Unit: Polynomials Chapter: Zero of Polynomials Reference: – Definition of a polynomial and its degree, Finding the zeroes (roots) of a polynomial function, Relationship between factors and roots of a polynomial, The Fundamental Theorem of Algebra, Methods for finding real and complex zeros, Synthetic division and long division for polynomials, The role of multiplicity in […]
Unit: Polynomials Chapter: Factoring polynomial – Manipulation of Polynomials Reference: – Understanding the structure of polynomials, identifying common factors in polynomial terms, Factoring using the distributive property, Factoring trinomials with multiple terms, Factoring by grouping, Difference of squares in polynomials, Perfect square trinomials, Recognizing special factoring patterns, Simplifying expressions through factoring After studying this chapter, […]
Unit: Quadratic Equations Chapter: Undefined Functions Reference: – Understanding Domain Restrictions, Division by Zero in Quadratic Expressions, Identifying Undefined Points in Graphs, Function Notation and Undefined Values, Roots Causing Undefined Outputs, Restrictions from Square Roots of Negatives, Denominators in Rational Quadratics, Discontinuities in Quadratic Functions, Identifying Excluded Values, Vertical Asymptotes from Undefined Expressions, Translating real-life situations […]
Unit: Quadratic Equations Chapter: Completing the Squares Reference: – Concept of completing the square, rewriting quadratic expressions in perfect square form, using algebra tiles or geometric visualization, solving quadratic equations by completing the square, converting standard form to vertex form, Application in finding vertex of a parabola, Role of square completion in deriving the quadratic […]
Unit: Quadratic Equations Chapter: Quadratic Formulas Reference: – Understanding the standard form of a quadratic equation, Derivation of the quadratic formula, identifying coefficients from standard form, Applying the quadratic formula to solve equations, Discriminant and nature of roots, solving equations with real and complex solutions, Simplifying square roots in the formula, avoiding common mistakes in […]
Unit: Quadratic Equations Chapter: Square Root Methods, Nature of Roots Reference: – Solving Quadratic Equations Using Square Roots, Understanding Perfect Square Trinomials, Applying the Principle of Square Roots, Working with Non-Perfect Square Roots, Interpreting the Discriminant, Classifying the Nature of Roots (Real, Imaginary, Rational, Irrational), Graphical Meaning of Roots, Real-life Applications of Square Root Method, […]
Unit: Quadratic Equations Chapter: Solving Using Factoring Methods Reference: – Recognizing Factorable Quadratic Expressions, Structure of a Quadratic Equation, Greatest Common Factor (GCF) Method, Factoring Trinomials with Leading Coefficient One, Factoring Trinomials with Leading Coefficient Not One, Difference of Squares, Perfect Square Trinomials, Solving by Factoring and Using Zero Product Property, Checking Solutions of Factored […]
Unit: Exponents and Roots Chapter: Exponents and Equivalent Expressions Reference: – Understanding exponential notation, simplifying exponential expressions, using properties of exponents, Rewriting expressions with rational exponents, converting between radical and exponential forms, identifying equivalent exponential expressions, multiplying expressions with exponents, dividing exponential expressions, Negative and zero exponents, Simplifying nested exponents, Applying exponent rules in algebraic […]
Unit: Exponents and Roots Chapter: Problems with Exponents and Roots Reference: – Simplifying expressions involving both exponents and roots, converting between radical and exponential forms, solving equations involving roots and exponents, applying exponent rules in multi-step expressions, Rational exponents and their interpretations, Operations with square roots and cube roots, Identifying extraneous solutions in radical equations, […]
Unit: Exponents and Roots Chapter: Exponent Rules Reference: – Understanding the laws of exponents, Multiplication of powers with the same base, Division of powers with the same base, Power of a power rule, Power of a product rule, Power of a quotient rule, Negative exponents and their meaning, zero exponent rule, Working with fractional exponents […]