Math How-Tos
How To: Solve a 3x3 linear system using Cramer's Rule
In this video the instructor shows how to solve a 3 x 3 linear system using the Cramer's rule. In this kind of problem you are given three equations in three variables x, y, z and you need to solve for the values of these equations. You can solve this using the Cramer rule which says that the value of x is Dx/D, where Dx and D are two different determinate. Now you have to figure out the determinate to get the value of variable x. The determinate D is called the foundation determinate and is ...
How To: Add consecutive odd numbers
Professor ElvisZap teaches you about adding consecutive odd numbers. You can learn this faster by drawing squares near the numbers themselves. If you are doing 2x2, draw 4 squares. They will be arranged in columns of two. For 9 you will draw 3 columns of 3. 16 are 4 columns of 4. 16 is also 1+3+5+7, which are all odd consecutive numbers. 25 are 5 columns of 5, but also 1+3+5+7+9. If you start counting 1 as the zeros odd number, then 3 as the first odd number, the nth odd number will be (2xN+1).
How To: Factor a trinomial, GCF, then unfoil
In this video the instructor shows how to factor a polynomial. A polynomial having three terms is called as trinomial. Now if you factor it you will obtain two binomials whose product will be the original polynomial. Before factoring a polynomial you need to find out if the polynomial has a GCF. Look out for the common variables in all the three terms and pull them out which is the GCF of the polynomial. This simplifies the original equation to a polynomial which is of lower degree. Now facto...
How To: Solve quadratic equations by factoring
This is a great educational video on how to solve quadratic equations by factoring. Let us take an example and try to learn the method. Here is a quadratic equation: (r+7) (r-9) = 0. Consider zero-factor property. For real a and b, if a.b = 0, then a = 0 or b = 0 or both are equal to zero. So r+7 = 0 or r-9 = 0 > r = -7 or r = 9. Hence, r = -7, 9. Similarly to solve a quadratic equation (13r+7) (6r-18) = 0, we will get 13r = -7 or r = -7 over 13. Also 6r = 18 or r = 3. So r= -7over 13, 3. Thi...
How To: Fill a cone
This is a very interesting instructional video on how to fill a cone. Pour oil into a cone of diameter 30 inches and depth 40 inches. Now find the volume of the oil as a function of its depth. Volume = 1 over 3 phi rsquare h. We don't know the height and depth of the oil poured into the cube. Draw similar right angled triangles. In one right angled triangle the height is 40 inches and in the other triangle it is h. Similarly the height is 40 inches and h respectively. Now rover h =15 over 40....
How To: Stretch, shift & reflect the graph of a square root
Professor ElvisZap teaches you how to stretch shift and reflect the graph of a square root. A square root function is the opposite of a squared function. You start with y=square root of (x-1) it becomes 0<=x-1. then 1 <=x. You use the graph and solve it as you would for any function using small values first, then you have y=square root of x - 1, the domain 0<=x. This shifted the graph down 1 unit. 0=square root of x - 1, 1=square root of x, 1=x. Then the range is [-1 + infinity). Continue in ...
How To: Discover the area of a triangle
Before you can find the area of any geometrical figure, recall what you are finding when you solve for the area. The area is the surface of a 2-dimensional shape. When trying to find the area of a right triangle, the easiest way is to first double the triangle so that it resembles a square. This is particularly important if you don't know the length of the hypotenuse. Using the knowledge that the area of a square is the length multiplied by the height, calculate the area of the square you cre...
How To: Find the area of triangles and other geometric shapes
The video shows us how to find the area of triangles and other geometric shapes. First, before starting to find the areas, we need to know the basics of what do those shapes actually mean and we need a little bit of vocabulary to back us up. First, the parallelograms are four sided figures with two sets of sides which are parallel to each other. The rectangles and the squares qualifies the parallelograms and also the parallelograms except that they have slanted sides and the triangles are thr...
How To: Do long division with remainders
This video goes through the step by step process of doing long division with remainders. Multiple examples are used throughout the video to give the viewer a better idea of how to properly complete the difficult task. Perfect for anyone learning long division for the first time, or for anyone attempting to relearn long division after forgetting how to do the process (an all to common occurrence in a world with calculators on every cell phone).
