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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
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