https://teddyrookbook.com/math/algebra-1/Recent content in Algebra 1 on Teddy Rook Bookhttps://teddyrookbook.com/img/share.jpghttps://teddyrookbook.com/img/share.jpgHugoenhttps://teddyrookbook.com/math/algebra-1/real-number-system/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/real-number-system/Sort numbers into natural, whole, integer, rational and irrational. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/rational-irrational-operations/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/rational-irrational-operations/Decide whether a sum or product is rational or irrational, and say why. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/evaluate-expressions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/evaluate-expressions/Substitute values, including negatives, and follow the order of operations. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/expression-structure/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/expression-structure/Name the parts of an expression and what each one means. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/units-quantities/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/units-quantities/Multiply by unit fractions to convert rates and keep track of units. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/justify-solution-steps/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/justify-solution-steps/Every step does the same thing to both sides, so the solutions stay the same. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/equations-fractions-decimals/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/equations-fractions-decimals/Multiply every term by the common denominator to get whole numbers. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/write-equations-words/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/write-equations-words/Translate a situation into an equation, then solve it. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/distance-rate-time/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/distance-rate-time/Use d = rt with a table to set up motion problems. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/literal-equations/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/literal-equations/Rearrange a formula to isolate the letter you want. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/absolute-value-equations/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/absolute-value-equations/Isolate the absolute value, then solve for both distances. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/multi-step-inequalities/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/multi-step-inequalities/Solve like an equation, flipping the sign when you multiply or divide by a negative. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/inequality-word-problems/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/inequality-word-problems/Write and solve inequalities for "at least," "at most" and "no more than." Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/compound-inequalities/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/compound-inequalities/Solve "and" and "or" inequalities and graph them. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/absolute-value-inequalities/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/absolute-value-inequalities/Turn |x − a| < b into an "and" and |x − a| > b into an "or." Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/function-notation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/function-notation/f(3) is the output when the input is 3. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/solve-function-equations/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/solve-function-equations/Solve f(x) = k to find which inputs give an output. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/domain-range/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/domain-range/Find the allowed inputs and the possible outputs. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/key-features-graphs/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/key-features-graphs/Read where a graph crosses the axes, rises, falls and peaks. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/average-rate-of-change/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/average-rate-of-change/Divide the change in output by the change in input over an interval. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/sequences-functions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/sequences-functions/A sequence is a function whose inputs are 1, 2, 3, …. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/arithmetic-sequences/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/arithmetic-sequences/Add the same amount each time; aₙ = a₁ + (n − 1)d. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/piecewise-functions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/piecewise-functions/Use the rule that matches the input's interval. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/absolute-value-functions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/absolute-value-functions/Graph V-shapes and see them as two linear pieces. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/step-functions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/step-functions/Graph functions like the floor function that jump between flat steps. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/function-transformations/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/function-transformations/See how f(x) + k, f(x − h), af(x) and f(−x) move a graph. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/graphs-as-solutions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/graphs-as-solutions/Every point on the graph of an equation makes it true, and no other point does. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/point-slope-form/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/point-slope-form/Write a line from a point and a slope: y − y₁ = m(x − x₁). Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/line-through-two-points/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/line-through-two-points/Find the slope, then use a point to write the equation. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/standard-form/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/standard-form/Graph Ax + By = C quickly using its two intercepts. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/horizontal-vertical-lines/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/horizontal-vertical-lines/y = k is flat with slope 0; x = h is vertical with no slope. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/parallel-perpendicular-lines/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/parallel-perpendicular-lines/Parallel lines share a slope; perpendicular slopes multiply to −1. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/linear-models-context/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/linear-models-context/Interpret the slope as a rate and the intercept as a starting value. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/inverse-linear-functions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/inverse-linear-functions/Undo a linear function by swapping inputs and outputs. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/linear-inequalities-2var/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/linear-inequalities-2var/Graph the boundary line and shade the side that works. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/systems-elimination/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/systems-elimination/Add the equations so one variable cancels. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/systems-elimination-multiply/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/systems-elimination-multiply/Scale one or both equations so a variable will cancel. