STEM Creations

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

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,

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

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

Summation or sigma notation is a way to express a long sum into a single compact expression. FINDING THE AREA UNDER THE CURVE OF A FUNCTION BY USING RECTANGLES Given a continuous function that is defined over an interval [a,b], we can approximate or find the exact the area under the curve of f(x) by using Riemann sums. This can be done by evaluating a lower or upper Sum of areas of (rectangles that lie above or below the graph) of f(x). Finally, find the exact area by evaluating: STEPS: The pro

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 curv

What is a metric system? The metric system is the measuring system based on the meter, liter, and gram as units of length, capacity, and weight or mass. The easier way to memorize the metric system is by using the memorization line: “King Henry Died by drinking chocolate milk” Where: King has K standing for Kilo Henry has He standing for Hecto Died has D standing for Deca By had b standing for the basic unit in this case meter, liter or gram drinking has d standing for deci chocolate has c

At the end of the lesson the student should be able to learn the process of finding the inverse of a 2 by 2 matrix. Examples relating to how to use the resulting inverse in solving systems of linear equations are also given.

IntroductionRobert Hooke proposed that the stretch of a spring is proportional to the force applied to the spring. This is commonly written as F= - k x where F is the force applied, k is the constant of proportionality, or spring constant, and x is the length of stretch caused by the force applied. The negative sign indicates the spring force is a restoring force; in other words, the spring is always trying to oppose any forces applied to it. Recall that a force is a vector quantity.

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

Objectives: Upon completion of this section, the student should be able to: • Find inflection points • Use the concavity test to determine the intervals of concavity of a function

This document describes what a quadratic function is. I have also described how quadratic equations are solved and finally, I present some applications of quadratic functions. In it you will find the following ideas. I. Quadratic Functions in Standard Form II. Solving Quadratic equations a.) By factorization b.) By using the principle of square roots c.) By the completing of squares method d.) By using the quadratic formula e.) By graphing III. Finally in the last section,

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

The students will solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. At the end of this lesson, the students should know the formulas for the volumes of cones, cylinders, and spheres and how to use them to solve volume related problems.

By the end of the lesson the student should learn how to construct a Rhombus, ABXQ, using just a compass and a ruler

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 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 or decay. The ideas have been laid out so that they are easy to follow. Questions and answers are given. Step by step solutions are a

Exponential growth can be modeled using an exponential function of the form: yA = P(a)^x P = initial value of y x = time or any value for x a = multiplication factor 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. This document discusses applied problems that relate to exponential growth. The ideas have been laid out so that they are easy to follow. Questions and answers are given and step by step solutions are also pr