List of Math Terms

Introduction to list of math terms:
List of math terms glossary of basic mathematics words from the level of kindergarten through college level. In many cases one or more definition is given. These lists of math terms are listed in order of difficulty, as younger students need only the earlier definitions. These lists are used to clear up the confusions of students so they could do duties related to math. This article listed the various list of math terms.

Names of List of Math Terms:

Algorithm - A step-by-step procedure of problem solving for solving computational mathematical problems.

Angle – Angle is formed by two rays starting at the same point.

Arc - A section of the circumference in the circle.

Area - The space measured in square units that any two-dimensional shape.

Arithmetic - A part of mathematics concerned with the four operations of positive numbers.

Base - The bottom of a figure, solid or three-dimensional objects

Bell Curve - The shape of the graph is indicates the normal distribution.

Binomial - A polynomial equation with two terms are joined by a plus or minus sign.

Centimeter - Metric units of measurement. It measure of length.

Circumference - The complete distance around the circle.

Chord - The segment which joins any two points on a circle.

Coefficient - A constant term with a variable.

Decagon - A polygon has ten sides, ten angles and ten straight lines.

Degree – it is unit of angle.

End Point - The point at which a line ends.

Equilateral – four side shape and all sides are equal.

Even Number - A number is divided or divisible by 2.

Exponent - The number is gives reference to the repeated multiplication required.

Some more List of Math Terms:

Face - The shape is joined by the edges on a three-dimensional object.

Factoring - The process of breaking numbers are down into all of their factors.

Graph Theory - A part of mathematics focusing on the properties of a variety of graphs.

Hexagon - A six side polygon and it has six angles.

Integers - Whole numbers, positive numbers, negative numbers including zero.

Isosceles - A polygon has two equal length sides.

Kilometer – it is the one of unit of measure. It is equals 1000 meters.

Like Terms - Terms have the same variable and different coefficient and the same exponents/degrees.

Mean - The mean is the like as the average.

Mixed Numbers - whole number with a fraction.

Obtuse Angle - An angle has a measure greater than 90°.

Quadrilateral - A four side polygon/shape.

Range - The difference between the high value and the low value.

Scalene Triangle - A triangle has 3 unequal sides.

Uniform – All are same.

Volume – one of the units of measure.

X-Axis - The horizontal line or axis in a plane.

Y-Axis - The vertical line axis in a plane.

Domain of Exponential Functions

Introduction to domain of exponential functions:

The exponential function in mathematics is defined as ex, where e is an integer. For example let us denote ex is an exponential function, Let us assume the value of x is zero, x = 0 then the solution is in the form of e0 = 1. Provided e.g. shows general concept of the exponential function. Here we are going to discuss about what is domain and the exponential function together as domain of exponential functions.

Domain of Exponential Functions:

Domain is the set of point or atlest a single point which refers an open connected space. We can say the domain in other words as group of all possible values from an independent variable of a function. The domain and range of the function is lies between (-infinity) to (+infinity).

First we have to start with the fundamental functions of the exponential function of base a,

f (x) = ax , a > 0 and also not equal to 1.

Then the value of the domain functions f is the set of all real numbers.

The range of f is the interval (0 , +infinity).

The given function have a horizontal asymptote which given by y = 0, then the function f has a y intercept at (0, 1).

When the value of the given function f is increased, then the value of a is greater than 1

When the value of the given function f is decreased, then the value of a is lesser than 1.

Example for Domain of Exponential Functions:

Example for domain of exponential functions 1:

Find out the domain of the given function f(x) = ln of (`sqrt (x^2 - 9x + 18)` )

Solution:

Step 1: Given exponential function is f(x) = ln of (`sqrt (x^2 - 9x + 18)` )

Step 2: When we take any value of the 'ln' then it must be a positive value. So:

`sqrt(x^2 - 9x - 18)` > 0

Therefore, `x^2` - 9x - 18 > 0

`x^2 ` - 3x - 6x + 18 > 0

x(x - 6) - 3 (x - 6) > 0

(x - 6)(x - 3) > 0

So either x - 6 and x - 3 are both positive, or x - 6 and x - 3 are both negative. So either x < 6 or x > 3. That's the domain. Having problem with help solve math problem keep reading my upcoming posts, i will try to help you.

Example for domain of exponential functions 2: Determine the domain of the function f(x) = log10 { 1 - log [`x^2` - 4x + 13]}

Solution:

Step 1: The given function is f(x) = log10 { 1 - log [`x^2` - 4x + 13]}

Step 2: Let there are two function present in log. Let we take outer log as nesting log and inner log as nested log.

