Unit: Linear Functions Graphing of Linear Functions, Rate of Change, Growth and Decay Linear functions are a specific type of function that create straight lines when graphed. They are fundamental in algebra and widely used to model relationships between variables. Definition and General Form A linear function is a function that can be written […]
Unit: Linear Equations in Two Variables Forms of Linear Equations and Solution Techniques Linear equations in two variables represent relationships between two quantities. They can be graphed as straight lines in the coordinate plane and are fundamental in algebra and coordinate geometry. Definition and Standard Form A linear equation in two variables can be […]
Unit: Linear Equations in One Variable Word Problems Involving Linear Equations Word problems involving linear equations require translating a real-world situation into a mathematical equation and then solving for the unknown variable. These problems often involve relationships between quantities, rates, and times. Steps to Solve Word Problems Read the Problem Carefully: Identify what you […]
Unit: Linear Equations in One Variable Solving Basic Linear Equations Linear equations in one variable are fundamental in algebra and represent the simplest form of equations. They are used to model and solve real-world problems involving relationships between quantities. Definition and Standard Form A linear equation in one variable can be written in the […]
Unit: Functions Interpretation and Manipulation Putting Variables in Terms of Other Variables Understanding how to interpret and manipulate functions is essential for solving complex algebraic problems, modelling real-world situations, and performing advanced mathematical analyses. This involves analyzing the function's behaviour, rewriting functions, and expressing one variable in terms of another. Interpreting Functions Interpreting functions […]
Unit: Zeros, Parabolas, And Polynomial Graphing Solving Functions, Graphing and Transformations Understanding how to solve functions, graph them, and apply transformations is essential for mastering algebra and calculus. This involves finding solutions to equations, representing functions visually, and manipulating graphs to understand their behaviour better. Solving Functions Solving functions typically involves finding the values […]
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 […]