Every lesson in the College Algebra slide course, in full text: 18 decks, 2498 slides.
Real Numbers, Exponents, and RadicalsThe foundation deck for College Algebra. It covers the real number sets, absolute value as distance, interval and set-builder notation, the order of operations, and the sign rules, then gives every integer exponent rule together with the reason behind it. From there it moves to scientific notation, simplifying and combining radicals, rational exponents, and rationalizing denominators. It targets the four errors that follow students all semester: distributing an exponent across a sum, reading a negative exponent as a negative number, dropping the absolute value out of an even root, and adding unlike radicals.
Polynomials and FactoringThis deck covers polynomial vocabulary, adding and subtracting polynomials, every way to multiply them, and the special products, then lays out a complete factoring strategy that runs from the GCF through grouping to the cubes. It targets the dropped subtraction sign, the missing middle term when a binomial is squared, trying to factor a sum of squares, and skipping the GCF and then calling what is left unfactorable.
Rational ExpressionsThis deck covers domain restrictions, simplifying by factoring, multiplying and dividing, the least common denominator, adding and subtracting, complex fractions, and the difference quotient. It targets the biggest error in the course - cancelling added terms instead of factors - along with restrictions lost after a cancellation, the dropped minus sign when subtracting, and a common denominator that is either wrong or needlessly huge.
Linear Equations and InequalitiesThis deck solves linear equations end to end. It starts with the balance-scale model, then covers clearing fractions and decimals, telling identities from contradictions, literal equations, applied linear models, and inequalities on the number line written in interval notation. It targets the forgotten inequality flip, multiplying only part of the equation by the LCD, calling a true collapsed statement "no solution", and writing an "or" union as an "and" intersection.
Absolute Value Equations and InequalitiesThis deck teaches absolute value from a single picture - distance from zero on the number line - and then uses it to solve every standard problem type: isolate-then-split equations, the no-solution and single-solution cases, absolute value on both sides, less-than inequalities as one interval, greater-than inequalities as a union of two rays, the always-true and never-true cases, and tolerance and error-bound applications. It targets the four errors that sink students here: splitting before isolating, swapping "and" with "or", negating only the constant on the other side, and forgetting to check candidates against a variable right-hand side.
Solving Quadratic EquationsThis deck covers every way to solve a quadratic equation, and how to pick the fastest one. It starts with standard form and the zero-product property, then works through factoring, the square root property, completing the square, the quadratic formula derived from it, and what the discriminant says about the number and type of solutions, before finishing with projectile, area, revenue, and Pythagorean applications. It targets the four errors that cost the most points: setting factors equal to a constant instead of zero, losing half the solutions by dropping the plus-or-minus, dropping the sign of a negative coefficient inside the quadratic formula, and dividing only one term by the leading coefficient while completing the square.
Radical, Rational, and Quadratic-Form EquationsThis deck covers rational equations cleared by the LCD, radical equations solved by raising both sides to a power, rational-exponent equations, and quadratic-form equations solved by u-substitution. Every method here can manufacture answers that are not answers, so the running thread is the one habit that saves you: check every candidate in the ORIGINAL equation. It targets skipping that check, squaring term by term, cancelling a variable factor and losing a root, and forgetting to substitute back from u.
Complex NumbersThis deck explains why the number system had to be extended, then introduces the imaginary unit and its one defining property, standard form, and the complex plane. It covers adding, subtracting, and multiplying, the four-step cycle of powers, the conjugate and division, complex solutions of quadratics with a negative discriminant, and the modulus. It targets the four errors that sink this unit: applying the radical product rule to two negative radicands, leaving the square of the imaginary unit unsimplified, slipping a sign when multiplying by a conjugate, and reporting the imaginary part with the unit still attached.
Functions, Domain, and Function NotationThis deck builds the single most important idea in College Algebra: a function is a machine with exactly one output for each input. It distinguishes relations from functions using mapping diagrams and the vertical line test, then covers function notation and evaluating at numbers and at expressions, the difference quotient, domain and range in interval notation, piecewise functions, increasing and decreasing intervals, relative extrema, average rate of change, and even against odd functions. It targets four classic errors: reading function notation as multiplication, substituting into only one copy of the variable, answering a domain question with a list of excluded values, and swapping domain with range.
Graphs, Transformations, and SymmetryThis deck is the visual half of College Algebra. It covers plotting and intercepts, the distance and midpoint formulas, and the library of parent-function shapes, then every rigid and non-rigid transformation and the order in which they must be applied, the three symmetry tests, and circles from standard form through completing the square. It targets four classic errors: shifting the wrong way for a horizontal translation, stretching before shifting, mixing up the two reflections, and reading the radius straight off the squared number.
