# Articles

## SHSAT Math Formulas

Are you preparing students for the SHSAT Math test? Looking for a comprehensive list of all math formulas students need to know before the test day? If so, then you are in the right place. How to prepare for SHSAT Math SHSAT Math Worksheets The Ultimate SHSAT Math Course Below you will find a list of all Math formulas your students MUST have learned before test day, as well as some explanations for how to use them and what they mean. Keep this list around for a quick reminder when your students need it. Let your students review them all, then help them to...
Effortless Math Team

## How to Divide Rational Expressions

Dividing Rational Expressions, divide a Rational Expression by another one, can be complicated. In this blog post, you will learn how to divide rational expressions in a few simple steps. Method of Dividing Rational Expressions To divide rational expression, use the same method we use for dividing fractions. (Keep, Change, Flip)Keep the first rational expression, change the division sign to multiplication, and flip the numerator and denominator of the second rational expression. Then, multiply numerators and multiply denominators. Simplify as needed. Examples Dividing Rational...
Reza

## How to Evaluate Logarithm

Since learning the rules of logarithms is essential for evaluating logarithms, this blog post will teach you some logarithmic rules for the convenience of your work in evaluating logarithms. Necessary Logarithms Rules Logarithm is another way of writing exponent. $$\log_{b}{y}=x$$ is equivalent to $$y=b^x$$. Learn some logarithms rules: $$(a>0,a≠0,M>0,N>0$$, and k is a real number.) Rule 1: $$\log_{a}{M.N} =\log_{a}{M} +\log_{a}{N}$$ Rule 2: $$\log_{a}{\frac{M}{N}}=\log_{a}{M} -\log_{a}{N}$$Rule 3: $$\log_{a}{(M)^k} =k\log_{a}{M}$$Rule 4: $$\log_{a}{a}=1$$ Rule...
Reza

## How to Solve Natural Logarithms

Logarithms that have Base e (natural logarithms) are important in mathematics and some scientific applications. This blog post explains the applications of natural logarithms with examples. Definition of Natural Logarithms A natural logarithm is a logarithm that has a special base of the mathematical constant $$e$$, which is an irrational number approximately equal to 2.71. The natural logarithm of $$x$$ is generally written as $$ln \ x$$, or $$log_{e}{x}$$. Examples Natural Logarithms - Example 1: Solve this equation for $$x: e^x=6$$ Solution: If $$f(x)=g(x)$$,then:...
Reza

## How to Rationalize Radical Expressions

As you may know, radical expressions cannot be in the denominator, so in this article, we will teach you how to get rid of them by rationalizing radical expressions. A step-by-step guide to Rationalizing Radical Expressions Radical expressions cannot be in the denominator. (number in the bottom) To get rid of the radicals in the denominator, multiply both numerator and denominator by the radical in the denominator. If there is a radical and another integer in the denominator, multiply both numerator and denominator by the conjugate of the denominator. The conjugate of $$(a+b)$$ is...
Reza

## How to Solve Rational Equations

An equation that consists of at least one Rational expression is a Rational equation, and in this article, we will teach you how to solve this type of equation using two methods. A step-by-step guide to solve Rational Equations For solving rational equations, we can use following methods: Converting to a common denominator: In this method, you need to get a common denominator for both sides of the equation. Then, make numerators equal and solve for the variable.Cross-multiplying: This method is useful when there is only one fraction on each side of the equation. Simply multiply the...
Reza

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## How to find Equation of a Circle

the equation of a circle provides an algebraic way to describe a circle and in this article, we teach you how to write two forms of the Equation of a Circle. Rules for Equation of a Circle Equation of circles in standard form: $$(x- h)^2+( y-k)^2= r^2$$ Center: (h,k), Radius: r Equation of circles in general form: $$x^2+y^2+Ax+By+C=0$$ Examples Equation of a Circle - Example 1: Write the standard form equation of each circle.$$x^2+ y^2-4x-6y+9=0$$ Solution: The standard form of circle equation is: $$(x- h)^2+( y-k)^2= r^2$$where the radius of the circle is $$r$$, and...
Reza

## How to Find Arc Length and Sector Area

To find the Arc Length and Sector Area of a circle, you need the formulas and in this article, we review and explain these formulas and their application. Formulas of Arc Length and Sector Area To find the area of a sector of a circle, use this formula:The area of a sector $$=πr^2 (\frac{θ}{360})$$, is the radius of the circle, and $$θ$$ is the central angle of the sector. To find the arc of a sector of a circle, use this formula:Arc of a sector $$=(\frac{θ}{180})πr$$ Examples Arc Length and Sector Area - Example 1: Find the length of the arc. Round your answers to the...
Reza

## How to Find Domain and Range of Radical Functions

There are several different methods to identify the Domain and Range of Radical Functions. In this blog post, you will learn how to find the Domain and Range of Radical Functions. Rules for Finding Domain and Range of Radical Functions To find the domain of the function, find all possible values of the variable inside radical.Remember that having a negative number under the square root symbol is not possible. (For cubic roots, we can have negative numbers)To find the range, plugin the minimum and maximum values of the variable inside the radical. Examples Domain and Range of...
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