How To: Multiply binomials with the FOIL method
Multiplying polynomials is a distributive property. If you are given with two binomials and asked to multiply them, you need to apply the distributive property and multiply the terms of binomial with the terms of second binomial. To do this first take a term of first binomial and multiply it with the second complete binomial. Now take the second term of first binomial and multiply it with the second binomial adding or subtracting it from the previous result depending on the sign between the f...
How To: Find a missing coordinate given: coordinate & equation
In this video, the instructor shows how to find an unknown coordinate given the other coordinate of that point and the equation that passes thought the point. A point is said to lie on the graph, if the point can satisfy that equation of the line. To check if a particular point satisfies an equation, all you have to do is substitute the value of the point in that equation and check if it validates the equation. Now, substitute the given point with an unknown coordinate in that equation. If th...
How To: Find the area between curves
This video shows how to find areas between curves. The basic idea is that we find the space trapped between two curves on a graph. The formula for finding this is top curve, subtract bottom curve and then integrate. The presenter shows a parabola that goes through the origin. Then he draws a line that runs through the origin. We try to find the area trapped between the two. You take your smallest x co-ordinate to the largest x co-ordinate, you take the curve on top (2x) and subtract the curve...
How To: Solve operations on rational functions (f o g)(x)
YAYMATH In order to use rational functions in intermediate algebra, Robert Ahdoot begins by setting values to the functions f(x) and g(x). He then adds these functions together, with the equation (f+g)(x). After addition comes subtraction, using the equation (f-g)(x). And finally multiplication, which is (ftimesg)(x). This is a little more complicated, requiring distribution of a binomial across a polynomial, but it's clearly demonstrated and explained. This video explains what to do with add...
How To: Find the slope of a line given 2 points
In this video the instructor shows how to find the slope of a line given two points that like on the line. Slope of a line is the measure of the steepness of the line compared to the angle made by the line with the x-axes. A line with positive slope slants forwards and a line with a negative slope slants backwards and a line parallel to x axes has zero slope. So if you are given two points (x1, y1) and (x2, y2), the slope of the line passing through those two points is equal to m = (y2 - y1)/...
How To: Simplify complex fraction w/ single fraction on bottom
This is a great instructional video on education. This educational video teaches you how to simplify a complex fraction with a single fraction on bottom. Let us learn this with an example. Let us assume we have to simplify the complex fraction 5 by x-4 divided by 5-4x by 5. When you simplify this you will get 5-4x over x divided by 5-4x over 5. You will now get 5-4x over x multiplied by 5 over 5-4x. This is equal to 5 over x. This is how we have to simplify a complex fraction with a single fr...
How To: Find the equation of a line given 2 points
This tutorial teaches you how to find a mathematical equation of a line given 2 points that exists on the line. The tutorial starts off with 2 points labeled (2,-4) and (3,6). The first step is to determine the slope of the line using the formula given in the tutorial in blue. The slope is then solved as 'm'. Plug the slope and the points into another formula given in green. The tutorial maker provides a tip that one can use x1 and y1 or x2 and y2, however, it must be consistent. After, solve...
How To: Understand the Pythagorean Theorem
In this video Ken teaches you about the Pythagorean Theorem. The Pythagorean Theorem is used to find the missing length of a side of a right triangle. By watching this video, you will learn how to find any the length of any side by using a simple mathematical formula. Ken walks you through various examples changing the dimensions of the triangle you are solving as well as changing the side you are solving. Ken even includes a real world application to further your understanding of the Pythago...
How To: Multiply and divide three rational expressions
In this video, the instructor shows how to multiply and divide rational expressions. To solve a rational expression that contains many terms, solve step by step by following the order of operations. Order of operations advises one to work the parenthesis part first; so solve the equation inside the parenthesis first. If you have a fraction multiplied by another fraction, first factorize the numerator and denominator of both the fractions. Cancel out any common factors simplifying it. In case ...
How To: Simplify fourth roots
In this video the instructor shows how to find out the fourth roots of a number. The properties of fourth root says that for any positive number of a, its fourth roots are real. And for any negative value a, its fourth roots are not real. So split the number inside the fourth root as the product of two perfect squares and then cancel out the power with the fourth root giving its roots. As the fourth roots of a positive number are real, the answer you get is correct. But you cannot find out th...