Step 3: First nesting log is simplified as,

1 - log (`x^2` - 4x + 13)

log (`x^2` - 4x + 13)  < 1

log10 (`x^2` - 4x + 13) < log1010

x2 - 4x + 13 < 10

x2 - 4x + 3 < 0

x - 3x - x + 3 < 0

(x - 3)(x - 1) < 0

x `in` (3, 1)

For nested log function,

`x^2` - 3x + 12 > 0

Here, from the given function squared terms and their co efficient are positive and also domain is > 0. There fore the inequality is true for every real numbers.

Practice Math Facts Online

Practice math facts online – Introduction:

In algebra basic arithmetic operation (addition, subtraction, multiplication, and division) generally used in day to day life. Addition defined as adding the two numbers. Subtraction (-) defined as the inverse of addition. Multiplication defined as the product of numbers. Division can be considered as repeated subtraction.

In online, students can learn about math facts. Through online, students can have interactive sessions with tutors. Online is one of the efficient tools for one to one learning. In these articles we are going to see about practice math facts online. Understanding What is a Line Segment is always challenging for me but thanks to all math help websites to help me out.

Practice Math Facts Online – Addition and Subtraction Rules and Examples:

Practice math facts online - Addition rule with examples:

Positive + Positive = Positive: 7 + 7 = 14

Negative + Negative = Negative: (- 5) + (- 6) = - 11

Addition of a negative and a positive integer: Use the sign of the larger number and subtract, examples are,

(- 5) + 4 = -1

7 + (-2) = 5

Practice problems:

1.  (-9) + 2 =?

Answer: (-7)

2.  5 + (-1) =?

Answer: 4

Practice math facts online - Subtracting rule with examples:

Negative - Positive = Negative: (- 4) - 2 = -4 + (-2) = -6

Positive - Negative = Positive + Positive = Positive: 4 - (-4) = 4 + 4 = 8

Negative - Negative = Negative + Positive = Use the sign of the larger number and subtract (Change double negatives to a non negative)

(-5) - (-2) = (-5) + 2 = -3

(-2) - (-4) = (-2) + 4 = 2

Practice problems:

1   (-9) – 2 =?

Answer: (-11)

2.   5 - (-1) =?

Answer: 6

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Practice Math Facts Online – Multiplication and Division Examples:

Practice math facts online - Multiplication rules:

Rule1: Multiplication of two integers by the related signs resolve be positive sign

a) Positive x positive = positive

b) Negative x negative = positive

Rule2: Multiplication of two integers by the unlike signs will be negative

a) Positive x negative = negative

b) Negative x positive = negative

Example problems:

1. Positive x positive = positive

Example: 2 * 4 = 8

2. Negative x negative = positive

Example: (-2) * (-6) = (12)

3. Positive x negative = negative

Example: 6 * (-3) = (-18)

4. Negative x positive = negative

Example: (-4) * 3 = (-12)

Practice problems:

1.  (-7) * 2 =?

Answer: (-14)

2.  (-5) * (-2) =?

Answer: 10

Practice math facts online - Division rules and example problems:

Rule 1: Division of two integers by the related signs resolve be positive sign

a) Positive ÷ positive = positive

b) Negative ÷ negative = positive

Rule 2:  Division of two integers by the unlike signs will be negative

a) Positive ÷ negative = negative

b) Negative ÷ positive = negative

Example problems:

1. Positive ÷ positive = positive

Example: 9 ÷ 3 = 3

2. Negative ÷ negative = positive

Example: (-14 ÷ (-2 = 7

3. Positive ÷ negative = negative

Example: 10 ÷ (-2) = (-5)

4. Negative ÷ positive = negative

Example: (-15) ÷ (3) = (-5)

Practice problems:

1.  (-9) ÷ 3 =?

Answer: (-3)

2.  25 ÷ (-5) =?

Answer: (-5)

Standard Deviation Z Value

Introduction for standard deviation z value:

In this article we shall discuss about the standard deviation z value. Standard deviation is the part of measurement of the z-value,standard scores are also called as z-values, z-scores, normal scores.The z-value be simply define the population parameter, because in standardized testing; but one just contain a sample set, next the similar calculation by sample mean also illustration standard deviation yield the Student's t-statistic.

