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Calculus Vocab-BHS1

QuestionAnswer
To put all like terms in a mathematical sentence together. simplify
A mathematical sentence without an equals sign expression
The number in front of a variable. coefficient
A fixed value that does not change. constant
A letter or symbol that represents a number. variable
A number that tells how many times a factor is to be multiplied. exponent
A number form that uses various roots of a number. radical
The answer to an addition problem. sum
The solution to a subtraction problem. difference
The answer to a multiplication problem. product
The solution to a division problem. quotient
Rules followed to simplify expressions in the proper sequence. order of operations
An expression that can be written as a fraction. rational
Any expression that can not be written with a numerator and a denominator. irrational
To find an answer to a particular problem. solve
A mathematical sentence with an equals sign. equation
An equation with at most one solution. linear
An equation with at most two solutions which may use the formula given ax^2 + bx + c = 0 such that x = (-b +/- sqrt(b^2 - 4ac))/(2a) quadratic
The shape of the graph usually formed by a quadratic equation. parabola
An equation with at most three solutions. cubic
An equation with at most four solutions. quartic
The distance a number or point is from zero. absolute value
A rule used to prove three segment lengths make a right triangle or a^2 + b^2 = c^2 Pythagorean Theorem
The trigonometric ratio for an angle made up of the ratio of the opposite side and the hypotenuse. sine
The trigonometric ratio for an angle made up of the ratio of the adjacent side and the hypotenuse. cosine
The trigonometric ratio for an angle made up of the ratio of the opposite side and the adjacent side. tangent
The acronym used to identify the basic trigonometric ratios. SOHCAHTOA
The reciprocal of the sine function or the ratio of the hypotenuse to the opposite side of an angle in a right triangle. cosecant
The reciprocal of the cosine function or the ratio of the hypotenuse to the adjacent side of the angle in a right triangle secant
The reciprocal of the tangent function or the ratio of the adjacent side of an angle to the opposite side of the same angle in a right triangle. cotangent
The horizontal number line on the coordinate plane. x-axis
The vertical number line on the coordinate plane. y-axis
The intersection of the horizontal and vertical number lines on the coordinate plane. origin
Two numbers that name a specific location on the coordinate plane. ordered pair
One of four sections on the coordinate plane. quadrant
Values where a line or curve crosses the horizontal axis. x-intercept (zeroes)
The place on the coordinate plane where a line or curve crosses the vertical axis. y-intercept
The quality of having balance or exact parts of a figure on either side of an axis. symmetry
A change in the position or direction of the graph of a function. transformation
A rule used to determine the behavior of the extreme left and extreme right parts of a graph. leading coefficient test
The rate of change or the rise over the run of a line. slope
A linear equation in the form y=mx+b slope-intercept form
Lines in the same plane that will never cross. parallel
Lines that intersect forming right angles. perpendicular
A set of ordered pairs. relation
A relationship in which each independent variable matches with exactly one dependent variable. function
A form of an equation and differentiation where an equation is not written in terms of one variable. implicit
A form of an equation and differentiation where an equation is written in terms of one variable. explicit
The independent variable of a function. domain
The dependent variable of a function. range
Any function whose graph is symmetric with the y-axis. even
Any function whose graph is symmetric with the origin. odd
A method used to determine if a relation is a function. vertical line test
Functions that are not algebraic such as trigonometric functions. transcendental
The process of combining two or more functions. composition
A method for determining if a relationship exists between two variables. regression analysis
A numerical value indicated by "r squared" that includes and is between -1 and 1 which measures the strength of the relationship between two variables. correlation coefficient
A numerical value indicated by "r squared" that includes and is between 0 and 1 which measures the percentage of data that is closest to the line of best fit helping to indicate the strength of a relationship. coefficient of determination
A line that intersects a curve only once in a given area whose slope represents the rate of change. tangent line
A line that connects any two points on a curve. secant line
The space inside a two-dimensional figure. area
Types of rectangles put on the inside of a function's graph. inscribed
Types of rectangles put on the outside of a function's graph. circumscribed
Given (x1, y1) and (x2, y2), then it equals sqrt((x1 - x2)^2 + (y1 - y2)^2)) distance formula
A value that a function or any situation approaches. limit
To approach or come together. converge
An analytical method of finding limits where radical parts in a denominator of a rational expression are eliminated. rationalization
The rule stating that if a function is between two functions and those two functions have the same limit at a given x value, the function in between also has the same limit. Squeeze Theorem
The property that a function has that is always defined and has a limit at every given x value thus making the graph unbroken. continuity
Any break in a function's graph. discontinuity
A discontinuity resulting in a hole in a graph that can be redefined at one point making the graph continuous. removable
It's what a removable discontinuity creates on a graph. hole
