresions up to two variables using some basic inequalities such as AM-GM and Cauchy-Schwarz inequalities.

Module

Lernziele:

1. Solve multi-step logarithmic and exponential equations using base conversion and identities.

2. Simplify nested radicals and rationalize complex denominators using radical conjugates.

3. Converting between different bases in Logarithmic problems

4. Stating and proving different Logarithmic identities.

Module

Lernziele:

1. Stating different properties of rational functions and graphing rational functions.

2. Determine whether a given function is odd or even or neither of both

3. Determine which functions can be expressed as the summation of an odd function and an even function.

4. Determine whether some functions are monotonically increasing or decreasing.

5. Finding the maxima or minima of some algebraic expressions by using inequalities, peroperties of strictly monotonic functions, and some algebraic manipulations.

Module

Lernziele:

1. Solve absolute value equations and inequalities through piecewise casework and geometric distance interpretation.

2. Manipulate floor, ceiling, and fractional part functions using inequality chains (n <= x < n+1).

Module

Lernziele:

1. Solve functional equations through strategic value substitution (0, 1, -1) and degree determination.

2. Handle cyclic functions and multi-variable systems using homogenization and symmetry.

Module