How To: Find the area of a circle with pi
This video shows how to find the area of a circle using a formula. The formula for area of circle is pie multiplied by square of radius. Pie is actually an infinite number but for the sake of convenience we consider the value of pie as 3.14. So we multiply the square of radius with 3.14. Radius is the distance between the center point of the circle to any of the outside arcs. It is actually half of the diameter (diameter is the distance between two arcs of a circle). As an example here the ra...
How To: Solve quadratic equations by square root method
In this video the instructor shows how to solve quadratic equation by the square root method. The square root property of equations states that if k is positive and a*a = k, then a is equal to square root of k or -1 times the square root of k. So to solve a quadratic equation by square root property first get the equation in the form of a*a = k. Now apply the square root property explained in the previous step to get the result. The instructor now demonstrates these concepts by solving some e...
How To: Convert from cubic yards to cubic feet and inches
brettman6533 teaches you how to convert from cubic yards to cubic feet and inches. The volume of a cube is side cubed. If the side of a cube is 1 foot, then the volume would be 1 foot squared. Knowing that a foot equals 12 inches, you transform that into 1 times 12 in times 12 in times 12, which equals 1728 inches squared. If you want to convert a cubic yard, you have to remember 1 yard equals 3 feet. So now 1 yard squared is 1 times 3 feet times 3 feet times 3 feet, which is 27 feet squared....
How To: Solve equations with fractions and decimals
In this tutorial the instructor shows how to solve equations with fractions and decimals. When you have a fraction first try to simplify it by canceling out the common factors in the numerator and the denominator. If there are any decimals convert them into fractions. Now if you have a number multiplying a equation apply distributive law and simplify the equation. Now finally try to get the variables on one side and numerical terms on the other side of the equation and finally solve for the u...
How To: Find the area of a parallelogram using geometry
The video shows us how to find the area of parallelogram using geometry. Here in this video it is done by using an example where the parallelogram is given ABCD. The area of the parallelogram is base times height (bh). Here the base is given as 15 but the height is not known but it is represented by the segment BD. To find the value of h, let’s use right triangle BDC on the right side of the figure. Since base is 15 and the opposite side of the parallelogram is congruent, the hypotenuse of th...
How To: Use geometry nets
Viewers learn that a net is the shape formed by "unfolding" a 3-dimensional figure, so a net shows all the faces that make up the surface area of the figure. Viewers are then asked to determine what type of 3-dimensional figure can be made from a given net (note that a cylinder has 2 circular bases, a pyramid has triangular faces, a cone has 1 circular base, and a prism has rectangular faces). Students are also asked to determine if a given net can be used to make a cube. This video will bene...
How To: Graph compounds sentences with the word "or" in hem
A Teacher shows us how to graph compound sentences with the word "or" in them. These graphs will have arrows pointing out in different directions. On the number line draw arrows from the numbers in your compound sentence. So for example if after solving a problem with inequalities the problem has two possible answers that it could be, you would record both of the answers that it could possibly be. For our example we will use x is greater than seven, and x is less than three. You would then dr...
How To: Solve the circumference of a circle using a cookie
In this video the instructor shows you the diameter, radius and also how to find the circumference of a circle using a cookie as an example. When you draw a line against the cookie passing through its center and touching its boundaries, it is a diameter of the circle. Radius of a circle is half the diameter of the circle. The length of the circle along the border of the circle is called circumference of the circle. The formula to compute the circumference of a circle is 2 * Pi * r, where r is...
How To: Understand parallelograms
This video helps us understand parallelograms and its properties. The video starts with the description of the basic properties of a parallelogram. The parallelogram is a four sided shape which has the sum of all four interior angles equal to 360 degrees. The opposite sides of a parallelogram are equal and parallel. Then the video talks about the angles in the parallelogram. The parallelogram has a lot of symmetry. This makes the opposite angles of a parallelogram equal. The same side angles ...
