Active Math Posts
How To: Find the distance between 2 points w/ distance formula
Algebra – The Distance Formula.
How To: Draw the "y=A|x-h|+k" graph
In this video, one teacher talked in detail about how to solve absolute value functions and how to translate different absolute value functions from one point in the matrix to another one horizontally and vertically. If the function is y=A|x-h|+k, generally, the diagram is symmetric based on the line of X and can be moved vertically based on k. The teacher gave several examples to explain how to illustrate the absolute value function. He started with a simple one: y=|x-h|, then continued with...
How To: Factor a trinomial with negative leading coefficient
In this video the instructor shows how to factor a trinomial with negative leading coefficient. Most of the students are confused when they have to factor a trinomial with a negative leading coefficient. But there are many ways to solve these kind of problems as shown in this video. One way you can do is that take out the greatest common factor (GCF) of -1 from the equation. So pulling the -1 gives you the original trinomial with all the signs of the terms changed. Now go on and factor the ne...
How To: Divide numbers using long division
This video focuses on how to do long division. She starts by dividing 1548 by 26, going incrementally between each value. She first take 26 into the first three numbers of 1548 (154) and gets 5, then takes the remainder of 24 (154-130) and brings down the 8 to get 248. She then divides 248 by 26 to get 9 with a remainder of 14. She then goes into some detail as to how to extract the decimal from the remainder by continuing the long division and adding zeros to the end of the divisor. At the e...
How To: Graph the absolute value of a function
This video shows the method to plot the graph of the absolute value of a function. The video shows the example of the function of cube root of 'x'. The demonstrator first plots the graph of a cube root function. This is done by taking the reference point of positive one and positive eight. The graph is drawn for both negative and positive values of 'x'. After this the graph of absolute function is drawn by taking the absolute value of the cube root function. The resultant graph comes out to b...
How To: Square expressions involving radicals
Here we look at squaring expressions that involve radicals because people tend to make some common mistakes while solving such expressions. Take 5 times the square root of y quantity squared, the answer here is not 5y. Here's the reason, square means to multiply something with itself so the square of 5 root y would be 5 root y into 5 root y. So 5 x 5 is 25 and under root y into under root y equals just y so the answer will be 25y.
How To: Solve a quadratic equation
In this video the instructor shows how to solve a quadratic equation. If you have a quadratic equation with complex fractional terms and you find that a particular term is repeating then equate that term to a new variable and replace the variable in the given equation. Now try to get the equation a*x*x + b*x + c = 0, and solve for the roots of the equation which gives the values of the intermediate variable. But this variable was replaced instead of another term. So equate that term to the va...
How To: Solve radical equations easily
In this video, the instructor demonstrates how to solve radical equations and inequalities. If you have an equation that contains radicals, re-,arrange the equation so that all the radicals are on one side and the integers are on the other side. To cancel a square root from an equation, square both sides of the equation. The square of the equation cancels out the square root, thereby removing the radical. Even after squaring if you still have a radical left, treat it as a new problem and appl...
How To: Factor a number
The following are the steps to describe how-to factor a number: 1. First we go into factoring a number we first need to know the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23 etc.
How To: Apply the Pythagorean Theorem to right triangles
In this video the instructor talks about Pythagorean theorem and how to apply it to right triangles. Pythagorean theorem states that in any right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse the sum of the squares of the lengths of the legs is equation to the square of the length of the hypotenuse. That is a*a + b*b = c*c. This theorem works only for right angled triangle. So if you have the lengths of the two legs of a right triangle substitute the va...
How To: Find the equation of a line
In this video the instructor shows how to find the equation of the line given its slope and a point that lies on it. If the slope of the line is m and the point that lies on it is (x,y) then you can find the equation of the line by substituting the values in the slope-intercept form of an equation which is y = mx + b. Now substitute the values in the above equation and solve it for the value if the y-intercept y. Now you have the slope m and y intercept b. Substitute these values in the gener...