Standard Deviation Z Value

Z value:

The z value formula is

` Z=(x- mu)/ sigma`

where

x is a raw value to be standardized

μ is the mean of the population

σ is the standard deviation of the population

In standard deviation, z value be the number of standard deviations to a value, x, be above or else below the mean.Value of x is fewer than the mean- z value negative.The value of x is more than the mean- z value positive and value of x equals the mean - z value zero.

Let us see some of the examples of standard deviation z value. Having problem with Finding the least Common Denominator keep reading my upcoming posts, i will try to help you.

Examples for Standard Deviation Z Value

Example 1:

Find the Z value to the raw data of 14 coming from the mean 8 and the standard deviation 3.

Solution:

The formula for the Z value is

` Z = (x-mu)/sigma`

Where, x =14, µ = 8 and σ = 3

`Z = (14-8)/3`

`Z = 6 / 3`

Z  = 2

The Z value is 2

Example 2:

The Z value  3 was observed from the outcome of the normal distribution with mean 16 and the standard deviation 6 and evaluate the raw data.

Solution:

The  Z value  formula is

`Z =(x-mu)/sigma`

Where, Z= 3, µ = 16 and σ = 6.

2 = `(x-16)/6`

6(2)=x-16

12=x-16

x = 16 + 12

x = 28.

The raw data for the Z value 3, mean 16 and standard deviation 6 is 28.

These are the examples of standard deviation z value.

Practice examples for standard deviation z value:

1.Measure the Z value to the raw data of 18 coming from the mean 6 and the standard deviation 3.

Answer : 4

2.Calculate  the Z value to the raw data of 8 coming from the mean 4 and the standard deviation 2.

Answer :  2

Area Perimeter Rectangles

Introduction to area perimeter of rectangles:

In mathematics, the rectangle is a polygon of 4 sides, it's called quadrilateral. The rectangle is one of the quadrilateral with it has the four right angle.

Area of rectangles:

The sum of surface occupied by a plane rectangle is labeled the area of rectangle. The units of the rectangle area are square units.

Perimeter of rectangles:

The length of the boundary of any rectangle is labeled the perimeter of rectangle. The units of perimeter of rectangle are units.



Formulas for Area and Perimeter of Rectangles:

Area and perimeter of a rectangle:

For a rectangle of length = l and breadth or width = b we have:

Area = (l x b) square units.

Length = `(Area)/(width)` and Width =`(Area)/(Leng th or Width)`

Perimeter = 2(l + b) units.

Diagonal =`sqrt(l^2 + b^2)` units.I like to share this free 8th grade math problems with you all through my article.

Examples for Area and Perimeter of Rectangles:

Example 1:

Determine the area and perimeter of rectangles of the length is 23 cm and width is 50 cm?

Solution:

Given:

length( l) = 23 cm.

breath or width( b) = 50 cm.

To find area of the rectangles:

area A = (l x b) square units.

= (23 x 50) square cm.

=  1150 cm2 or square cm.

Therefore, Area of Rectangles = 1150 square cm.

To find perimeter of the rectangles:

Perimeter = 2(l + b) units.

= 2(23 + 50) cm.

= 2(73) cm.

= 146 cm.

Therefore, Perimeter of Rectangles = 146cm.

Example 2:

Find the area and perimeter of rectangles, if length is 12 inches and width or breadth is 5 inches?

Solution:

Given:

Length = 12 inches.

Width or breadth = 5 inches.

To find area of rectangle:

Area = (l x b) square units.

= (12 x 5) square inches.

= 60 square inches.

Therefore, Area of Rectangles = 60 square inches.

To find the perimeter of rectangle:

Perimeter = 2(l + b) units.

= 2(12 + 5) inches

= 2(17) inches.

= 34 inches.

Therefore, Perimeter of Rectangles = 34 inches.

Function Machines in Math

Introduction to function machines in math:

In this article function machines in math, we will discuss about basic arithmetic operation in the mathematics. Function machine should perform the following operation like addition, subtraction, multiplication and division of single and two digit number. And also half the number, double the number, addition of half and single digit number, subtraction of half and single digit number etc. Let us see some problems for function machines in math.