A discontinuity that can not be redefined at one point to make a graph continuous. nonremovable
A "step" function which gives back the largest positive, neutral, or negative of a value. greatest integer function
A rule stating that on a closed interval [a,b] with a given value k between f(a) and f(b), there exists a number c in [a,b] such that f(c)=k. Intermediate Value Theorem
The line x=c that a function approaches if the function approaches infinity or negative infinity as x nears c form either side. vertical asymptote
The line y=d that a function approaches as the function's x values near infinity or negative infinity. horizontal asymptote
The foundational equation for the derivative or the slope of the tangent line given by lim (delta x approaches 0) of f(x + delta x) - f(x) all divided by delta x. difference quotient
One of the fundamental operations of Calculus that finds the rate of change of a function. differentiation
An equation used to determine the location of an object relative to time. position function
The beginning speed at which an object starts. initial velocity
The change in position divided by the change in time. average velocity
The change in position of an object at a specified time. instantaneous velocity
The change in speed or velocity of an object. acceleration
The rule used to differentiate two expressions that are multiplied or f'(x)g(x) + f(x)g'(x). product rule
The rule used to differentiate two expressions that are divided or (f'(x)g(x) - f(x)g'(x))/(g(x))^2. quotient rule
A rule used to differentiate a function inside a function. chain rule
A maximum or a minimum over a closed interval. absolute (global) extrema
A rule stating that a function has both a minimum and a maximum on a closed interval if the function is continuous. Extreme Value Theorem
A maximum or a minimum on an open interval relative extrema
A value where the derivative is equal to 0 or is undefined. critical number
A rule stating that on a differentiate function on a closed interval, instantaneous velocity equals average velocity must equal at least once (slope of secant line equals slope of tangent line once. Mean Value Theorem
A rule stating that if a function has two x values with the same y value and is differentiable between those two x values, then there exists a value in between where the derivative equals zero. Rolle's Theorem
It's what a function is doing if x1 < x2 and f(x1) < f(x2). increasing
It's what a function is doing if x1 < x2 and f(x1) > f(x2). decreasing
Any function that is either entirely increasing or entirely decreasing. monotonic
The type of direction or shape of a graph that can be determined through the second derivative. concavity
A place where the concavity of a function's graph changes. point of inflection
A line that a graph does not cross that is present in a rational function where the degree of the numerator is one greater than the degree of the denominator slant asymptote
Applictions involved in determining a mininum or maximum value. optimization
The main equation or formula that is to be optimized. primary equation
An equation or formula that is substituted into an equation that is to be optimized. secondary equation
A technique used to approximate the real zeroes or x-intercepts of a function that uses tangent lines and the derivative Newton's Method
A repetition of a process. iteration
An infinitely small change in a variable denoted by dx or by dy. differential
A difference in measurements that when computed into other equations or formulas leads to this measure of inaccuracy. propogated error
The ratio of the propogated error and the actual result of a given situation. relative error
An equation involving a derivative and its variables which can be solved by integration methods. differential equation
The process of finding a function given derivative. integration
Summation symbol sigma
Archimedes method for determining the area of a region with sums rather than integrals by squeezing the region between two polygons whose number of sides increases. exhaustion method
A method used to approximate area or an integral using summation. Riemann Sums
The numerical limit of Riemann Sums or of an antiderivative or an interval. definite integral
The rule stating that the derivative and the integral are inverses of each other such that the integral from d to c of f(x)dx is equivalent to F(d) - F(c). Fundamental Theorem of Calculus
The mean of a function f(x) on the interval [c, d] given by 1/(d - c) times the integral from c to d of f(x)dx. average function value
A rule allowing for the integration in general by changing the variables. Second Fundamental Theorem of Calculus
Approximation techniques used to evaluate a definite integral. Simpson's & Trapezoidal Rules
An alternate way to express a number using exponents and a variety of numerical bases, of which 10 is the most common. logarithm
An alternate way to express a number using exponents and a base of 'e' natural logarithm
An equation formed by interchanging the domain and the range. inverse
A method used to determine if a function has an inverse. horizontal line test
The shape taken by something flexible suspended from two points. catenary
The curve that an object makes that is being pulled. tractrix
A graphical representation of the solution to a differential equation. slope field
A number that increases or decreases another quantity at a set rate over time. proportionally constant
A three-dimensional figure formed by rotating a curve about an axis. solid of revolution
A line that a curve rotates around in the creation of a solid. axis of revolution
The amount of space inside a solid. volume
A method of finding the volume of a solid of revolution. disk method
A method of finding the volume of a solid of revolution with a hole in it. washer method
The amount of material needed to make the outside of a geometric solid. surface of revolution
Created by: mbarnard