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ALGEBRA I & II CONCEPTS A.) The Real Number System - Number line and Real Numbers B.) Ratios and Proportions C.) Surface areas of different solids D.) Special triangles E.) Properties(Rules) of exponents F.) Radicals G.) Polynomials and Factorization H.) Linear equations: Slopes, parallel /perpendicular lines, distance of a line, midpoint of a line I.) Quadratic functions and equations J. Solving Quadratic equations by factorization, completing of squares, the principle of zero produ

Geometric Constructions: A Step-by-Step Guide for Teachers & StudentsThis comprehensive Geometric Constructions guide is the perfect resource for both teachers and students to master the art of geometric constructions using just a straightedge (ruler) and compass. Designed for middle and high school Geometry classes, this document makes learning constructions interactive, engaging, and fun—ensuring students not only understand the concepts but also enjoy the process. Why Teachers Love This R

The method of finding volumes using known bases and cross sections is a fundamental application of integral calculus. This technique allows us to compute the volume of complex three-dimensional solids by integrating the areas of their cross sections.

This document covers the different types of finding limits algebraically and analytically. The following limits techniques are covered in great detail: Direct SubstitutionFactoringConjugate MultiplicationL'Hôpital's RuleSqueeze Theorem

Covers Limits, Function continuity, Differentiation, Applications of Differentiation, Introduction to integration, and Applications of Integration. Topics: 1. Limits i. Introduction to Limits ii. Finding Limits Graphically, Numerically & Algebraically iii. Function continuity 2. Differentiation i. Using Limits to define the derivative of a function ii. Common derivative rules iii. Product rule iii. Quotient rule iv. Chain rule v. The process of Implicit differentiatio

A matrix is a way to organize data in columns and rows. A matrix is written inside brackets [ ]. Each item in a matrix is called an entry. In mathematics, a matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers. This guide is an excellent one for anyone who wants to learn a little more about matrices. In this e-book, I will discuss the following: 1. Addition and Subtraction of Matrices 2. Multiplying a matrix by a scalar quantity 3. Finding the Determinant of a

At the end of the lesson: 1. The student should be able to know how to convert a decimal number into a fraction, a percent, and a ratio 2. The student should be able to know how to convert a percent number into a fraction, a decimal, and a ratio 3. The student should be able to know how to convert a fraction number into a decimal, a percent, and a ratio 4. The student should be able to know how to convert a ratio into a fraction, a decimal, and a percent

This lesson on using Riemann sums to find the area under the graph of a function is intended for students enrolled in AP Calculus AB or BC, Calculus Honors, or College Calculus. The procedure outlined in this e-book is a step by step example on how one can approximate the net area between the x-axis and the curve y=f(x) for a ≤ x ≤ b using Riemann Sums. Given any continuous function f(x), and the values a, b and n, the number of subintervals, it is possible to approximate the area under the cur

In this e-document we describe the process of finding the difference quotient formula of a function. Next we show how we can use the difference quotient to find the derivative ( rate of change function) of a function. Some examples on how to use the derivative to find the slope of tangent line at a specific point on the graph of a function is give.

Are you interesting in teaching students about matrices in a fun and exciting way! In this document, I present Math transformation by using basic matrix operations. Object transformations is a code word for six specific ways to manipulate the location of a point, the shape of a line, or any object. The original shape of the object is called the pre-image and the final shape and position of the object is the image under the transformation. In this document, we will translate, reflect, rotate,

In mathematics, a piecewise-defined function (also called a piecewise function or a hybrid function) is a function which is defined by multiple sub functions, each sub function applying to a certain interval of the main function's domain (a sub-domain). To evaluate the y value for a piecewise function, one must identify the location of x, which happens to be restricted in one of the intervals given. Once the location of the x is found, the next step is to choose f(x) or g(x) or h(x) to evaluate

One of the most confusing topics to students when teaching trigonometry is the concept of reference angles and triangles. Many books do not tie this concept holistically so that students can understand how to compute the reference angle of any angle and also to come up with the reference triangle for that angle. This e-book will give both the teachers and the students the exact ideas that must be used to compute the reference angle of any angle. The first part of this e-book shows how to label t

This lesson on using Riemann sums to find the area under the graph of a function is intended for students enrolled in AP Calculus AB or BC, Calculus Honors, or College Calculus. In this document, we explore the following: 1. How to find the limit of a function graphically with examples. 2. How to find the limit of a function numerically with examples. 3. How to find the limit of a function algebraically with examples. 4. How to determine whether a function is continuous at a point and over an in

This lesson is intended to provide a general overview of the concepts of differentiation and integration. Knowledge of these concepts is required for students enrolled in AP Calculus AB or BC, Calculus Honors, or College Calculus. Differentiation is the process of computing (finding) derivatives. A derivative is also called the instantaneous rate of change. It is also called the slope of the tangent line to a curve at a given point. The derivative of an equation tells us the rate of change (de

PREREQUISITE KNOWLEDGE: The student should know how to find the derivative of any given function. This step by step guide will meet the following objectives: Objectives: --------------------------------------- Upon completion of this section, the student should be able to: • Use derivatives to determine the intervals of increase and decrease of a given function • Use the First Derivative Test to determine any local maximum or minimum points • Find inflection points • Use the concav

Logarithms helps us represent large numbers in very compact form. It can also be used to tell us how many of one number we must multiply to get another number. The exponential function y=a^x is one of the most important functions in mathematics, physics, and engineering. Applications relating to radioactive decay, bacterial growth, population growth, continuous interest all involve exponential functions. We know that logarithmic and exponential functions are inverses. This means one can chan

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

In this document, the students will learn about the graphs of several trigonometric functions. These are the graphs of sine, cosine, and tangent functions. They will learn how the graphs of y=sin(θ), y=cos(θ), y=tan(θ) and their reciprocals look. It is essential that they also practice how to graph these functions on their own.

One of the most compelling Number Patterns in Mathematics is The Pascal's Triangle which is named after Blaise Pascal, a famous French Mathematician and Philosopher. To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern. Each number is just the two numbers above it added together. The Binomial Theorem is a quick way of multiply out a binomial expression that has been raised to some (generally inconveniently large) power. For instance, t

Geometry deals with shapes and the properties of those shapes. This documents discusses basic concepts of geometry. This e-book will be useful to students taking Geometry in high school and will become handy to those taking the SAT , GRE, GMAT Math section. The topics that are discussed in this e-book are as follows: 1. Polygons 2. Angles 3. Angles Properties in Circles 4. Circles, Chords, Tangents and Quadrilaterals