Topics covered by Infinite Precalculus in index order ----------------------------------------------------- Absolute value Complex numbers Adding Vectors Angles Measures of Reference Sketching Area Heron's Formula Of triangles using trig Area under a curve Approximating Using limit of sums Arithmetic mean Arithmetic sequences Arithmetic series Binomial Theorem Calculus, introduction Approximating area under a curve Area under a curve by limit of sums Definition of the derivative Indefinite integrals Instantaneous rates of change Limits at essential discontinuities Limits at infinity Limits at kinks and jumps Limits at removable discontinuities Limits by direct evaluation Motion along a line Power rule for differentiation Combinations Basics Probability Versus permutations Complex numbers Absolute value De Moivre's Theorem Division Euler's Formula Exponential form Graphing Multiplication Polar and rectangular form Powers of Roots of Compound interest Conic sections Circles, graphing & properties Circles, writing equations Ellipses, graphing & properties Ellipses, writing equations Hyperbolas, graphing & properties Hyperbolas, writing equations Parabolas, graphing & properties Parabolas, writing equations Rotations Conjugate Root Theorem Continuity Custom question De Moivre's Theorem Degrees Converting to radians Derivative, definition Descartes' Rule of Signs Determinants Dilations Functions Trig functions Discrete Mathematics Combinations Mathematical induction Permutations Permutations vs combinations Sample spaces and The Fundamental Counting Principle The Binomial Theorem Division Complex numbers Polynomials Synthetic Equations Exponential, not requiring logarithms Exponential, over complex numbers Exponential, requiring logarithms Logarithmic, properties not required Logarithmic, properties required Matrix Polynomial Rational Trig, factoring and fundamental identities Trig, Multiple-Angle Identities Trig, simple Euler's Formula Exponential functions And complex numbers Compound interest Equations not requiring logarithms Equations over complex numbers Equations requiring logarithms Graphing Functions Average rates of change Continuity Inverses Operations Piecewise Polynomial Power functions Power series Fundamental Theorem of Algebra Geometric mean Geometric sequences Geometric series Graphing Complex numbers Compositions of trig functions and their inverses Exponential functions Inverse trig functions Parabolas Piecewise functions Polar equations Polynomial functions Rational functions Transformations Trig functions Vectors Heron's Formula Identities Cofunction Identities Double-Angle Half-Angle Multiple-Angle Odd-Even Identities Product-to-Sum Pythagorean Sum and Difference Sum-to-Product Induction Inequalities Polynomial Rational Integrals, indefinite Law of Cosines Finding angles and sides Finding area Heron's Formula Law of Sines Finding angles and sides Finding area Lemniscates Limacons Limits At essential discontinuities At infinity At kinks and jumps At removable discontinuities By direct evaluation Logarithms And complex numbers Condensing Equations, properties not required Equations, properties required Evaluating Expanding Graphing Inverses of Properties of Rewriting Writing in terms of others Matrices Determinants Equations Inverses Operations Mean, arithmetic and geometric Multiplication Complex numbers Vectors multiplied by a scalar Parabolas Equations of Graphing Properties of Parametric equations Parametric equations Projectile motion Partial fraction decomposition Permutations Basics Probability Versus combinations Points in three dimensions Polar coordinates Graphs of polar equations Polar and rectangular forms of equations Polar coordinates Polar forms of conic sections Polynomial functions Bounds of real zeros Complex zeros Conjugate Root Theorem Conjugate roots Descartes' Rule of Signs Dividing End behavior Equations Fundamental Theorem of Algebra Graphing Inequalities Rational Root Theorem Real zeros Synthetic division Synthetic substitution The Remainder Theorem Writing functions Power functions Power series Powers of complex numbers Probability Independent and dependent events Independent and dependent events, word problems Mutually exclusive events Mutually exclusive events, word problems Using permutations and combinations Projectile motion Proofs Induction Trig, with Fundamental Identities Trig, with Multiple-Angle Identities Trig, with Sum and Difference Identities Radians Converting to degrees Rates of change Average Instantaneous Rational functions Equations Graphing Inequalities Partial fraction decomposition Rational Root Theorem Reflections Functions Remainder Theorem Roots Complex numbers Roses Rotations of conic sections Sequences Arithmetic General Geometric Missing middle terms Series Arithmetic General Geometric Power Spirals Subtracting Vectors Synthetic division Synthetic substitution Transformations Functions Trig functions Translations Functions Trig functions Trigonometry Angles Area of triangles Cofunction Identities Double-Angle Identities Equations, factoring and fundamental identities Equations, Multiple-Angle Identities Equations, simple Fundamental identities Graphing trig functions Half-Angle Identities Heron's Formula Inverse trig functions Law of Cosines Law of Sines Multiple-Angle Identities Odd-Even Identities Product-to-Sum Identities Radians and degrees Right triangle trig: Finding ratio values Right triangle trig: Finding sides and angles Sum and Difference Identities Sum-to-Product Identities Trig functions of any angle Vectors Adding and subtracting Angle between Component form Components of Cross product Direction angle Dot product Graphing In 3D space In the coordinate plane Magnitude Multiplication by a scalar Operations in space Operations with Opposite Orthogonal Parallel Perpendicular Rectangular components of Resultants of Unit Word problems Independent and dependent events Mutually exclusive events Projectile motion