Algebra 1

Explore number sets in algebra 1, including natural numbers, whole numbers, integers, rational and irrational numbers, imaginary numbers, and their place as subsets of real and complex numbers.

Explore fractions as portions of a whole, including proper, improper, and mixed forms, and learn to add, subtract, multiply, divide, convert, and simplify using the GCF.

Learn the basics of exponents, defining the base and exponent, evaluating positive and negative exponents via reciprocals, and applying rules for zero and even or odd powers.

Explore radical expressions by evaluating square roots and cube roots, simplify with perfect squares, and apply rules for real numbers, negative signs, and factoring under radicals.

Discover how variables, like x, represent unknown numbers, learn common letter conventions for angles, exponents, sums, time, coordinates, and practice combining like terms and using coefficients.

Solve basic equations by keeping both sides equal and isolating the variable, using addition, subtraction, multiplication, and division. Apply fractions and reciprocals when needed, and handle multi-step problems with consistency.

Solve equations using roots and radicals by applying inverse relationships with exponents, isolating the unknown, and balancing both sides, illustrated through square and cube roots.

Learn to solve algebraic word problems by extracting numerical values, identifying variables, and translating language into equations. Practice with age problems and other examples to solve for unknowns.

Compute rate of change between two points using m = (y2 - y1) / (x2 - x1) and classify slope of a line as positive, negative, zero, or undefined on coordinate plane.

Explore how linear equations are represented by the slope-intercept form y = mx + b, identify the slope and y-intercept, and graph lines by plotting points and intercepts.

Master the point-slope form y - y1 = m(x - x1) to write line equations from a slope and a point, and use the slope formula to find m from two points.

Learn how parallel lines share the same slope and perpendicular lines have a negative reciprocal slope, verified by graphing, and practice deriving equations in point-slope and slope-intercept forms.

Explore linear inequalities and the symbols less than, greater than, less than or equal to, and greater than or equal to, flipping signs when multiplying or dividing by negatives.

Master combined inequalities by distinguishing conjunctions and disjunctions, solving each part, and graphing solutions on a number line, with emphasis on open and closed circles and your logical checks.

Graph linear inequalities by drawing the boundary line, using a solid line for ≤ or ≥ and a dashed line for < or >, then shade the correct region.

Graph systems of linear equations on the coordinate plane to find their intersection as an ordered pair, after converting to slope-intercept form and verifying by plugging in.

Use the substitution method to solve systems of linear equations by isolating a variable, substituting into the other equation, and checking solutions.

Learn to solve systems of linear equations using the elimination method by scaling to align like terms and cancel a variable, then solve and substitute.

Translate word problems into two equations using x and y, solve via substitution or elimination, and verify by substituting back, illustrated by adult and child ticket totals.

Translate word problems into systems of linear inequalities by defining variables, writing constraints, graphing to identify the overlapping feasible region, and interpreting the solution for real-world decisions.