Algebra 1 - A Complete Course

Master solving multi-step equations by combining like terms and isolating the variable using the coefficient. Apply distributive property in practice problems, including shirt and bumper sticker costs, and verify solutions.

Solve multi-step equations using distributive property and combining like terms, including fractions and the lowest common denominator. Isolate the variable by dividing by coefficients and check answers by substitution.

Master solving multi-step equations through isolating variables, applying the distributive property, handling fractions, and verifying answers.

Learn to solve equations with variables on both sides by moving terms across the equals sign, combining like terms, and verifying the solution by substitution.

Learn solving equations with variables on both sides (part 2), using distribution and combining like terms; check solutions and identify identities or no-solution cases.

Review solving equations with variables on both sides, including combining like terms, moving terms across the equals sign, and checking the solution for identity or no-solution cases.

Explore literal equations by modeling real scenarios, solving for x, isolating the variable, and using coefficients and formulas to find radii, heights, areas, or budgets.

Learn to solve literal equations by isolating a variable, simplifying fractions, and using cross-multiplication, then apply these skills to word problems like miles per gallon and verify your answer.

Solve proportions using cross-multiplication, the butterfly method, and proportional reasoning, with checks to verify solutions across fractions and real-world examples.

Review solving proportions using cross-multiplication and unit conversions to solve real-world word problems, including windows in a building and ticket deals.

Explore proportions and similar figures using corresponding angles and sides in similar triangles, and apply cross multiplication to solve real-world height, distance, and scale problems.

Identify similar figures, establish corresponding sides, and use proportions to determine unknown measurements across maps and scale models, including calculating map scales and real-world distances.

Solve multi-step inequalities by isolating the variable, applying sign changes when dividing by negatives, and verifying solutions; explore cases with all real numbers, no solutions, and checking via substitution.

Explore solving multi-step inequalities and related word problems through review exercises, including variable setup and solving for x in age and budgeting scenarios.

Explore compound inequalities and number line graphing, distinguishing and or cases, with open vs closed boundaries, and apply these to an average problem to bound a final test score.

This lecture reviews compound inequalities in algebra 1, teaching how to solve with separating, cross-multiplication, and graphing on a number line, including union and intersection of intervals.

Explore relating two quantities with graphs, using time as the independent variable and volume or height as the dependent variable; assess linear trends, slopes, and matching tables to graphs.

Relate two quantities with graphs by identifying constant rates and slopes in linear relationships, using pool volume and distance over time as examples, and note temperature changes during activity.

See how the number of rectangles relates to the perimeter through a linear function, with perimeter = 2x + 12, and extend the idea to triangles and pattern-based equations.

Explore patterns linking triangle counts to perimeter, derive the linear relation P = x + 2, and identify slope and function concepts through distance and time examples.

Explore patterns and nonlinear functions by analyzing tables and figures, distinguishing linear from non-linear relationships, and identifying rules such as y=2^x and x^2.

Explore patterns and nonlinear functions by analyzing x–y changes, identifying linear versus nonlinear relationships, and examining examples like x^3 and the circumference as a function of radius.

Graph linear functions using slope-intercept form, identify slope and y-intercept, and plot points with rise over run. Apply to a weight-capacity example to build a five-point graph.

Distinguish continuous versus discrete graphs and model scenarios with functions. Identify independent and dependent variables, using 16 ounces per gallon of cheddar to relate gallons, ounces, and money.

Graphing a function rule (review) covers slope concepts, identifying discrete functions, and sketching graphs of parabolas and cubic curves by plotting key points.

Explore writing a function rule that links outdoor temperature to cricket chirps, and apply function models to landfill waste growth, concert revenue, and a rectangle's area.

Learn to write a function rule from problems, modeling earnings from hours at 7.25 per hour with zero intercept, and apply first-mile taxi rates and rectangle and triangle area formulas.

Explore domain and range for relations and functions, illustrate with mapping diagrams and the vertical line test, and identify function status by x-value uniqueness.

Explore when a relation is a function through the vertical line test, domain and range, and mapping. Compare a function example with a non-function example.

Use function notation to model words read in minutes with w(x)=250x, evaluate f(x) on given x, and find domain from range; apply to painting with a(q)=100q, domain 0≤q≤3, range 0≤a≤300.

Explore function notation by evaluating inside-out operations with f and g, substituting inputs (like g(3)=10, f(10)=20) and composing functions, including a time-distance example.

Explains rate of change as the slope of a linear relation, using a marching band to show 260 feet per minute and change in y over change in x.

