17.1 学院

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  学院预估学

   

  30-60-90:

  A 30-60-90 triangle is a special right triangle with angles of 30°, 60°, and 90°.

  45-45-90 Triangle:

  A 45-45-90 triangle is a special right triangle with angles of 45°, 45°, and 90 °.

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  ::A

  Absolute Deviation:

  The sum total of how different each number is from the mean.

  Absolute Extrema:

  The points with the $\begin{align*}y\end{align*}$ -values that are the highest or lowest of the entire function.

  Amplitude:

  One-half of the difference between the minimum and maximum values of a wave, and can be related to the radius of a circle.

  Angle of Depression:

  The angle formed by a horizontal line and the line of sight down to an object, when the image of the object is located beneath the horizontal line.

  Angle of Elevation:

  The angle formed by a horizontal line and the line of sight up to an object, when the image of the object is located above the horizontal line.

  Angular Velocity:

  For a rotating object, the change in angle of the object divided by the change in time.

  Arc Length:

  Found using the formula  $\begin{align*}s=r\cdot \theta, \end{align*}$  where  $\begin{align*}s\end{align*}$  is the length of the arc,  $\begin{align*}r\end{align*}$  is the radius, and  $\begin{align*}\theta \end{align*}$  is the measure of the angle in radians.

  Arithmetic Growth:

  Occurs when a quantity increases by the same amount in each given time period (repeated addition).

  Arithmetic Sequence:

  Has a common difference between each two consecutive terms, which are also known as arithmetic progressions.

  Arithmetic Series:

  The sum of an arithmetic sequence, a sequence with a common difference between each two consecutive terms.

  ASA:

  Angle-side-angle, refers to two known angles in a triangle with one known side between the known angles.

  Asymptotes:

  A line on the graph of a function representing a value toward which the function may approach, but does not reach (with certain exceptions).

  Asymptotic:

  A function is asymptotic to a given line if the given line is an asymptote of the function.

  Augmented Matrix:

  A matrix formed when two matrices are joined together and operated on as if they were a single matrix.

  Average Rate of Change:

  Of a function, the change in y-coordinates of a function, divided by the change in x-coordinates.

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  B
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  Bar Chart

  A graphic display of categorical variables that uses bars to represent the frequency of the count in each category.

  Base Case

  In an induction proof, the anchor step. It is the 1st domino to fall, creating a cascade and thus proving the statement true for every number greater than the base case.

  Bearing:

  How direction is measured at sea. North is 0°, east is 90°, south is 180°, and west is 270°.

  Bimodal:

  If there are two numbers that occur equally frequently in a set of data, then the data is said to be bimodal.

  Binomial Expansion:

  The process of raising a binomial such as (x+2) to a power. The process can be time-consuming when completed manually, particularly with higher exponents.

  Binomial Theorem:

  An efficient formula for calculating the expansion of binomials. It states that $\begin{align*}(x + y)^n = \sum_{r = 0}^n \left (\binom{n} {r} x^{n - r} y^r \right)\end{align*}$ .

  Bivariate Data:

  Consists of two paired sets of data.

  Bounds on Zeros Theorem:

  States that if $\begin{align*}f\end{align*}$  is continuous on [a, b] and there is a sign change between  $\begin{align*}f(a)\end{align*}$  and  $\begin{align*}f(b)\end{align*}$  (that is,  $\begin{align*}f(a)\end{align*}$  is positive and  $\begin{align*}f(b)\end{align*}$  is negative, or vice versa), then there is a  $\begin{align*}c\in(a,b),\end{align*}$  such that  $\begin{align*}f(c) = 0\end{align*}$ .

  Boxplot:

  Graphic display of quantitative data that illustrates the five-number summary.

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  Carrying Capacity:

  The maximum sustainable population that the environmental factors will support. In other words, it is the population limit.

  Categorical Variable:

  A variable that can take on one of a limited number of values. Examples of categorical variables are TV stations, the state someone lives in, and eye color.

  Center:

  Of a circle, the point that defines the location of the circle. All points on the circle are equidistant from the center of the circle.

  Circle:

  The set of all points at a specific distance from a given point in two dimensions.

  Closed Interval:

  Interval with square or box brackets, [ ], in which the interval includes the endpoints.

  Cofunction:

  Cofunctions are functions that are identical except for a reflection and horizontal shift. Examples include sine and cosine, tangent and cotangent, and secant and cosecant.