How To: Simplify rational expressions
When you need to compute the square root of a number you can do it by breaking it into perfect squares. When you can split the given number into small perfect squares you can cancel out the square root of the expression to the square of the perfect squares. You cannot always write the number inside the square root as a perfect square, but try to write this number as a product of a perfect square and another number. Now you can pull out the perfect square out of the radical and leave the remai...
How To: Find the equation of a perpendicular line
In this video the instructor shows how to find out an equation of a perpendicular line. If you need to find the equation of a line passing through the given point and perpendicular to another line, the first thing you need to do is compute the slope of the given line. Obtain the slope of the equation by writing it in the form of y = mx + b. Now the product of slopes of two perpendicular lines is negative one. So the slope of our required line will be negative inverse of the slope of given lin...
How To: Understand nth roots and operations on radicals
This video teaches us the concept of nth roots. The video starts with the square root of constants. We find the number which when multiplies by itself for two times results in the constant inside the square root. Then we find the square root of variables. Here again the same concept is used. We find the variable which when multiplied by itself for two times results in the given variable. Then we find the cube root. Here we find the number which when multiplied by itself for three times result...
How To: Find the area of triangle using fraction measurement
This video demonstrates the way to find the area of a triangle using fraction measurements. The person presenting this video first writes the actual formula for calculating the area of the triangle. The formula is: the area of the triangle denoted by ‘A’ is equal to half of ‘b’ times ‘h’ where ‘b’ and ‘h’ are the base and height of the triangle, respectively. Now, to make it into fractions, he writes ‘b’ and ‘h’ over ‘1’. Then he asks you to calculate “what is one times ‘b’ times ‘h’” which i...
How To: Simplify complex fractions in math
In this tutorial the instructor shows how to simplify complex fractions. A complex fraction is the same as a normal fraction, but has a fraction problem in the numerator and a fraction problem in the denominator. The first thing to do is arrive at a simple fraction both in the numerator and the denominator. To do this take the lcm of the denominators of the fractions in the numerator and simplify it. Similarly do this in the denominator. Now both the numerator and the denominator have a simpl...
How To: Divide decimals
Here we are, learning how to divide decimals. So we are dividing a whole number or a fraction by a fraction. How this presenter does this is by moving the decimal two places to the right on both the top and bottom of the sum. In other words, he multiplies the two numbers by 100. So 2 becomes 200 and .25 becomes 25. So much easier to divide 200 by 25 than to divide 2 by .25. Provided you've multiplied both the top and bottom by the same amount, the result will be the same, because the relative...
How To: Interpret a graph
YouTube user NotesCollegeAlgebra teaches you how to interpret a graph. You will learn how to read it and extract information. You go to the graph to see that f(-4)=-2. f(1.5)=2, so it's positive. You then have the question: For what x-values is f(x)<0? You go to the graph and see that you come up with (-5,3). The x-int is (3,0) (4,0). The y-int is (0,4). The domain is (-5,4) and the range is (-4,4). You then have the question: how often does y=7/5 intercept the graph? The answer is 4 times. T...
How To: Solve an equation using the point slope form
In this video the instructor shows how to derive a general equation for a line in Point-Slope form. The slope of an equation is the ratio of difference of y coordinates to the difference of x coordinates. In other words, slope is the change of y up on change of x. So you have the basic slope equation m = (y2 - y1)/(x2 - x1). When you have fractions you can simplify them by multiplying the denominator to the numerator on both sides. So multiply the equation by (x2-x1) on both sides. This gives...
How To: Prove congruent triangles with SSS and SAS
This is a video tutorial on how to prove congruent triangles with SSS and SAS test. SSS means side-side-side and SAS means side-angle-side. For applying the SSS test of congruency, each side of one triangle must be congruent to the corresponding side of the other triangle. For applying the SAS test of congruency, two corresponding sides of the two triangles must be congruent as well as the angle between those two sides of each triangle must be congruent. Follow the rest of the video to unders...