Explore rate of change and slope through rise over run, two-point formulas, and interpretations, including horizontal and vertical cases, with practical examples of pages per minute and mass per page.

Explore rate of change and slope through real-world examples like miles per gallon, mph, and newspaper delivery, teaching how to compute slope from coordinates and time.

Identify direct variation using y = kx, determine k as y/x, and verify the origin intercept; apply the concept to examples such as weight on Earth and Mars.

Identify direct variation in equations and determine the constant of variation k; learn to express y = kx, find values, and graph relationships through the origin.

Learn to express lines in slope-intercept form y = mx + b, identify slope m and y-intercept b, and apply rise-over-run to graph and model costs.

Master slope-intercept form through quick practice of identifying slope and y-intercept, solving for lines where slope is given, and recognizing horizontal lines with zero slope.

Learn to apply the point-slope form of a line, y − y1 = m(x − x1), through a point with a given slope (not vertical), with examples.

Review point-slope form and its relation to slope-intercept form using a given point and slope. Learn to write and transform line equations and graph them.

Explore standard form, Ax + By = C, learn to find x- and y-intercepts, convert to slope-intercept form, determine the slope, including vertical lines when B is zero.

Review standard form concepts, solve for x and y, and graph lines using intercepts and slope. Identify horizontal and vertical lines; locate axis intercepts.

Identify parallel lines with equal slopes, identify perpendicular lines as negative reciprocals, and convert between point-slope and slope-intercept forms to find line equations.

Explore transformations of linear functions, including vertical and horizontal translations, reflections across the x- and y-axes, and both inside and outside scaling that changes slope.

Discover how linear functions transform through vertical reflections across the x-axis, horizontal reflections across the y-axis, and vertical and horizontal translations, with examples like f(x) and 2x+1.

Explore scatter plots to visualize relationships between x and y, identify positive, negative, or no correlation, and use a trend line or line of best fit to model the data.

Learn to create scatter plots, understand trend lines, identify positive correlations, compare line strength, and derive equations from two points to predict values, including population estimates.

Analyze how systems of linear equations may intersect, be identical, or be parallel, and determine their solutions by graphing the intersection point, with an application modeling growing alligators.

Solve systems by graphing to find the intersection of two linear equations, verify by substitution, and compare two dogs' linear weight models, which equal nine pounds after four months.

Learn to solve systems of equations using substitution, substituting y in terms of x or x in terms of y, verify solutions in equations, and recognize no or infinite solutions.

This lecture reviews solving systems by substitution, isolating a variable and substituting into the other equation, including no solution and infinite solutions with t-shirts and pants price problems.

Apply the elimination method to solve linear systems, eliminate a variable, then substitute to find both x and y. Practice with real-world examples like tickets and car-wash times.

Apply elimination to solve linear systems by multiplying equations to align coefficients, then add or subtract to eliminate a variable, and determine unique, infinite, or no solutions.

Master solving systems of linear equations using elimination, balancing coefficients, and adding or subtracting equations to cancel a variable, then solve for x and y and verify with substitution.

This lesson demonstrates solving linear systems by substitution or elimination and by graphing to find break-even where income equals expenses, using y = 5.5x + 700 and y = 12.5x.

Explore solving linear systems from two real world scenarios, tank fill rates and bacterial decay, by equating expressions, considering initial values, rates, and viable solution constraints.

Explore solving linear systems through real-world word problems, including investments with different interest rates, pricing plans, and wind-speed distance problems, using substitution and reasoning.

Test points in linear inequalities and distinguish them from equations. Graph the solution region above or below the boundary line, using solid or dashed lines to indicate inclusion.

Graph linear inequalities by drawing the boundary line y = 3x − 6 and shade the region where y ≤ 3x − 6 or y ≥ 3x − 6.

Explore how to graph a system of linear inequalities, identify the solution region as the overlap of the two inequalities, and distinguish between solid and dashed boundary lines.

Identify the two variables and graph the system of inequalities x+y ≤ 6, x < 2, and y ≥ 1.5 to locate the feasible region where all conditions meet.

Review solving systems of linear inequalities by graphing and shading the feasible region, identifying the intersection as the solution set, illustrated with a car-wash and dog-walking problem.

Master zero and negative exponents by applying a^0 = 1 and a^(-n) = 1/a^n, and simplify expressions with negative powers while exploring a doubling growth model.

Master zero and negative exponents by simplifying fractions and expressing expressions as one over terms, including powers.