  Combination:

  Distinct arrangements of a specified number of objects without regard to order of selection from a specified set.

  Common Difference:

  Every arithmetic sequence has a common or constant difference between consecutive terms. For example, in the sequence 5, 8, 11, 14, ..., the common difference is 3.

  Common Logarithm:

  A log with base 10. The log is usually written without the base.

  Common Ratio:

  Every geometric sequence has a common ratio, or a constant ratio between consecutive terms. For example, in the sequence 2, 6, 18, 54, ..., the common ratio is 3.

  Complement:

  A mutually exclusive pair of events are complements to each other. For example, if the desired outcome is heads on a flipped coin, the complement is  tails.

  Completing the Square:

  A common method for rewriting quadratics. It refers to making a perfect square trinomial by adding the square of one half of the coefficient of the x-term.

  Compound Interest:

  Interest earned on the total amount at the time it is compounded, including previously earned interest.

  Conic:

  Conic sections are those curves that can be created by the intersection of a double cone and a plane. They include circles, ellipses, parabolas, and hyperbolas.

  Conjugate Pairs Theorem:

  States that if  $\begin{align*}f(z)\end{align*}$  is a polynomial of degree $\begin{align*}n\end{align*}$ , with $\begin{align*}n\ne0\end{align*}$  and with real coefficients, and if $\begin{align*}f(z_{0})=0\end{align*}$ , where $\begin{align*}z_{0}=a+bi\end{align*}$ , then  $\begin{align*}f(z_{0}^{*})=0\end{align*}$  where $\begin{align*}z_{0}^{*}\end{align*}$  is the complex conjugate of  $\begin{align*}z_{0}\end{align*}$ . 

  Continuously Compounding:

  Refers to a loan or investment with interest that is compounded constantly, rather than on a specific schedule. It is equivalent to infinitely many but infinitely small compounding periods.

  Correlation Coefficient:

  Standard quantitative measure of best fit of a line. It has the symbol r and has values from -1 to +1.

  Cosecant:

  Of an angle in a right triangle, a relationship found by dividing the length of the hypotenuse by the length of the side opposite to the given angle. This is the reciprocal of the sine function.

  Cosine:

  Of an angle in a right triangle, a value found by dividing the length of the side adjacent to the given angle by the length of the hypotenuse.

  Cotangent:

  Of an angle in a right triangle, a relationship found by dividing the length of the side adjacent to the given angle by the length of the side opposite to the given angle. This is the reciprocal of the tangent function.

  Coterminal Angles:

  Angles with the same terminal side but expressed differently, such as a different number of complete rotations around the unit circle, or angles being expressed as positive versus negative angle measurements.

  Cramer's Rule:

  A formula involving ratios of determinants for the solution of a system of linear equations.

  Cross Product:

  Of two vectors, a 3rd vector that is perpendicular to both of the original vectors.

   

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  Decreasing

  A function is decreasing over an interval if its y-values are getting smaller over the interval. The graph will go down from left to right over the interval.

  Degenerate Conic:

  A conic that does not have the usual properties of a conic section. Since some of the coefficients of the general conic equation are zero, the basic shape of the conic is merely a point, a line, or a pair of intersecting lines.

  Derivative:

  Of a function, the slope of the line tangent to the function at a given point on the graph. Notations for derivatives include  $\begin{align*}f'(x)\end{align*}$ , $\begin{align*}\tfrac{dy}{dx}\end{align*}$ , $\begin{align*}y'\end{align*}$ , $\begin{align*}\tfrac{df}{dx}\end{align*}$ , and $\begin{align*}\tfrac{df(x)}{dx}\end{align*}$ .     

  Descartes's Rule of Signs:

  A technique for determining the number of positive and negative real roots of a polynomial.

  Descriptive Statistics:

  In descriptive statistics, the goal is to describe the data that is found in a sample or given in a problem.

  Determinant:

  A single number descriptor of a square matrix. The determinant is computed from the entries of the matrix, and has many properties and interpretations explored in linear algebra.

  Dihedral Angle:

  An angle between two planes in three-dimensional space.

  Directrix:

  Of a parabola, the line that the parabola seems to curve away from. All points on a parabola are equidistant from the focus of the parabola and the directrix of the parabola.