How To: Convert temperature using a point slope equation
In this video the instructor shows how to convert temperature using the point slope form. In this kind of problem sometimes you are given a temperature in Fahrenheit and its equivalent in Celsius and an other temperature similarly in both Fahrenheit and Celsius. Now you are asked to find a linear equation for these pair of temperatures. To solve these kind of problems assume that the given temperatures represent the point (x, y). Now you have two points. Substitute this value in the point slo...
How To: Figure out the area and circumference of a circle
Bill, Bobbie, and Drew present information on a circle. The presentation defines the key points of a circle. The area of a circle is Pi (3.14) x radius x radius. The diameter of a circle is the line drawn from one end to another inside the circle. The radius is the center of the circle to the edge. To find Pi, one simply takes the circumference/diameter. Circumference/diameter will always equal Pi (3.14) no matter the circle’s size. The final point is “what makes a circle a circle”? It is a b...
How To: Solve problems about linear equation
In this video the instructor shows how to write a linear equation. If you need to find the equation of a line that passes through the two given points then you need to find the linear equation of that line. The first step is to find the slope of the line that passes through these points. The slope can be calculated by finding the ratio of the difference of y coordinates to the difference of the x coordinates i.e. the change in y up on the change in x. Now substitute the value of slope and any...
How To: Calculate the area of a triangle using a basic formula
Free Math Tutoring teaches you in this video how to calculate the area of a triangle using a basic formula. The area of a triangle is (b times h)/2. B is the base of the triangle and h is the height. This formula works for all kinds of triangles. Sometimes you won't have the height in the triangle, so you need to draw a line from one angle to the base opposite that, at a 90 degree angle. Measure that and you have your height. It might seem difficult at first, but practice helps you understand...
How To: Do Celsius to Fahrenheit temperature conversion
The video teaches how to convert degrees Celsius to degrees Fahrenheit. First the boiling points of 32 degrees Fahrenheit and 100 degrees Celsius are plotted on the Y and X axis. Then a line is drawn to join them both. The value m is delta Y (boiling point minus freezing point, i.e., 212-32)/ delta X (boiling point minus freezing point, i.e., 100-0). So m works out to 180/100 or 1.8. Then the formula y=mx+b (intercept of y = 32) is used, substituting X with Celsius and y with Fahrenheit, to c...
How To: Add & subtract rational expressions
In this video the instructor shows how to add and subtract rational expressions. When you have an addition or subtraction problem of rational expressions, first look and compare the denominator of all the terms. If all of them have the same denominator then the expression can be written as a fraction whose denominator is the original common denominator and whose numerator is the sum of numerators of all the other terms. Simplifying the numerator by adding and subtracting the like terms gives ...
How To: Complete the square and solve the quadratic equation
In order to solve a quadratic equation by completing the square, take a quadratic equation and make sure that the coefficient of the first squared term in one. If it is not factor it by pulling the term out to get it to one. Now just write down the first two terms in side a bracket and after it add the third term. Now take the coefficient of the x term and take one half of it and square it and put that number back into the bracket. Now as you added a new number, to cancel it out subtract it f...
How To: Solve direct & inverse variation word problems
In this video the instructor teaches about direct and inverse variation. Two variables x and y are said to be in direct variation with each other if you can write them in the form y = K * x. The value of y varies directly corresponding to the value of x. Y is said to be directly proportional to x. If you have a sample value of x and y, you can substitute the values in the above equation to compute the value of the constant K. Using this formula you can always find the value of one variable x ...
How To: Figure out the slope of a line
In this video you will learn how to find a slope of a line. The man in the video shows in a practical and easy way, how to do it with formulas. First he teaches how to find slopes of lines containing both negative and positive points. He shows with formulas how to do it. He teaches how to find slopes on a flat line and demonstrates that the slope of it is equal to 0. Next, he teaches a "trick" to help students learn how to identify zero and no slope lines. In the last example, he demonstrates...
