College Algebra

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• Real numbers and the number line ~15 min
• Properties of real numbers and order of operations ~20 min
• Exponents and radicals ~25 min
• Polynomials and factoring ~30 min
• Simplifying rational expressions ~20 min
• Multiplying and dividing rational expressions ~20 min
• Adding and subtracting rational expressions ~20 min
• Complex fractions and the difference quotient ~25 min

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• Solving linear equations ~20 min
• Applications and problem solving ~25 min
• Absolute value and inequalities ~25 min
• Quadratic equations ~30 min
• Rational and radical equations ~30 min
• Solving rational inequalities ~20 min
• Polynomial inequalities ~20 min

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• Distance and midpoint ~20 min
• Symmetry and circles ~25 min
• Slope and line equations ~25 min
• Parallel and perpendicular lines ~25 min
• Function fundamentals ~25 min
• Reading function graphs ~10 min
• Average rate of change ~10 min
• Even and odd functions ~8 min
• Piecewise and step functions ~12 min
• Transformations of functions ~25 min
• Composition and inverse functions ~25 min

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• Quadratic models ~35 min
• Graphs of polynomial functions ~25 min
• Dividing polynomials with long division ~8 min
• Synthetic division, the speed-run ~7 min
• The Remainder and Factor Theorems ~7 min
• The Rational Zero Theorem ~8 min
• Complex numbers and the Fundamental Theorem ~25 min
• Locating zeros with the Intermediate Value Theorem ~6 min
• Descartes' Rule of Signs ~7 min
• The Upper and Lower Bound Theorem ~6 min
• Irrational zeros travel in pairs ~6 min
• Asymptotes, holes, and graphs of rational functions ~25 min

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• Square and cube root functions ~20 min
• Power functions and end behavior ~20 min
• Absolute value functions ~20 min
• Direct and inverse variation ~20 min
• Joint and combined variation ~20 min
• Regression and correlation ~25 min
• Choosing a model type ~20 min
• Fitting a model to data ~25 min

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• Exponential functions ~25 min
• Logarithms ~25 min
• Solving exponential and logarithmic equations ~18 min
• Half-life and doubling time ~10 min
• Newton's Law of Cooling ~10 min
• Expanding and condensing logarithms ~25 min
• Logarithmic scales ~20 min
• Logistic growth models ~20 min
• Exponential and logarithmic inequalities ~18 min

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• Angles and standard position ~20 min
• Radian measure ~25 min
• Arc length and sector area ~20 min
• Linear and angular speed ~20 min
• The six trigonometric ratios ~25 min
• Special right triangles ~20 min
• Solving right triangles ~25 min
• The unit circle definitions ~25 min
• Reference angles and exact values ~25 min
• Domain, range, and period ~25 min

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• Graphing sine and cosine ~20 min
• Amplitude, period, and phase shift ~25 min
• Graphing tangent, cotangent, secant, and cosecant ~20 min
• Modeling with sinusoids ~25 min
• Simple harmonic motion ~20 min

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• Reciprocal, quotient, and Pythagorean identities ~25 min
• Even, odd, and cofunction identities ~20 min
• Simplifying and verifying trigonometric identities ~25 min
• Sum and difference formulas ~25 min
• Combining sine and cosine into a single sinusoid ~20 min
• Exact values and reduction formulas ~20 min
• Double-angle identities ~25 min
• Power-reduction and half-angle identities ~25 min
• Product-to-sum and sum-to-product identities ~20 min
• Why domains must be restricted ~20 min
• Inverse sine, cosine, and tangent ~20 min
• Compositions of trig and inverse trig functions ~25 min
• Basic equations on an interval ~25 min
• Equations requiring identities ~25 min
• Multiple-angle equations ~25 min

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• Oblique triangles and the Law of Sines ~20 min
• The ambiguous case: SSA ~20 min
• Law of Cosines: SAS and SSS triangles ~25 min
• Triangle area and Heron's formula ~20 min
• Angles of elevation, depression, and bearings ~25 min
• Surveying and real-world trig models ~25 min
• Geometric and component vectors ~25 min
• Vector arithmetic and unit vectors ~25 min
• Dot product and projection ~25 min
• Modulus, argument, and polar form ~20 min
• Products, quotients, and De Moivre's Theorem ~25 min
• nth roots of complex numbers ~25 min

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• Circles and ellipses ~25 min
• Parabolas and hyperbolas ~30 min
• Identifying a conic from its equation ~20 min
• Rotation of axes ~25 min
• Translated conics and completing the square ~25 min
• The polar coordinate system ~20 min
• Converting between polar and rectangular ~25 min
• Graphing polar curves ~25 min
• Polar equations of the conics ~20 min
• Parametric curves and plotting ~20 min
• Eliminating the parameter ~20 min
• Projectile motion with parametric equations ~20 min

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• Systems of linear equations ~25 min
• Matrices and row reduction ~35 min
• Computing determinants ~13 min
• Cramer's Rule and the 2×2 Matrix Inverse ~8 min
• Finding a Matrix Inverse ~12 min
• Matrix Transpose ~3 min
• Distinct linear factors ~25 min
• Repeated linear factors ~25 min
• Irreducible quadratic factors ~25 min
• Nonlinear systems: substitution and elimination ~25 min
• Graphing systems of inequalities ~20 min
• Linear programming ~25 min

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• Arithmetic and geometric sequences ~28 min
• Series and the Binomial Theorem ~30 min
• Counting, permutations, combinations, and probability ~22 min
• Permutations with repeated objects ~10 min
• Expected value ~10 min
• Conditional probability ~20 min
• The induction principle ~25 min
• Proving summation formulas ~25 min
• Divisibility and inequalities by induction ~25 min
• Odds, Bayes' theorem, and binomial probability ~24 min
• Annuities and amortization ~20 min