Learn how to multiply expressions with the same base by adding exponents, handle coefficients and negative exponents, and simplify complex power expressions.

this lecture reviews multiplying powers with the same base, showing how to combine exponents and simplify expressions in algebra 1.

Explore multiplication properties of exponents, including base rules, zero and negative exponents, powers of products and quotients, and practical applications like area calculations and kinetic energy.

Explore the multiplication properties of exponents, including handling negative and fractional exponents, simplifying expressions, and applying exponent rules to volume calculations using pi r^2 h.

Apply the division properties of exponents to subtract exponents on like bases, and convert negative exponents to reciprocals while simplifying fractional powers.

Apply division properties of exponents to simplify expressions by flipping fractions and combining like bases. Compute examples with negative exponents and powers to show how numerator and denominator interact.

Learn to simplify radical expressions and convert between radicals and exponents using root rules, with practical examples like cube and fourth roots, and apply Kleiber's metabolic-rate formula to body mass.

Explore rational exponents and radicals, convert between radical and exponential forms, and simplify expressions like 64 = 4^3 and 27^(2/3) = 9.

Master the multiplication and division properties of square roots and learn to simplify radicals by extracting largest square factors, with rationalization techniques for denominators.

Explore simplifying radicals by factoring inside the radicand to extract square factors, combine factors to form squares, and rationalize denominators, with multiple worked examples.

apply the pythagorean theorem to find missing sides of right triangles using a^2 + b^2 = c^2, identify the hypotenuse as the side opposite the 90-degree angle.

Apply the pythagorean theorem to find missing sides using a^2 + b^2 = c^2, and practice with square roots like sqrt(144)=12 and sqrt(1225)=35.

Identify whether a sequence is arithmetic or geometric by inspecting differences or ratios. Derive explicit formulas using the first term and common difference or ratio to generate any term.

Review arithmetic and geometric sequences, define the common difference and common ratio, and test sequences with division checks to determine whether they are arithmetic, geometric, or neither.

Learn how to express arithmetic sequences with a recursive formula using the previous term plus the common difference, and convert it to the explicit form a_n = a_1 + (n-1)d.

Analyze arithmetic sequences using recursive definitions and explicit formulas. Determine the first term and common difference to generate sequence terms.

Learn how to write geometric sequences in recursive form, determine the common ratio, and use explicit and recursive formulas for problems like price markdowns.

Explore geometric sequences using the recursive formula, determine the first term and common ratio, and compute subsequent terms through the recurrence.

Explore how to classify polynomials by degree and terms, from monomials to binomials and trinomials, and learn to add or subtract them by combining like terms in standard form.

Master adding and subtracting polynomials by combining like terms, arranging terms from highest to lowest degree, and recognizing monomials, trinomial structures, and polynomial degrees.

Multiply and factor polynomials using the distributive property, identify the greatest common factor, and factor trinomials with x and exponents through clear examples.

Practice multiplying and factoring polynomials, identify the greatest common factor, factor out the common factors, and work through example problems to simplify expressions.

Explore how to multiply binomials using distribution, work through binomial–trinomial products, and consolidate results by combining like terms for clear polynomial expansion.

Review how to multiply binomials in algebra 1, and practice collecting terms to reach the final simplified expression. Confirm the final answer when no further like terms can be collected.

Learn how to square binomials using the (a+b)^2 and (a−b)^2 rules, including identifying the first term, second term, and twice the product, with practical examples.

Explore multiplying special cases, simplify expressions using squaring patterns and the difference of squares, and apply area calculations by subtracting small square areas to find the shaded region results.

Factor x^2 + bx + c by selecting two numbers that multiply to c and add to b, then write (x + m)(x + n) as binomials and verify by expansion.

Master factoring quadratics by choosing two numbers that multiply to c and add to b, with guidance on negative and positive cases, and verify results by expansion.

Master factoring x^2 + bx + c by selecting two numbers that multiply to ac and add to b, with practical examples and negative factor reasoning.

Learn the ac method for factoring ax^2+bx+c when a ≠ 1, using split middle term and grouping, with examples like 5x^2+11x+2 and 6x^2+13x+5.

Learn to factor ax^2 + bx + c by extracting a common factor, splitting the middle term, and factoring by grouping to obtain a product of binomials.

Learn to factor quadratic trinomials of the form ax^2+bx+c, including factoring out a common factor and using the ac method to find two numbers that sum to b.

Learn to factor special cases by recognizing perfect square trinomials and the difference of squares, and by factoring out common factors to reveal binomial products.

Review factoring special cases by recognizing perfect square trinomials and differences of squares, using square roots and the middle term.

