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# Calculus Vocab-BHS1

Question | Answer |
---|---|

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