  Discontinuities:

  The points of discontinuity for a function are the input values of the function where the function is discontinuous.

  Discontinuous:

  A function is discontinuous if the function exhibits breaks or holes when graphed.

  Displacement Vector:

  Models the movement between one point and another on a coordinate plane.

  Domain:

  Of a function, the set of x-values for which the function is defined.

  Dot Product:

  The inner or scalar product. The two forms of the dot product are  $\begin{align*}\vec{a} \cdot \vec{b} = \Big \| \vec{a}\Big \| \ \Big \| \vec{b}\Big \| \cos \theta\end{align*}$  and  $\begin{align*}\vec{a} \cdot \vec{b} = x_a x_b + y_a y_b\end{align*}$ . 

  Double Angle Identity:

  Relates the trigonometric function of two times an argument to a set of trigonometric functions, each containing the original argument.

   

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  e:

  An irrational number that is approximately equal to 2.71828. As  $\begin{align*}n \rightarrow \infty, \left(1+ \frac{1}{n}\right)^n \rightarrow e\end{align*}$ .

  Eccentricity:

   A measure of how much the conic section deviates from being circular. The eccentricity of circles is 0, of ellipses is between 0 and 1, of parabolas is 1, and of hyperbolas is greater than 1. For ellipses and hyperbolas,  $\begin{align*}eccentricity =\frac{c}{a}\end{align*}$ . 

  Ellipse:

  Conic sections that look like elongated circles. An ellipse represents all locations in two dimensions that are the same distance from two specified points called foci.

  Empirical Rule:

  States that for data that are normally distributed, approximately 68% of the data will fall within 1 standard deviation of the mean, approximately 95% of the data will fall within 2 standard deviations of the mean, and approximately 99.7% of the data will fall within 3 standard deviations of the mean.

  End Behavior:

  A description of the trend of a function as input values become very large or very small, represented as the "ends" of a graphed function. 

  Even Function:

  A function with a graph that is symmetric with respect to the y-axis, and has the property that  $\begin{align*}f(-x) = f(x)\end{align*}$ . 

  Expected Value:

  The return or cost you can expect on average, given many trials. 

  Explicit Formula:

  Defines each term in a sequence directly, allowing one to calculate any term in the sequence without knowing the value of the previous terms. 

  Exponential Decay:

  Occurs when a quantity decreases by the same proportion in each given time period.

  Exponential Function:

  A function whose variable is in the exponent. The general form is  $\begin{align*}y=a \cdot b^{x-h}+k\end{align*}$ . 

  Exponential Growth:

  Occurs when a quantity increases by the same proportion in each given time period.

  Extreme Value Theorem:

  States that in every interval [a, b] where a function is continuous, there is at least one maximum and one minimum. In other words, it must have at least two extreme values.

   

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  Factored Form:

  The factored form of a quadratic function  $\begin{align*}f(x)\end{align*}$  is  $\begin{align*}f(x)=a(x-r_{1})(x-r_{2})\end{align*}$ , where $\begin{align*}r_{1}\end{align*}$  and  $\begin{align*}r_{2}\end{align*}$  are the roots of the function. 

  Factor Theorem:

  States that if  $\begin{align*}f(x)\end{align*}$  is a polynomial of degree  $\begin{align*}n>0\end{align*}$  and  $\begin{align*}f(c)=0\end{align*}$ , then $\begin{align*}x-c\end{align*}$  is a factor of the polynomial $\begin{align*}f(x)\end{align*}$ .  

  Factorization Theorem:

  States that if  $\begin{align*}f(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}\end{align*}$ , where $\begin{align*}a_{n} \ne 0\end{align*}$ , and $\begin{align*}n\end{align*}$  is a positive integer, then $\begin{align*}f(x)=a_{n}(x-c_{1})(x-c_{2})\cdots(x-c_{0}),\end{align*}$  where the numbers  $\begin{align*}c_{i}\end{align*}$  are complex numbers.  

  First Quartile:

  Also known as  $\begin{align*}Q_1\end{align*}$ , the median of the lower half of a set of data. 

  Five-Number Summary:

  Of a set of data, it is the minimum, 1st quartile, 2nd quartile, 3rd quartile, and maximum.

  Foci:

  Two points that define an ellipse or hyperbola. The sum of the distances from any point on an  ellipse to the foci is constant. For every point on a hyperbola, the difference of the distances to each focus is constant.

