Algebra 1 Mastered

Define sets, explore subsets and set builder notation, and introduce real numbers, numerical and algebraic expressions; learn to evaluate and translate phrases into algebraic expressions.

Explore the real numbers and their components, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers, and their subset relationships, with common notation Z, Q, and R.

Explore the real number line and interval notation, including square vs round brackets, filled vs hollow dots, and graphical representations for intervals and infinities.

Explore the commutative, associative, and distributive properties of real numbers with examples for addition and multiplication, and note the noncommutativity of subtraction and division.

Explore algebraic expressions as combined variables, constants, and operations, identify terms and literal factors, and simplify by combining like terms and numerical coefficients.

Learn how to evaluate algebraic expressions by substituting variables with constants, simplify by combining like terms, and compute results for chosen x and y values, including powers.

Download the summary sheet to review the major concepts covered in this algebra 1 section.

Learn to solve first-degree equations by balancing both sides, moving terms, and applying operations such as addition and division, with examples like x equals seven and root verification.

learn to solve algebraic equations with fractions by clearing denominators with the least common multiple, then multiply through and solve for x.

Expose students to inequalities, distinguish numerical vs algebraic inequalities, and demonstrate solving by isolating x, applying addition and multiplication properties, and flipping signs when multiplying by negatives.

Explore how to multiply and divide monomials by adding or subtracting exponents, apply the power rules, distribute exponents over products, and avoid distributing over sums.

Factoring is the opposite of multiplication, shown by turning x^2 - x - 6 into (x+2)(x-3). The lesson uses the distributive property to factor polynomials by pulling out common factors.

Identify the highest common monomial factor from terms to factor polynomials, then express the result in a completely factored form with integral coefficients, and verify no further factorization is possible.

Learn how factoring extends solving equations via the zero product property and roots. Apply methods to x^2+6x and 3x^2-5x to verify solutions.

Apply factoring techniques, especially the difference of squares, to solve equations and find roots, illustrated by x^2=16, 7x^2-7=0, and the two-square area problem.

Download the attached summary sheet to review all major concepts covered in this section and reinforce your understanding.

Understand root properties for real numbers, including the principal square root and cancellation with exponents. Apply distribution of roots over products and quotients under real-number conditions, with odd-root restrictions.

Learn to combine radicals with variables, using index rules to simplify square and cube roots. Determine simplest radical form and rationalize denominators when needed.

Explore how the imaginary unit i works, its powers cycle every four, and how to rewrite sqrt of negatives as i times the root to multiply complex numbers.

Master completing the square to solve any quadratic equation. Divide by a, isolate terms, add B/2 to form a perfect square trinomial, then take square roots to find the roots.

Explore the discriminant in the quadratic formula to determine the nature of roots. Learn when the equation has one real root, two real roots, or two non-real complex solutions.