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/systems-word-problems/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/systems-word-problems/Name two unknowns, write two equations, and solve. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/systems-inequalities/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/systems-inequalities/Find the region where both shadings overlap. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/rational-exponents/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/rational-exponents/x^(1/n) means the nth root of x, and x^(m/n) its mth power. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/rational-exponent-rules/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/rational-exponent-rules/Use the exponent rules to simplify roots written as powers. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/simplify-square-roots/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/simplify-square-roots/Pull perfect-square factors out: √72 = 6√2. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/radical-operations/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/radical-operations/Combine like radicals and multiply roots. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/exponential-functions/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/exponential-functions/In f(x) = a·bˣ, the output multiplies by b each time x goes up by 1. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/linear-vs-exponential/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/linear-vs-exponential/Linear grows by equal differences; exponential grows by equal factors. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/geometric-sequences/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/geometric-sequences/Multiply by the same ratio each time; aₙ = a₁·rⁿ⁻¹. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/exponential-growth-decay/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/exponential-growth-decay/A 5% increase multiplies by 1.05; a 5% decrease by 0.95. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/exponential-models/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/exponential-models/Build a = a₀·bᵗ from a starting value and a rate or two data points. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/exponential-equivalent-forms/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/exponential-equivalent-forms/Use exponent rules to change a yearly rate into a monthly one, and back. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/polynomial-basics/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/polynomial-basics/Name terms, degree and leading coefficient, and order terms by degree. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/add-subtract-polynomials/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/add-subtract-polynomials/Combine like terms; subtracting changes the sign of every term. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/multiply-monomial-polynomial/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/multiply-monomial-polynomial/Distribute and use exponent rules on each term. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/multiply-binomials/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/multiply-binomials/Multiply each term by each term; an area model keeps track. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/special-products/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/special-products/(a + b)² = a² + 2ab + b² and (a + b)(a − b) = a² − b². Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/multiply-polynomials/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/multiply-polynomials/Multiply polynomials with any number of terms. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/factor-gcf/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/factor-gcf/Write 6x² + 9x as 3x(2x + 3). Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/factor-x2-bx-c/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/factor-x2-bx-c/Find two numbers that multiply to c and add to b. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/factor-ax2-bx-c/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/factor-ax2-bx-c/Split the middle term using ac, then group. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/factor-special-products/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/factor-special-products/Spot differences of squares and perfect-square trinomials. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/factor-grouping/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/factor-grouping/Group terms in pairs and pull out a shared binomial. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/factor-completely/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/factor-completely/Take out the GCF first, then keep factoring until nothing more factors. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/quadratic-graphs/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/quadratic-graphs/A parabola has a vertex, an axis of symmetry and opens up or down. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/vertex-form/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/vertex-form/In y = a(x − h)² + k the vertex is (h, k). Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/zero-product-property/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/zero-product-property/If a product is 0, one of the factors must be 0. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/factored-form-zeros/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/factored-form-zeros/The zeros of a(x − p)(x − q) are p and q, where the graph meets the x-axis. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/solve-square-roots/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/solve-square-roots/Isolate the square, then take both the positive and negative roots. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/completing-the-square/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/completing-the-square/Add (b/2)² to make a perfect square, then solve or find the vertex. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/quadratic-formula/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/quadratic-formula/x = (−b ± √(b² − 4ac)) / 2a solves any quadratic. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/discriminant/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/discriminant/b² − 4ac tells how many real solutions there are. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/quadratic-models/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/quadratic-models/Use parabolas for falling objects and areas, and read the vertex and zeros in context. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/linear-quadratic-systems/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/linear-quadratic-systems/Find where a line meets a parabola by substitution. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/graph-intersections/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/graph-intersections/The x-coordinates where two graphs meet solve f(x) = g(x). Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/compare-function-families/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/compare-function-families/Choose a model by looking at differences and ratios in data. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/two-way-relative-frequency/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/two-way-relative-frequency/Use row and column percents to look for associations. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/lines-of-fit-residuals/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/lines-of-fit-residuals/Fit a line to data and use residuals to judge the fit. Algebra 1 · Math Ladderhttps://teddyrookbook.com/math/algebra-1/correlation-causation/Mon, 01 Jan 0001 00:00:00 +0000https://teddyrookbook.com/math/algebra-1/correlation-causation/The correlation coefficient measures linear strength; it does not prove cause. Algebra 1 · Math Ladder