  Focus:

  Of a parabola, the point that "anchors" a parabola. Any point on the parabola is exactly the same distance from the focus as from the directrix.

  Frequency:

  Of a trigonometric function, the number of cycles that a periodic function completed in 1 unit interval . 

  Function Composition:

  Involves "nested functions" or functions within functions. Function composition is the application of one function to the result of another function.

  Function Notation:

  The notation used to describe a function, often written as $\begin{align*}f(x)\end{align*}$ . 

  Fundamental Counting Principle:

  States that if an event can be chosen in $\begin{align*}p\end{align*}$  different ways and another independent event can be chosen in $\begin{align*}q\end{align*}$  different ways, the number of different arrangements of the events is  $\begin{align*}p \times q\end{align*}$ . 

  Fundamental Theorem of Algebra:

  States that if  $\begin{align*}f(x)\end{align*}$  is a polynomial of degree  $\begin{align*}n\ge 1\end{align*}$ , then $\begin{align*}f(x)\end{align*}$  has at least one zero in the complex number domain. In other words, there is at least one complex number  $\begin{align*}c\end{align*}$  such that  $\begin{align*}f(c)=0\end{align*}$ . The theorem can also be stated as follows: an $\begin{align*}nth\end{align*}$  degree polynomial with real or complex coefficients has, with multiplicity, exactly  $\begin{align*}n\end{align*}$  complex roots.

   

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  Gauss-Jordan Elimination:

  Putting a matrix into reduced row echelon form is a result of performing Gauss-Jordan elimination.

  Geometric Sequence:

  A sequence with a constant ratio between successive terms. Geometric sequences are also known as geometric progressions.

  Geometric Series:

  A geometric sequence written as an uncalculated sum of terms.

  Global Extrema:

  Of a function, the points with the y-values that are the highest or the lowest of the entire function.

  Global Maximum:

  Of a function, the largest value of the entire function. Symbolically, it is the highest point on the entire graph.

  Global Minimum:

  Of a function, the smallest value of the entire function. Symbolically, it is the lowest point on the entire graph.

   

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  ::H

  Half Angle Identity:

  Relates a trigonometric function of one-half of an argument to a set of trigonometric functions, each containing the original argument.

  Half-Life:

  Refers to the time required for a radioactive material to decay to one-half of its initial concentration.

  Histogram:

  A display that indicates the frequency of specified ranges of continuous data values on a graph in the form of immediately adjacent bars. 

  Horizontal Line Test:

  Says that if a horizontal line drawn anywhere through the graph of a function intersects the function in more than one location, then the function is not one-to-one and not invertible.

  Hyperbola:

  A conic section formed when the cutting plane intersects both sides of a cone, resulting in two infinite U-shaped curves.

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  Identity:

  A mathematical sentence involving the symbol "=" that is always true for variables within the domains of the expressions on either side.

  Identity Matrix:

  A matrix with zeros everywhere except along the diagonal, where there are ones.

  Included Angle:

  In a triangle, the angle between two known sides.

  Increasing:

  A function is increasing over an interval if its y-values are getting larger over the interval. The graph will go up from left to right over the interval.

  Independent Events:

  Two events are independent if the occurrence of one event does not impact the probability of the other event.

  Induction:

  A method of mathematical proof typically used to establish that a given statement is true for all positive integers. 

  Inductive Hypothesis:

  In an induction proof, the inductive hypothesis is the step where you assume the statement is true for $\begin{align*}k\end{align*}$ .

  Inductive Step:

  In an induction proof, the inductive step is the proof. It is when you show the statement is true for  $\begin{align*}k+1\end{align*}$  using only the inductive hypothesis and algebra.

  Inferential Statistics:

  With inferential statistics, your goal is to use the data in a sample to draw conclusions about a larger population.

  Instantaneous Rate of Change:

  Of a curve at a given point, the slope of the line tangent to the curve at that point.

  Integral:

  Used to calculate the area under a curve or the area between two curves.

  Intercepts:

  Of a curve, the locations where the curve intersects the x and y axes. An x-intercept is a point at which the curve intersects the x-axis. A y-intercept is a point at which the curve intersects the y-axis.