Linear Functions and ModelingThis deck covers everything linear. It shows a constant rate of change in a table, in a graph, and in an equation, finds slope from two points and reads it as a rate with units, and works through slope-intercept, point-slope, and standard form, along with horizontal and vertical lines and the slopes of parallel and perpendicular lines. It then builds a model from a description or from two data points and predicts with it, and closes with scatter plots, best-fit lines, and correlation. It targets four classic errors: subtracting the coordinates in mismatched order, confusing zero slope with undefined slope, taking only half of a negative reciprocal, and reading the y-intercept off an equation that has not yet been solved for y.
Quadratic Functions, Parabolas, and OptimizationThis deck covers everything a parabola can tell you: vertex form and the sign trap hiding inside it, the vertex formula from standard form, converting between forms by completing the square, intercepts and what the discriminant says about how many there are, domain and range, and applied optimization for maximum area, maximum revenue, and projectile height. It targets the four errors that cost the most points: flipping the sign of the vertex, dropping the negative in the vertex formula, reporting where the maximum happens instead of the maximum value, and assuming that every parabola crosses the axis twice.
Combining Functions, Composition, and InversesThis deck covers adding, subtracting, multiplying, and dividing functions, and the domain of each result. It then works through composition from the inside out, why composition is not commutative, the domain restrictions it hides, and decomposition, before moving on to one-to-one functions, the horizontal line test, and finding inverses by swapping and solving. It targets reading the inverse notation as a reciprocal, composing in the wrong order, reading a composite's domain off the simplified form, and undoing only part of the rule.
Polynomial Functions, Division, and ZerosThis deck covers degree and the four end-behavior cases, then zeros, multiplicity, and whether the graph crosses the axis or merely touches it. It works through long division with placeholder terms and synthetic division, the Remainder, Factor, and Rational Zero Theorems, and the full strategy for finding every zero of a cubic or quartic, including the Fundamental Theorem of Algebra and conjugate pairs. It targets synthetic division done with the wrong sign or a non-linear divisor, missing placeholders in long division, treating rational-zero candidates as though they were answers, and getting cross-versus-touch backwards.
Rational Functions, Asymptotes, and InequalitiesThis deck covers domains, holes, and vertical, horizontal, and slant asymptotes, then sign charts and full sketches of rational functions, and finishes with polynomial and rational inequalities. It targets the classic errors: calling a cancelled factor a vertical asymptote, reading a horizontal asymptote off the constant terms, multiplying a rational inequality by a denominator whose sign is unknown, and including a zero of the denominator in a non-strict solution set.
Exponential Functions and GrowthThis deck builds exponential functions from the ground up. It contrasts a constant rate with a constant ratio in a table, explains the restrictions on the base and why they exist, and covers growth and decay graphs with their horizontal asymptote and the transformations that move it. It then introduces the natural base e as the limit of compounding more and more often, computes compound and continuous interest with real numbers, and works through growth, decay, half-life, and cooling models, fitting a model to two data points, and solving exponential equations with a common base. It targets four killer errors: confusing a variable base with a variable exponent, multiplying the base by the exponent, forgetting that a vertical shift moves the horizontal asymptote, and using the annual interest formula when the problem says monthly.
Logarithmic Functions and Properties of LogsThis deck builds logarithms from the ground up, starting from the log as the inverse of the exponential - the log IS the exponent. It covers fluent conversion between exponential and logarithmic form, evaluating by inspection, common and natural logs, domain and the vertical asymptote, and the graph as a reflection across the line y equals x. It then gives the product, quotient, and power rules with a reason for each, expanding and condensing, change of base, and the log scales: decibels, pH, and Richter. It targets four killer errors: splitting the log of a sum, pulling out only part of an exponent, ignoring a domain violation, and inverting the change-of-base fraction.
Exponential and Log Equations, and Systems of EquationsThis deck closes the exponential and logarithmic thread and opens systems. It solves exponential equations by matching bases and by taking logarithms, isolating the exponential factor first, then condenses and converts logarithmic equations and checks every candidate against the domain. From there it covers doubling time and half-life, and moves into two-variable systems by graphing, substitution, and elimination, inconsistent against dependent systems, three-variable and nonlinear systems, systems of inequalities, and applied mixture, break-even, and investment problems. It targets four killer errors: skipping the domain check on a log equation, taking the log of each term instead of the whole side, multiplying only one term during elimination, and calling a dependent system "no solution".
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