Single Step Performance - Function Machines in Math

Consider the variable x and y as a single digit number

1.Double the number 2x

2.Half the number` x/2`

3.Adding of single digit number  x+y

4.Subtracting of single digit number  x-y (Here the x is a largest number and y is a smallest number)

5.Multipling of single digit number  x(y)

6.Dividing of single digit number ` x/y`

Consider the variable x and y as a two digit number

7.Adding of double digit number  x+y

8.Subtracting of double digit number  x-y (Here the x is a largest number and y is a smallest number)

Two step performance -  Function machines in math

1.Double the number x and add a single digit number 2x+y

2.Double the number x and subtract a single digit number 2x-y

3.Half and add a single digit number `(x/2)+y`

4.Half and subtract a single digit number `(x/2)-y`

5.Add half of the number with itself `(x/2)+x`

Worked Example - Function Machines in Math

Perform the function math operation to the single and two digit number.

Single step performance

Consider the following  single digit number x=5 and  y=2

1.Double the number 2x=2(5)=10

2.Half the number x/2=5/2=2.5

3.Adding of single digit number  x+y=5+2=7

4.Subtracting of single digit number  x-y=5-2=3

5.Multipling of single digit number  x(y) = 5(2)=10

6.Dividing of single digit number  `x/y=5/2=2.5`

Consider the following two digit number x=20 and y=15

7.Adding of double digit number  x+y=20+15=35

8.Subtracting of double digit number  x-y =20-15=5

Two step performance

1.Double the number x and add a single digit number 2x+y => 2(5)=10+y=10+5=15

2.Double the number x and subtract a single digit number 2x-y => => 2(5)=10+y=10+5=15

3.Half and add a single digit number `(x/2)+y =gt 5/2=2.5+y=2.5+5=7.5`

4.Half and subtract a single digit number `(x/2)-y =gt 5/2=2.5+y=2.5-5=-2.5`

5.Add half of the number with itself`(x/2)+x =gt 5/2=2.5+x=2.5+5=7.5 `

Example of Cubic Function

Introduction of cubic function:

A Cubic function is a small different from a quadratic function. A Cubic functions have a 3 x intercept, The cubic function refer to as 3 degrees. The example of a cubic function is y=(x-1)(x+3)(x-4). it has 3 x intercepts which loaded on (1,0)(-3,0)(4,0).A cubic function is one of the functions which is formed as, F(x) =ax3+bx2+cx+dwhere a- nonzero (or) say polinomial of degree three. Quadratic function is derivation for cubic function. Also, a intergral for a cubic function.By ƒ(x) = 0 and assuming a ≠ 0 gives the cubic formula of the form:ax3+bx2+cx+d=0Coefficient a, b, c, d are real numbers. However, most of theory is also legal if they belong to field of characteristic other than 2 or 3.

Example Problems on Cubic Function:

Roots of a cubic function:

Each cubic equation with real coefficients have at least one solution x among the real numbers; this is a consequence of the Intermediate value theorem. We are able to differentiate several likely cases using the discriminant.

`Delta=18abcd-4b^3d+b^2c^2-4ac^3-36a^2d^2`

The next cases require to be measured

If Δ > 0, the equation have three distinct real roots.
If Δ = 0, the equation has a multiple root along with all its roots are real.
If Δ < 0, t the equation have one real root along with two non real complex conjugate roots.


Let us see some examples of cubic function:
Example 1:

Solving the factors of the cubic of the equation  x3-3x2-25x+75.

Solution:

The given equation is x3-3x2-25x+75.

This form as ax3 + bx2 + cx + d

So,  (x3-3x2) + (-25x+75)

Take a common variable:

=x2(x-3) -25(x-3)

=( x2-25) (x-3)

Here x2 – 25 in the form of a2 + b2 = (a + b) (a - b)

So, x2 – 25 = (x + 5)(x - 5)

=(x-5)(x+5)(x-3)

Answer: The solutions are 5,-5,3

Example 2:

Solving the factors of the cubic of the equation 6x3-36x2 = -54x

Solution:

This equation can be written as 6x3-36x2 + 54x=0.

This form as ax3 + bx2 + cx + d

So, 6x(x2-6x+9) =0.

Here x2 – 6x + 9 in the form of Ax2 + Bx + C so we find the factor.I like to share this Free math problem solver with you all through my article.

6x(x-3)(x-3) =0.

x=0, x=3, x=3.

Answer: The solutions are 0, 3, and 3.

Example 3:

Solving the factors of the cubic  of the equation x3-4x2-100x+400.

Solution:

The given cubic equation is (x3-4x2) + (-100x+400)

=x2(x-4) -100(x-4)

=( x2-100) (x-4)

=(x-10)(x+5)(x-3)

Answer : The solutins are 5,-5,3