  Intermediate Value Theorem:

  States that if  $\begin{align*}f(x)\end{align*}$  is continuous on some interval $\begin{align*}[a, b]\end{align*}$  and  $\begin{align*}n\end{align*}$  is between  $\begin{align*}f(a)\end{align*}$  and  $\begin{align*}f(b)\end{align*}$ , then there is some $\begin{align*}c\in[a,b]\end{align*}$  such that $\begin{align*}f(c) = n\end{align*}$ .   

  Interval Notation:

  The notation  $\begin{align*}[a,b)\end{align*}$ , where a function is defined between $\begin{align*}a\end{align*}$  and  $\begin{align*}b\end{align*}$ . Use ( or ) to indicate that the end value is not included and [ or ] to indicate that the end value is included. Never use [ or ] with infinity or negative infinity.  

  Inverse Function:

  Two functions are inverses of each other if their graphs are reflections of each other over the line $\begin{align*}y=x\end{align*}$ . Formally,  $\begin{align*}f(x)\end{align*}$  and  $\begin{align*}g(x)\end{align*}$  are inverse functions if  $\begin{align*}f(g(x))=g(f(x))=x\end{align*}$ . 

  Inverse Properties of Logarithms:

  Inverse properties of logarithms are  $\begin{align*}\log_b b^x=x\end{align*}$  and  $\begin{align*}b^{\log_b x}=x, b \ne 1\end{align*}$ . 

  Irrational Number:

  A number that cannot be expressed exactly as the quotient of two integers.

   

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  L
  ::L

  Law of Cosines:

  A rule relating the sides of a triangle to the cosine of one of its angles. The law of cosines states that  $\begin{align*}c^2=a^2+b^2-2ab\cos C\end{align*}$ , where $\begin{align*}C\end{align*}$  is the angle across from side  $\begin{align*}c\end{align*}$ .  

  Law of Sines:

  A rule applied to triangles stating that the ratio of the sine of an angle to the side opposite that angle, is equal to the ratio of the sine of another angle in the triangle to the side opposite that angle.

  Limit:

  The value that the output of a function approaches as the input of the function approaches a given value.

  Limit Notation:

  A way of expressing the fact that a function gets arbitrarily close to a value.

  Linear Combination:

  A set of terms that are added or subtracted from each other with a multiplicative constant in front of each term.

  Linear Correlation:

  A measure of the strength of the linear relationship between two random variables.

  Linear Regression:

  In statistics, a process that attempts to model the relationship between two variables by fitting a linear equation to the data.

  Linear Velocity:

  Of an object, the change in position of an object divided by the change in time.

  Local Extrema:

  Of a function, the points of the function with y-values that are the highest or lowest of a local neighborhood of the function.

  Local Maximum:

  The highest point relative to the points around it. A function can have more than one local maximum.

  Local Minimum:

  The lowest point relative to the points around it. A function can have more than one local minimum.

  Logarithmic Function:

  Inverse of an exponential function. Recall that  $\begin{align*}\log_b n=a \end{align*}$  is equivalent to  $\begin{align*}b^a=n\end{align*}$ . 

  Logistic Function:

  A function that grows or decays rapidly for a period of time and then levels out. It takes the form  $\begin{align*}f(x)=\frac{c}{1+a \cdot b^x}\end{align*}$ . 

   

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  M
  ::M

  Magnitude:

  Of a line segment or vector, the length of the line segment or vector.

  Major Axis:

  Of an ellipse, the longest diameter of the ellipse.

  Matrix:

  A rectangular arrangement of data elements presented in rows and columns.

  Matrix Operations:

  The primary matrix operations are addition, subtraction, and multiplication.

  Mean:

  Often called the average, the mean of a numerical set of data is simply the sum of the data values divided by the number of values.

  Mean Absolute Deviation:

  An alternate measure of how spread out data are. It involves finding the mean of the distance between each data value and the mean. While this method might seem more intuitive, in statistics it has been found to be too limited and is not commonly used.

  Median:

  Of a dataset, the middle value of the organized dataset. 

  Minor Axis:

  Of an ellipse, the shortest diameter of the ellipse.

  Mode:

  Of a dataset, the value or values with greatest frequency in the dataset.

  Monotonic:

  A function is monotonic if it does not switch between increasing and decreasing at any point.

  Multimodal:

  When a set of data has more than two values that occur with the same greatest frequency, the set is called multimodal.

