Public learning track
General Binomial Series and Rational Exponents
11th Grade · Math · Open Global Math
6 lessons
Goal
Expand (1 + x)ⁿ and (a + bx)ⁿ for any rational exponent n, determine radius of convergence, and perform numerical approximations.
Featured Diagrams
The General Binomial Theorem for Rational Exponents
6 lessons
0 of 6 done
- 1The General Binomial Theorem for Rational ExponentsUp nextStart
- 2Determining Validity and Convergence Conditions for Binomial SeriesPremiumNot started yet
- 3Expanding Expressions with Negative and Fractional ExponentsNot started yet
- 4Factoring Out Leading Constants in General Binomial ExpansionsNot started yet
- 5Approximating Roots and Fractions Using Binomial SeriesNot started yet
- 6Combining Partial Fractions with Binomial Series ExpansionsNot started yet
Standards Covered
- OGM.12.ALG.5Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Expand binomial expressions (a + bx)^n using Pascal's triangle, combinatorics (nCr, n!), and the general binomial series for any rational exponent n when |bx/a| < 1, using expansions for numerical approximation.
- OGM.12.ALG.2Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Decompose rational functions into partial fractions for denominators with non-repeated and squared linear factors (with at most three linear factors in total).
Curriculum Framework
11th Grade · Math · Open Global Math
1
9 lessons
Polynomial Theorems, Division, and Advanced Factoring
Master polynomial operations, algebraic long division, the Remainder and Factor Theorems, and factoring techniques for higher-degree polynomials.
2
5 lessons
Rational Expressions and Algebraic Fractions
Simplify, add, subtract, multiply, and divide complex rational expressions and simplify compound algebraic fractions.
3
6 lessons
Partial Fraction Decomposition
Decompose proper and improper rational expressions into partial fractions with distinct linear, repeated linear, and irreducible quadratic denominators.
4
6 lessons
Advanced Quadratic Forms, Discriminant, and Optimization
Analyze quadratic forms using discriminant analysis, solve equations reducible to quadratics, and optimize objective functions via completing the square.
5
6 lessons
Simultaneous Equations and Nonlinear Systems
Solve simultaneous linear and nonlinear systems in two variables algebraically and interpret solutions geometrically.
6
6 lessons
Linear and Quadratic Inequalities
Solve single-variable linear and quadratic inequalities, graph two-variable inequality regions, and express solution sets using interval and set notation.
7
5 lessons
Binomial Theorem with Positive Integers
Expand binomial expressions with positive integer powers using Pascal's triangle, combinatorics, and sigma notation.
8
6 lessons
General Binomial Series and Rational Exponents
Expand (1 + x)ⁿ and (a + bx)ⁿ for any rational exponent n, determine radius of convergence, and perform numerical approximations.