How To: Simplify a complex fraction w/ binomial denominators
To simplify a complex fraction, turn it into one fraction on the top divided into a fraction on the bottom. Once this is complete, you will turn the division into the two into a multiple by the reciprocal, factor, and then cancel. To make a division, find the lowest common denominator of both the top and the bottom. Once you get this division equation, look carefully at the equations. If something can be easily canceled, go ahead and cancel it out at this time. If you cannot cancel anything a...
How To: Find the parallel line to a given equation
This videos explains how one can easily find the parallel line to a given mathematical equation. He starts by explaining what it means for two lines to be parallel mathematically speaking. Defining two lines, then comparing the slope of both lines you can mathematically determine that they are in fact parallel. He then moves to common math problems found on tests where you are given a point and a linear equation. He then forms a T-table with one column being line one and line two and illustra...
How To: Find the geometric mean
It doesn’t matter how long ago your last geometry class was, you can still impress your friends by finding a geometric mean. The geometric mean can be used to find the average of numbers with out unusually high or low results effecting the result.
How To: Draw a hypercube
This clip shows how you can draw a hypercube, which is a complex shape composed of cubes. You start with a series of equally spaced horizontal lines. Then you draw a vertical line from the origin (o, o, o). From the same point, you draw a horizontal line of the same length and two more lines at 45 degrees and 135 degrees from the horizontal. The vertical line and the 45 degree line form two of the vertices of one of the cubes. The vertical line and the 135 degree line form two of the vertices...
How To: Determine the area of a trapezoid
Need to figure out the area of a trapezoid for a household project? Even if you just want to sound smart, there is a simple formula that can be used every time you need to find the area of a trapezoid. Try the formula and see how good you are at geometry.
How To: Solve equations & inequalities with absolute value
In this tutorial the instructor talks about various strategies for solving equations and inequalities involving absolute value. To do this the first step is to isolate an absolute value. An absolute value is exactly equal to a number. If that number is less than zero then there is no solution. So, if you have an absolute value that is less than a number it means that the real value lies in between negative and positive value of that number. If your number is less than zero then it is empty se...
How To: Graph using the slope intercept equation of a line
This video shows us how to draw a linear equation using the slope and intercept technique. First, the narrator explains how to simplify the equation in order to get the slope and intercept out. He then shows how the coefficient of x equals the slope and the constant term tells us the y position of the intercept point. The technique for drawing the final line is plotting the intercept at the right height on the y axis, then running for some distance along the x axis and rising some amount. Thi...
How To: Add rational expressions with different denominators
This video shows the method to add rational expressions with different denominators. The first step in this process involves finding the LCD. After this is done, the numerator and denominator are multiplied by a specific number so that the fractions are rewritten with common denominators. In the second step the numerators are added or subtracted according to the problem with LCD in the denominator. Simplify the numerator by adding or subtracting like terms. After this, we get a rational expre...
How To: Find the percent increase or decrease in a quantity
This video shows us the method to find the percent increase or decrease in a quantity. This can be done in 30 seconds. The formula states that the percentage increase or decrease is equal to the product of the ratio of amount (increase or decrease) and the original amount and 100. This is explained by two examples. In the first example the amount of increase of the price of groceries is found by taking the difference of the new price and the old price. This is divided by the original price an...
How To: Understand the basics of matrices
In this video you learn how to understand the basics of matrices. The video includes how to do matrices with addition, subtraction and multiplication. The teacher explains in this exercise that you will need to know the number of rows and columns. He breaks down all of the steps required to solve these problems. Not only does he show how to understand the basics of matrices, but he does it dressed up like a king and with a little reggae music. You can hear the class's reactions to his jokes i...
How To: Find the equation of a circle given: center & tangent
In this video, the instructor shows how to find the equation of a circle given its center point and a tangent line to it. To do this, take a graph and plot the given point and the tangent on that graph. Now, from the center of the circle, measure the perpendicular distance to the tangent line. This gives us the radius of the circle. Using the center point and the radius, you can find the equation of the circle using the general circle formula (x-h)*(x-h) + (y-k)*(y-k) = r*r, where (h,k) is th...