Master factoring by grouping for three- or four-term polynomials by identifying common factors in paired terms, regrouping, and factoring out to form a common factor across grouped terms.

Review factoring by grouping to factor expressions with multiple terms, identify common factors, and apply grouping techniques to simplify polynomials.

Learn to simplify rational expressions by factoring and canceling common factors, and identify restrictions or excluded values that keep denominators nonzero.

Learn to simplify rational expressions by factoring and canceling common factors, and identify domain restrictions that prevent denominators from being zero.

Learn how to divide polynomials using long division, identify the dividend and divisor, and obtain the quotient and remainder with clear step-by-step rules.

Review dividing polynomials using long division to find the quotient and simplify expressions with x terms and coefficients, reinforced through worked examples.

Explore quadratic graphs and their properties, including the standard form y = ax^2 + bx + c, the parabola, vertex, and axis of symmetry.

Analyze how the coefficient a stretches or compresses and vertical shifts affect quadratic graphs, then apply to a downward opening acorn height model, determining domain and range.

Explore quadratic graphs and their properties, identify the vertex and axis of symmetry, determine maximum or minimum values, and relate domain and range to graph transformations.

learn to determine the axis of symmetry x = -b/(2a) and the vertex, then graph quadratics using symmetry and three symmetric points including the y-intercept.

Explore quadratic functions by locating the vertex and axis of symmetry, using x = -b/(2a). Apply to a projectile height model to find maximum height and time to hit ground.

Learn how to transform quadratic functions with vertical and horizontal reflections, stretches, compressions, and translations, distinguish inside (input) versus outside (output) changes, and apply the proper transformation order.

The lecture reviews transformations of quadratic functions, emphasizing horizontal shifts from x minus h, vertical translations, and the standard form y = a(x-h)^2 + k with focus on rightward moves.

Learn to express a quadratic in vertex form y = a(x - h)^2 + k, identify the vertex (h, k) and axis of symmetry, and determine domain and range.

Learn the vertex form of a quadratic, y = a(x - h)^2 + k, identify the vertex and axis of symmetry, and determine domain, range, and a from a point.

Explore solving quadratic equations by graphing the related function to find zeros, roots, and solutions, and apply square roots when appropriate, with real-world examples.

Review solving quadratic equations through graphing and algebra, identifying when no real solution exists and locating zeros. Apply square roots to find real solutions.

learn factoring to solve quadratic equations using the zero-product property. apply to real-number examples and word problems, verify solutions by substitution.

Master how to factor quadratic expressions and solve for roots by applying the zero product property. Practice selecting factor pairs and verify solutions within algebraic problems.

Learn to write quadratic functions from given zeros by factoring into linear factors, identify roots and solutions, and build the function from its zeros.

Review quadratic equations by factoring, identify roots, and transform between forms, including writing quadratics in vertex form and verifying with standard form.

Learn completing the square by turning quadratics into a perfect square trinomial, such as x^2 + Bx + (B/2)^2, using B to find C and solve with square roots.

Complete the square to convert the quadratic into a perfect square, then solve for x. The process yields x = 1 or x = -1.

Explore the quadratic formula and the discriminant to solve quadratics, learning when D>0 yields two real solutions, D=0 one, and D<0 none, with factoring, completing the square, or graphing.

Apply the quadratic formula and the discriminant to solve quadratic equations, identifying two or one real solutions through worked examples.

Explore exponential functions of the form y = a b^x with a ≠ 0, b > 0, b ≠ 1. Identify growth vs decay and the x-axis as an asymptote.

Explore exponential functions, including growth and decay, by graphing and analyzing domain and range. Identify asymptotes and intersections to model real-world scenarios like population growth.

Identify exponential functions from data points, examine their domain and range, and apply an exponential model such as 15000(1.06)^t to project costs rising over time.

Explore exponential growth and decay through growth factor models, initial amounts, and time, including compound interest and applications like population dynamics and restaurant spending projections.

Investigate exponential growth and decay by deriving yearly and monthly growth factors, solving for subscriber counts over years, and applying compound interest formulas with quarterly and monthly compounding.

Explore exponential growth and decay through growth factors, initial amounts, and the compound interest formula, applying to revenue projections and monthly growth.

Identify whether car depreciation data is best modeled by an exponential or linear function, using differences and ratios, and apply regression analysis to fit the chosen model.

Learn to model exponential data with regression, identifying the parameters a and b and the initial value around 99.8. Observe constraints: greater than zero, trial counts between 0 and 100.