STEM Creations

This book describes how we use rules of exponents and Radicals in Mathematics to simplify algebraic expressions. The simple rules outlined in this E-article allows anyone to master these ideas and to use them in simplifying any algebraic expressions that involves radicals or exponentiation. The rules are well outlined and examples are given. This is a perfect E-book for your students. It will serve as great notes to master the subject. The E-book is geared towards grades 7-12 and even college

At the end of this lesson, the students must be able to learn how to solve rational equations. The steps involved in solving a rational equation are: 1. Find the least common denominator of the equation. 2. Multiply each expression in the equation by the least common denominator. 3. Simplify each expression completely. 4.Solve the simplified equation 5. Check the solution(s) found to make sure there isn't an extraneous solution.

SAT Mathematics is a required entrance exam to many colleges and universities. Despite its importance, many students continue to struggle in it yet this exam is based on very common basic Math principles. When these ideas are reviewed in depth, any student is bound to boost their SAT score tremendously. This study guide is based on ideas that I have used to help students study SAT Math. I have had immense success in helping students succeed. One of my students recently scored a 770/800 in the

A quadratic equations is an equation of the form ax^2 + bx + c=0. There are several other ways of solving a quadratic equation. In this document, we discuss how one can use the Quadratic formula to determine the type of solutions in a quadratic equation. The discriminant (D) is given by: D= b^2 - 4ac   The Discriminant tells us whether the equation will have one real solution or two real solutions or two imaginary solutions in a quadratic equation. If D=0 , then the quadratic equation has only

In this e-document, I will examine basic area concepts that relate to the process of finding the area of a square and rectangle. Manipulation facts are also discussed. Using this document, instructors can have students work in groups and have them find areas of irregular figures that can be portioned into squares and rectangles. The formulas for for finding the finding the areas of squares and rectangles are also given.

After teaching Math for many years, I have realized that many students lack the holistic approach to the concept of ratios, rates & fractions. Using these ideas in Math computations continues to be a challenge to many students in grade school, middle and high schools and even in colleges. With this e-book, it is my hope that I can help fill any gaps. Although this E-book is intended for grades 5-8; anyone who needs to understand the concept of ratios, rates and fractions and how we use them in

Exponential growth or decay can be modeled using an exponential function of the form: y= P ( a) ^x P = initial value of y x = time or any value for x a = multiplication factor i. If a>1 then the function y is an exponential growth where a = 1 + r and r is the growth rate as a decimal number. ii. If then the function y is an exponential decay where a = 1 - r and r is the decay rate as a decimal number. This document discusses applied problems that relate to exponential growth

In this New SAT Review, we present with examples the following: A. Quadratic functions and parabolas: Questions with answers B. Quadratic functions and Equations: Questions with answers C. Arithmetic and geometric sequence: Questions with answers D. Solving Ratios and proportions equations: Questions with answers

OBJECTIVES 1. The student should be able to express quadratic equations in standard form: ax^2 + bx+c =0 and be able to extract the numbers, a, b and c. 2. The student should be able to find the discriminant, D= b^2 - 4ac in the quadratic formula and be able to identify the three types of solutions that one can get when solving a quadratic equation. 3. The student should be able to solve quadratic equations by using the quadratic formula.

A 2 by 2 matrix with a, b, c and d as the elements of the matrix has its determinant to be the result: ad – bc. Generally, the determinant of A can be represented as det(A) or |A|. At the end of this lesson, the student should be able to i.) Identify a 2 by 2 matrix ii.) Find the determinant of a 2 by 2 matrix ii.) Use the determinant to find the inverse of a 2 by 2 matrix iii.) Verify that the product of matrix A and its inverse is a unit matrix

A conic is the intersection of a plane and a right circular cone. The four basic types of conics are parabolas, ellipses, circles, and hyperbolas. This document discusses the concept of circles. A circle is a set of all points in a plane that are a fixed distance, called the radius, and from a point called its center. Equation of a circle: The distance formula can be used to find the equation of a circle. Let the center of the circle be represented by the ordered pair ( h, k) and the rad

Simplifying a Complex fraction A complex fraction is a fraction that has one or more fractions in the numerator, denominator or both. To simplify a complex fraction, we multiply the numerator and denominator of the complex fraction by the least common denominator of all the component fractions in the complex fractions. This process is often called the “clearing fractions.” As a result, we end up simplifying the complex fraction into a simple fraction. We call the least common denominator “the

OUTLINE In order to multiply and simplify two rational expressions: 1. Factor each numerator polynomial and multiply out the factors 2. Factor each denominator polynomial expression and multiply out the factors 3. Apply the fundamental principle of fractions by dividing the common factor or factors. 4. The simplest form will be the quotient of the product of remaining

Solve Systems of Linear Equations by Graphing A system of equations is a set of two or more equations considered together. A solution to a system of equations in two variables is an ordered pair that is a solution to every equation in the system. To solve a system of linear equations by graphing, one has to graph each of the equations on the same x-y plane and determine the common point of intersection of equations given. The solution to the system is the x value and y value at the point of in

This e-document demonstrates how we can find the area of a triangle by using the formula that the area of a triangle is one half the area of a rectangle with the same base and height. The document also describes how we can use different triangles to show the relative positions of altitudes of triangles. Students should also be able to identify the basic formula for finding the area of a triangle.

A quadratic equations is an equation of the form ax^2 + bx + c=0. There are several other ways of solving a quadratic equation. In this document, we discuss how one can use the Quadratic formula to determine the type of solutions in a quadratic equation. The discriminant (D) is given by: D= b^2 - 4ac   The Discriminant tells us whether the equation will have one real solution or two real solutions or two imaginary solutions in a quadratic equation. If D=0 , then the quadratic equation has only

Any expression of the form (A+B)^2 or (A-B)^2 can be expanded to yield a perfect square trinomial. The perfect square trinomial is A^2 + 2AB + B^2 or A^2 - 2AB + B^2. In this document, we provide examples to show how students can recognize perfect trinomials and to be able to factorize them quickly into the square of their binomials. This product is for a single teacher license use only in your own personal classroom only and is not transferable. Other teachers within your school who need th

OUTLINE 1. Determine if the given rational expressions have the same Least common denominators. 2. If not, find their Least common denominator. 3. Rewrite the given rational expressions as equivalent rational expressions with the same common denominator. 4. Apply the basic definition of subtracting rational numbers with a common denominator. 5. Simplify the final result by canceling out common factors in the numerator and denominator of the final result to attain the simplest form.

OUTLINE 1. Determine if the given rational expressions have the same Least common denominators. 2. If not, find their Least common denominator. 3. Rewrite the given rational expressions as equivalent rational expressions with the same common denominator. 4. Apply the basic definition of adding rational numbers with a common denominator. 5. Simplify the final result by canceling out common factors in the numerator and denominator of the final result to attain the simplest form.

SOLVING A SYSTEM OF LINEAR EQUATIONS BY SUBSTITUTION The graphing method for solving a system of linear equations only works well when the ordered pair solution are only integers. Therefore, we need an algebraic method for solving systems of equations. There are two algebraic methods that we can use to solve a system of equations. These are: I. The Substitution Method II. The Elimination Method. This e-book discusses the Substitution Method The steps involved when solving a system of linear