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    • ▾Precalc
      • ▸Conic sections
        • •Intro to conic sections
        • •Center and radii of an ellipse
        • •Foci of an ellipse
        • •Intro to hyperbolas
        • •Foci of a hyperbola
        • •Maximizing the product of two integers, given their integer sum
        • •Hyperbolas not centered at the origin
        • •Standard equation of a circle
      • ▸Functions and relations
        • •Composition of functions
        • •Operations with functions
        • •Graphing the sum of trig functions from their graphs
        • •Finding and verifying the inverse of a nonlinear function
        • •Graphically finding the increasing, decreasing, and constant intervals
        • •Vertical and horizontal line tests
        • •Restrict the domain then find the inverse
        • •Sketching the inverse of a function from its graph
      • ▸Characteristics of functions
        • •Finding extrema graphically
        • •End behavior
      • ▾Rational functions
        • •Partial fraction decomposition
        • •Simplifying the difference quotient
        • •Pick's theorem
      • ▸Sigma notation and the binomial theorem
        • •Converting sums between sigma notation and expanded form
        • •Properties of sigma notation
        • •Using the binomial theorem
      • ▸Series
        • •Geometric series
        • •Geometric series with summation notation
        • •Arithmetic series with summation notation
      • ▸Logic
        • •De Morgan's laws for propositional logic
     › Precalc › Rational functions

    Partial fraction decomposition

    Students will learn how to perform partial fraction decomposition with linear factors, repeated linear factors, quadratic factors, repeated quadratic factors, and improper fractions, in that order. They'll also learn how to use the cover-up method, which is a fast method for algebraic fractions with linear factors, whether repeated or not. After that, students will learn why the cover-up method works. Before attempting this section, students must know how to perform polynomial long division, and how to factor a wide variety of polynomials, using various methods, such as factor by grouping, difference of squares, etc.

    Conclude by giving your students these challenges:

    • Playground Snapshot by NRICH
    • Bicentric Quadrilaterals by NRICH
    • Squares, Squares and More Squares by NRICH
    • Angle Trisection by NRICH
    • 2003 AMC 8, Problem 19

    Lessons and practice problems