Unit: Non-linear functions Rational, Radical and Other Nonlinear Functions Understanding different types of nonlinear functions is crucial for advanced algebra and calculus. This includes rational functions, radical functions, and other nonlinear functions such as exponential, logarithmic, and piecewise-defined functions. Rational Functions Definition: A rational function is a ratio of two polynomials f(x) , where […]
Unit: Polynomials Factoring Polynomial & Finding Zeroes of Polynomials Factoring a polynomial involves expressing it as a product of simpler polynomials. This process simplifies solving equations and finding the roots (zeroes) of the polynomial. Common Methods of Factoring Factoring Out the Greatest Common Factor (GCF): Identify the largest common factor of all terms. Factor […]
Unit: Quadratic Equations Techniques of Solving Quadratic Equations Splitting middle term: There is a method that works in simple cases. With the quadratic equation in this form: ax2 + bx + c = 0 Step1: Find two numbers that multiply to give ac (in other words a times c), and add to give b. Example: x2 + 4x […]
Unit: Exponents and Roots Exponent Rules, Roots and Equivalent Expressions First Law If m is any non-zero rational number and p and q are natural numbers, then: mp X mq= m p+q Generalization form of the above law: If m is any non-zero rational number and p, q and r are natural numbers […]
Unit: Expressions and System of Equations Real World Problems Involving Systems of Equations Unveiling the Power of Systems What are Systems of Linear Equations? Remember those times you had to juggle multiple tasks with different requirements? Systems of equations are similar – they consist of two or more linear equations (containing x and y) […]
Unit: Expressions and System of Equations Understanding Expressions and System of Linear Inequalities Expressions: Basics: Expressions are mathematical phrases that combine numbers, variables, and operations (like addition, subtraction, multiplication, and division). Types: Algebraic: Contains variables and constants. Example: 3x + 5. […]
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: Functions Interpretation and Manipulation Chapter: Putting Variables in Terms of Other Variables Reference: – Understanding dependent and independent variables, solving for one variable in terms of another, manipulating linear equations to express a variable, using substitution to solve equations, Interpreting formulas in context, converting word problems into variable expressions, simplifying algebraic expressions for clarity, […]
Unit: Zeros, Parabolas, And Polynomial Graphing Chapter: Function Transformations Reference: – Understanding vertical and horizontal shifts of functions, Effects of vertical and horizontal stretches and compressions, Reflections of functions across the x-axis and y-axis, Combinations of multiple transformations in sequence, identifying parent functions and their transformed versions, writing equations for transformed graphs, sketching graphs using […]
Unit: Zeros, Parabolas, And Polynomial Graphing Chapter: Zeros of Function Reference: – Definition of zeros of a function, finding zeros of polynomial functions, Relationship between factors and zeros, solving for zeros of quadratic functions, Identifying the multiplicity of zeros, Using the Factor Theorem, using synthetic division to find zeros, Graphical interpretation of zeros, The Rational […]