Some definitions

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Acute Angle

Acute angle is an angle that has measures less than 90º.

 

 

Angle

An angle is the figure formed by two lines diverging from a common point.

 

 

Arcsin

arcsin is the inverse function of the sine function.

This means that if x is a value between 0º and 90º, then

arcsin(sin x) = x and sin(arcsin x) = x

 

 

Arccos

arccos is the inverse function of the cosine function.

This means that if x is a value between 0º and 90º, then

arccos(cos x) = x and cos(arccos x) = x

 

 

Arctan

arctan is the inverse function of the tangent function.

This means that if x is a value between 0º and 90º, then

arctan(tan x) = x and tan(arctan x) = x

 

 

Base

In exponential notation, the base is the factor being multiplied.

For example, in ab4, a is the base.

 

Binomial

Binomial is a polynomial consisting of two terms.

 

Check

Solution check is a the process of verifying whether the solutions that were found are valid.

It is accomplished by substituting all potential solutions in the original equation and simplifying it.

If the result of the simplification yields a true statement (such as 0 = 0), the solution is valid. Otherwise, it is not.

 

Circle

Circle is a curve with the following equation:

(x - a)^2 + (y - b)^2 = r^2

where r is the radius of the circle and (a, b) is its center.

 

 

Coefficient

Coefficient is the numerical factor of a term.

 

Complex Conjugate

The complex conjugate of a complex number is found by changing the sign of its imaginary part.

 

 

Complex Fraction

Any fraction that contains a fraction in its numerator, or denominator (or both) is called a complex fraction.

 

Complex Number

Any number that can be expressed in the form a + bi, where a and b are real numbers and i is the square root of (-1) is called a complex number.

 

 

Coordinate

Coordinates are two numbers used to determine the position of a point with respect to a fixed reference called origin.

 

Degree

Degree of a term is the sum of the exponents of all the variables in that term.

 

Equation

Equation is a mathematical sentence containing an equal sign.

 

Evaluate

Evaluating is the process of substituting numbers for variables in an algebraic expression and simplifying the resulting expression.

 

Expand

Expanding is the process of carrying out multiplication or exponentiation.

 

Exponent

Exponent is a number or variable that indicates the number of times the base appears as factor.

 

Exponential Equation

Exponential equation is an equation that contains a solution variable in the exponent.

 

Expression

Expression is a mathematical sentence containing constants, variables and operations.

 

GCF

The greatest common factor (GCF) of a sequence of terms is the largest term that divides each of them exactly.

 

Graphable form

Standard form in which equations of curves are commonly written

 

Horizontal

Parallel to the x-axis.

 

Imaginary Unit

Imaginary unit i is equal to the square root of (-1).

 

 

Inequality

Inequality is a mathematical sentence that contains an inequality sign.

 

Inverse Trigonometric functions

Inverse trigonometric functions are the inverse functions of trigonometric functions.

For example, arcsin is the inverse function of the sine function, arccos is the inverse function of the cosine function, and arctan is the inverse function of the tangent function.

 

 

LCM

The least common multiple (LCM) of a sequence of terms is the smallest term that can be divided by each of them exactly.

 

Linear

Linear equation is any equation of the form mx + c = 0, where m and c are real numbers and x is the variable.

 

Linear Inequality

Linear inequality is an inequality where every term has a degree less than or equal to one.

 

Mixed Number

Mixed number is any number consisting of one integer followed by a fraction.

 

 

Non Linear

Non-linear equation is an equation that has a degree greater than one.

 

Non Linear Inequality

Non-linear inequality is an inequality that has degree greater than one.

 

Perfect Square

Perfect square is a whole number that is the square of an integer or an expression which can be expressed as the square of a binomial

 

Point

Point is an ordered pair of numbers, (x,y).

The first number is called x-coordinate and the  second one is called the y-coordinate.

 

Polynomial

Polynomial is a sum of terms each of which is either a number or the product of a numerical factor and one or more variable factors raised to whole number powers.

 

Power

Power is a term that can be written in exponential notation.

 

Prime

Prime number is an integer larger than 1 whose only positive divisors are 1 and itself. All of the following are prime numbers: 2, 3, 5, 7, 11, 13

 

Quadratic

Term 'quadratic' refers to a second degree polynomial.

 

Radical

Radical expression is a mathematical expression containing at least one radical sign.

 

 

Radical Index

For example, in the expression radical the radical index is 3

 

 

Radical Equation

Radical equation is an equation containing one or more radical signs.

 

 

Radicand

The radicand is the expression whose root is being considered in a radical

For example, in the expression radical the radicand is x+2

 

 

Rational

Rational number is any number that can be written in the form p/q where p and q are integers and q is not equal to zero.

 

Rationalize

Rationalizing the denominator is the process of eliminating radicals from the denominator.

 

 

Right Triangle

Right triangle is any having one right angle (i.e. one angle that measures 90º).

 

 

Root

naThe expression is read nth root of a.

 

 

Simplify

Simplifying is the process of expressing a mathematical expression in the simplest (and usually shortest) terms.

Note that only expressions can be simplified; equations have to be solved.

 

Slope

The rate at which the ordinate of a point on a line on a coordinate plane changes with respect to the change in the abscissa.

 

Solve

Solving is the process of finding the solution set of an equation, inequality or system of equations or inequalities.

This process usually involves explicitly expressing the solution value(s), and checking whether the solutions that were found are valid.

 

Space holder – a space in an algebraic expression that the editor ‘reserves’ for further input, so that the correct algebraic form is preserved. For example, when you enter a /, the editor will display spaceholder to remind you that denominator has not yet been entered. While you can skip the space holder and continue entering the expression, you will not be able to solve the problem before replacing or deleting the space holder.

 

Square

Square is equivalent to the second power.

For example, the expression : asq could be read "a squared".

 

Term

Term is any expression written as a product or quotient.

 

Trinomial

Trinomial is a polynomial consisting of three terms.

 

Variable

Variable is a character used to represent any number from a specified set of numbers.

 

Vertical

Parallel to the y-axis.

 

Worksheets vs. workspace

"Worksheet" refers to a basic unit of space in the software that is used to store a single problem and possibly its solution. Several worksheets make up a workspace. When you open or save a file, you are opening or saving a workspace rather than individual worksheets. It is of course possible to have only a single worksheet in a workspace, but this is rather inefficient (it creates too many small files). A logical workspace would, for example, be a single homework assignment (containing several problems).

 

hint2 Worksheets can be cleared, renamed and deleted by right-clicking on their respective tabs.

Note that workspace files use .alw as the file name extension.

 

x-intercept

x -intercept is the x-coordinate of the point where a line (or some other curve) intersects the x-axis.

Note that the y-coordinate at that point is always equal to 0.

 

y-intercept

y-intercept is the y-coordinate of the point where a line (or some other curve) intersects the y-axis.

Note that the x-coordinate at that point is always equal to 0.