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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: 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...

How To: Solve linear absolute value equations & inequalities

In this video the instructor shows how to solve linear absolute value equations and inequalities. You need to remember basic rules to solve these kind of problems. When the absolute value is equal to a number then the real value of it is equal to either the positive value of that number or negative value of that number. In case the absolute value is less than or equal to a number, then the real value lies in between the positive and negative values of that number. In the third case, if the ab...

How To: Find the circumference of a circle quickly

In this instance we are going to Find the circumference of a circle by applying formula C=2pr where 'C' is circumference of a circle, approximate value of 'p' is 3.14 because it is irrational number and 'r' stands for radius i.e. half of diameter. So by applying this formula we can easily calculate circumference of a circle if radius is given or we can also calculate radius if circumference of a circle is given. One thing to remember is that unit we use for circumference of a circle is cm, in...

How To: Find the area of a rectangle using geometry

This video shows how to compute the area of a rectangle given the length of one of its sides and its diagonal. First start by drawing the picture of the rectangle. Now draw the diagonal and label the known lengths. In the diagram, the diagonal and two sides of the rectangle form a right-angled triangle. The breadth of the rectangle can be computed using the Pythagorean theorem. Finally, compute the area of the rectangle by multiplying its length to its breadth.

How To: Understand parallel and perpendicular lines

In this video the instructor talks about parallel and perpendicular lines. Parallel lines are lines whose slope is the same. Now take the equations of a couple of parallel lines. Graph those lines on a coordinate axes and you can see that the lines are parallel to each other and never intersect each other. Perpendicular lines are those whose product of slopes is negative one. Perpendicular lines intersect each other and they make a perfect 90 degrees with each other at the point of intersecti...

How To: Solve problems with inverse functions

In this video the instructor teaches about inverse functions. Normally in inverse functions problems you are given a function that has a set of points and you are asked to find the inverse of that function. So if the function has a point in the form (x, y) then the inverse function has its points in the form of (y, x). Now when you are given a function f(x) that is in the form of x and asked to find its inverse, equate the function to y. Solve the equation to get the value of variable x in th...

How To: Factor the difference of squares

In this video the instructor shows how to factor the difference of squares using a formula. The formula to find the difference of squares can only be applied if you have two perfect squares. The formula is (a * a - b * b) = (a - b) * (a + b). That is the difference of squares of two numbers is the product of sum of two numbers and difference of two numbers. So when you need to find the difference of squares of two numbers substitute the values in the above formula to directly solve for the fa...

How To: Multiply and divide fractions

Fractions are vital to mathematics and essential in everyday life. As such, it's good to know how to multiply and divide them. This video demonstrates the process. For detailed, step-by-step look at multiplying and dividing fractions, watch this mathematics how-to.

How To: Graph quadratic equations

In this video, the instructor shows you how to graph quadratic equations. When you have a quadratic equation in terms of x and y, first try to identify the coefficients of the terms. Now use front end of the quadratic formula to find the line of symmetry which is the first half of the vertex using the formula x = -b/2a. This gives the line of symmetry. Next, plot the line using a few points starting at the line of symmetry. Take sample values of x and find the corresponding values of y on eit...

How To: Determine the age of a fossil using carbon-14

If you have a fossil, you can tell how old it is by the carbon 14 dating method. This is a formula which helps you to date a fossil by its carbon. If a fossil contains 60% of its original carbon, how old is the fossil? The half life of carbon 14 is 5600 years. That means this is how long it takes for half the nuclei to decay. After 5600 years, if we start with a gram, we end up with half a gram. This rather complex formula shows you how to solve this puzzle using accepted scientific methods.

How To: Use math reflections in pre-Algebra

The tutorial is part of a full lesson of pre algebra. This video teaches you what reflection is as a mathematical term. In the beginning of the video, the video maker draws 4 shapes labeled MNOPQ, ABCDE, FGHIJ and RSTUV. The first question in the video asks to "Name the figure that represents a reflection of ABCDE over the X-axis." The woman in the video repeats the question, stating the horizontal line is the X-axis and asks for the reflection image. She puts her hand on ABCDE and flips her ...

How To: Understand mean and standard deviation

Keith M. Bower explains the meaning of mean and standard deviation. This educational video gives insight in the basics of statistics. The relations between population mean and sample mean and between population standard deviation and sample standard deviation are explained. The mean gives an idea on the central tendency. Standard deviation gives an idea about how spread out the data are. Keith also explains how these two parameters, the joint sufficient statistics, define a normal distributio...

How To: Solve word problems with proportions

In this video the instructor shows how to use proportions to solve fractions. When you have a proportions problem with an unknown term, cross multiply and divide it to get the value of that unknown term. For example if given 7/8 = m/4, cross multiply 7/8 with 4, giving 7/2 which is the value of the unknown variable m. So if two quantities are proportionate then you can equate them as shown in the video and cross multiply to get the value of any unknown variable. Proportions are just fractions...

How To: Simplify expressions with different exponents

This video shows the method to simplify expressions with different exponents. The video starts with the explanation of 16 raised to the power 1/4. This can be solved by taking the nth or the 4th root of 16 where n stands for the denominator of the fraction. Then the video explains 8 raised to power 4/3. This can be solved in two ways. First one involves taking the cube root of 8 and raising it to the power of 4. The second method involves converting 8 into 2 raised to the power 3 and taking t...

How To: Understand deductive reasoning

In this video, Robert Ahdoot becomes "surfer dude" and shows us the ways of deductive reasoning, as relating to geometry. He begins with a simple example of a syllogism, taking two premises and using them to form a conclusion. This is called the Law of Syllogism. This concept is then used for geometric statements. If two angles are complementary, they sum to 90 degrees. If two angles sum to 90 degrees, then they are acute. By the law taught, it can be said that if two angles are complementary...