How To: Find the percent change using proportions
In this video, the instructor shows how to identify the percentage change using proportions. When a given quantity increases or decreases by certain amount then we can calculate the percentage change in the quantity, which can be either increase or decrease based on the new value of the quantity. To solve these kind of situations you should know that the ratio of amount of increase (or decrease) of an amount to its original amount is equal to the ratio of percentage increase (or decrease) to ...
How To: Solving for "x" using addition and subtraction
The first operations you will need to know when learning to use algebra to solve for an unknown variable “x” will be using addition and subtraction. You can check you work by checking the balance of the equation when you are done.
How To: Solve for "x" with powers and parenthesis
Solving for ‘x’ in an algebraic equation can seem difficult when presented with different situations. Here are a few examples and tip for how to solve for x when there are powers and parentheses in the polynomial equation.
How To: Use implicit differentiation to find a 2nd derivative
An educational video by http://JustMathTutoring.com that shows how to use implicit differentiation to find a 2nd derivative of an equation.
How To: Understand the basics of trigonometry
Learn and understand the basics of Trigonometry in this entertaining video. Taught by an experienced YayMath instructor, viewers gain knowledge in the study of trigonometry: the relationship of angles and the triangles they are in. Trigonometry is relevant in many forms of everyday living and careers including architecture. Watch as the experienced instructor gives easy-to-follow instructions and examples including solving "x for y" equations using the 'SOHCAHTOA' method, an abbreviation for ...
How To: Solve multi-step equations
In this video the instructor shows how to solve multi-step equations. In a multi-step equation, the equals to sign divides the two sides of the problem. To solve this kind of problem, the first thing
How To: Understand and work with rational & irrational numbers
In this video the instructor explains the concepts of rational and irrational numbers. Multiplying a number by itself gives the value of its square. If you apply the square root to that squared number it returns to you the original number. This square root is also called a radical. A square root of a positive number can have two values. For example the square root of 81 is either 9 or -9; this is because when you multiply 9 with itself the square is 81 and even when you multiply -9 with itsel...
How To: Graph linear functions by finding X & Y Intercept
This video shows the method to graph a linear function by finding the X and Y intercept. Only two points are needed to graph linear functions. So we find the point on Y axis or the Y intercept and the point on the X axis or the X intercept. We notice that on the Y axis the X coordinate is zero. So, we find the Y intercept by putting x=0 in the given equation and solving for y. In the same way, we find the X intercept by putting y=0 in the given equation and solve for x. We join the two points...
How To: Solve a linear system by graphing in math
This video teaches you how to solve a linear system by mathematically graphing it out. The video starts off with a problem, asking to solve the system, with two given equations. To solve the system, one would insert 0 for x and solve for y in the first equation to obtain a point. Then one would insert 0 for y and solve for x at the second point. Afterwards, insert 1 for x and solve for y to obtain the third point. For the second equation, do the same thing, inserting 0 for x, 0 for y and 1 fo...
How To: Find the remainder in algebraic long division
This is a educational instructional video on mathematics. This video teaches you to find the reminder in algebraic long division. Let us take an example. Divide xcube+2xsquare-3 by x-2. When you divide you will get xsquare first. You will get xcube-2xsquare. Now subtract this from xcube +2xsquare. You will get 4xsquare. Now you have to divide 4xsquare+0x by x-2. Now you will get 4x. Now you have to subtract 4xsquare-8x from 4xsquare+0x. You will get 8x. Now you have to divide 8x-3 by x-2. You...
How To: Simplify radical expressions
In this video the instructor shows who to simplify radicals. If you have a term inside a square root the first thing you need to do is try to factorize it. First factorize the numerical term. Write down the numerical terms as a product of any perfect squares. Now split the original radical expression in the form of individual terms of different variables. Now you can pull out the perfect square numerical factors out of the radical. Similarly for the variable terms write the variables as power...
How To: Complete the square
This is an instructional video on how to "complete the square", which is an algebraic technique for solving a quadratic equation. The instructor starts by showing you what a quadratic equation actually is. He describes what "completing the square" actually means, and how it can help simplify a problem that is difficult to factor. He shows a few examples of completing the square, and then shows how it applies to the quadratic equation. He works through a step by step, so it's easy to follow an...