How To: Use simulations in pre-Algebra

This is a video from yourteacher.com on simulations for Pre Algebra. It explains what simulations are and gives an example problem. The teacher reminds us that it is important to remember that there can be more than one simulation for a problem. The teacher suggests a simulation for the problem given and suggests how many times to run the simulation. The teacher makes a simulation for what sex a child is by flipping a coin and suggests to flip the coin 50 or 100 times. The teacher also explai...

How To: Find the point slope form of a line equation

This is a mathematical instructional video on finding the point slope form of a line equation. This technique allows you to find the x and y intercepts of a line. The point slope form is (y-y1)=m(x-x1). The instructor tells you what each of the variables represents, and shows an example. He then shows you how to find the slope-intercept form from the point slope form. Finally, he shows you how to graph the line using both of the equations. He shows you how to find the equations with different...

How To: Algebraically solve mixed quantities problems

In this video the instructor shows how to solve mixture problems using two variables. Usually in these kind of questions the problem statement goes like, if A costs $x for a pound and B costs $y for a pound, in what ratio should they be mixed such that one pound of the new mixture sells for $z a pound. So, in these kind of problems start with a box where you list down all the given data in the form of a table as shown in the video. Now denote the unknown quantity of A and B by two variables a...

How To: Factor trinomials in a very simple way

In this video, they demonstrate how to factor a trinomial. A trinomial is a polynomial with a quadratic term in the form, ax^2+bx+c. To factor this polynomial first multiply the a and c term. You must fine two numbers that multiply to a*c and add up to b. Once you have figured out the two numbers you place the two numbers (D and E for example) in the equation (1/a)(ax+D)(ax+E). It takes a bit of practice to be good at deciding what D and E are, but the best way is to make sure that D*E = a*c ...

How To: Use the Chain Rule for finding derivatives

JustMathTutoring This video shows the procedure of finding derivatives using the Chain Rule. The Chain Rule states that the derivative of a composition of functions is the derivative of the outside function evaluated at the inside multiplied by the derivative of the inside. This can be stated as if h(x) = f[g(x)] then h'(x)=f'[g(x)]g'(x). This is explained by two examples. In the first example we find the derivative of the sine of square of 'x'. We take the derivative of sine at square of 'x'...

How To: Simplify complex fraction w/ 3 fractions top & bottom

You Tube User robichaudd teaches you how to simplify a complex fraction with 3 fractions top and bottom. Your result should be 1 fraction over 1 fraction. To do this you must find the L.C.D. at the top, which x cubed. That is the largest variable there. Thus, the L.C.D. at the bottom is x squared. Now you want to make each x below the fraction line be x cubed, respectively x squared. You then have one large fraction over one large fraction. But that is just one large fraction multiplied by th...

How To: Multiply rational expressions with opposite signs

In this video the instructor shows how to multiply and write rational expressions in lowest terms. The fist thing you need to do is cancel out the common factors in the numerator and the denominator. You can cancel a term in the top with a term in the bottom even if they are diagonal as long as one is in numerator and the other is in the denominator. After cancellation if you have a term in numerator and an identical term in the denominator but with opposite signs, then pull out the negative ...

How To: Solve a system of equations w/ the elimination method

The video shows us how to solve a system of equations with the elimination method. First write the two equations one on top of the other, as it is going to be elimination method and it is recommended to write it in that way. Here the 2 equations are x+y=-3 and x-y=1. In the elimination method we need to add the 2 equations by columns. So adding it column wise we get to have 2x=-2 and solving this we will get the value of x=-1. Then you need to substitute this value of x in any of the two equa...

How To: Graph x squared & the square root of x

In this video the instructor shows how to sketch the graph of x squared and square root of x. The first equation is the x squared which is y = x * x. Now to sketch this take a sample values of x and substitute in the equation to get the value of y. Similarly find the set of points for the equation. Finally plot these points and sketch this graph which is in the form of a parabola. The curve is in the form of alphabet 'U' with its vertex at the bottom. Now similarly take the square root of x e...

How To: Factor and collect like terms

In this video, the instructor shows how to collect like terms and factorize. When you are given a linear equation, the first thing you do is to try to organize it. Pair up the like terms. Add the numerical coefficients of terms with the same variables. This is called collecting the like terms. In case you see any common factor across all the terms, pull it out and tag it to the parenthesis. In this way, you can factorize the equation. Next, bunch together your like terms and sum them up. The ...

How To: Derive the area of triangle using trigonometry

This video teaches the method to find the area of triangle using law of cosines and law of sines together with the area formula. Law of cosines is used when you have the length of three sides. It states that the square of side 'a' is equal to addition of the squares of sides 'b' and 'c' minus the product of 2, b, c and cosA. The values of sides are substituted and angle A is found. This is substituted in the area formula which states that the area of a triangle is equal to the half of the pro...

How To: Understand fractions with patterns

This is an educational site where we can learn about math lessons with example videos, interactive practice problems and can do self-test. The associate teacher in the video teaches us about fraction problems. She has written four numbers on the board, which is 1 1/4, 1 1/2, 1 3/4, and 2. She explains how to find the next three numbers following the same pattern. The teacher in the video tells that the key in solving the problem is to think of 1 1/2 as 1 2/4. Each number in the given problem ...

How To: Understand equivalent fractions

In this video the instructor teaches about equivalent fractions. When given a problem to determine if two fractions are equivalent fractions the first thing to do is write them in the lowest terms. A fraction is said to be in the lowest terms if the greatest common divisor of both numerator and denominator is one. So cancel the common factors in the numerator and the denominator till you arrive at the lowest form and finally compare them to determine if they are equivalent. An equivalent frac...