  Multiplicative Inverse:

  Of a number, the reciprocal of the number. The product of a real number and its multiplicative inverse will always be equal to 1 (which is the multiplicative identity for real numbers). 

  Multiplicity:

  Of a term, describes the number of times the given term acts as a zero of the given function.

   

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  N
  ::N

  Natural Log:

  A logarithm with base  $\begin{align*}e\end{align*}$ . The natural logarithm is written as "ln." 

  Normal Curve:

  The curve that defines the probability density graph for a normally distributed variable.

  Normal Vector:

  A vector that is perpendicular to a given surface or plane. A unit normal vector is a normal vector with a magnitude of one.

  Normalcdf:

  The normal cumulative distribution function. It calculates the area between any two values for data that are normally distributed, as long as you know the mean and standard deviation for the data. Your calculator has this function built in, and it produces an exact answer as opposed to the empirical rule. 

  N-Roots Theorem:

  If  $\begin{align*}f(x)\end{align*}$  is a polynomial of degree  $\begin{align*}n\end{align*}$ , where $\begin{align*}n \ne 0\end{align*}$ , then $\begin{align*}f(x)\end{align*}$  has at most  $\begin{align*}n\end{align*}$  zeros.

   

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  ::O

  Oblique Asymptote:

  A diagonal line marking a specific range of values toward which the graph of a function may approach, but generally never reach. An oblique asymptote exists when the numerator of the function is exactly one degree greater than the denominator. An oblique asymptote may be found through long division.

  Odd Function:

  A function with the property that  $\begin{align*}f(-x) = -f(x)\end{align*}$ . Odd functions have rotational symmetry about the origin. 

  One-Sided Limit:

  The value that a function approaches from either the left side or the right side.

  One-to-One Function:

  A function is one-to-one if its inverse is also a function. A one-to-one function passes both the horizontal and vertical line tests.

  Open Interval:

  Does not include the endpoints of the interval.

  Order:

  Of a matrix, describes the number of rows and the number of columns in the matrix.

  Orthogonality:

  To be orthogonal is to be perpendicular.

   

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  ::P

  Parabola:

  The characteristic shape of a quadratic function graph, resembling a U. Specifically, the set of points that are equidistant from a fixed point on the interior of the curve, called the "focus," and a line on the exterior, called the "directrix." The directrix is vertical or horizontal, depending on the orientation of the parabola.

  Parametric Form:

  Means to define $\begin{align*}x\end{align*}$  and $\begin{align*}y\end{align*}$  as a function of a 3rd variable, often $\begin{align*}t\end{align*}$ .

  Partial Fraction Decomposition:

  A procedure that undoes the operation of adding fractions with unlike denominators. It separates a rational expression into the sum of rational expressions with unlike denominators.

  Pascal's Triangle:

  A triangular array of numbers constructed with the coefficients of binomials as they are expanded. The ends of each row of Pascal's Triangle are ones, and every other number is the sum of the two nearest numbers in the row above.

  Payoff:

  Of a game, the expected value of the game minus the cost.

  Period:

  Of a wave, the horizontal distance traveled before the $\begin{align*}y\end{align*}$ -values begin to repeat. 

  Periodic Function:

  A function with a predictable repeating pattern. Sine waves and cosine waves are periodic functions. 

  Permutation:

  An arrangement of objects where order is important.

  Phase Shift:

  A horizontal translation or shift of a period function.

  Pi (π):

  π (pi) is the ratio of the circumference of a circle to its diameter. It is an irrational number that is approximately equal to 3.14.

  Pie Chart:

  A graphic display of categorical data where the relative size of each pie slice corresponds to the frequency of each category.

  Piecewise Function:

  A function that pieces together two or more parts of other functions to create a new function.

  Polar Coordinates:

  Describe locations on a grid using the polar coordinate system. The location of each point is determined by its distance from the pole and its angle with respect to the polar axis.

  Polynomial Function:

  A function defined by an expression with at least one algebraic term.

  Polynomial Inequality:

  Generally used to describe an inequality with an $\begin{align*}x\end{align*}$ -term coefficient of three or greater.

  Population:

  In statistics, the entire group of interest from which the sample is drawn.

  Power Function:

  A polynomial of the form  $\begin{align*}f(x)=ax^{n},\end{align*}$  where  $\begin{align*}a\end{align*}$  is a real number and  $\begin{align*}n\end{align*}$  is an integer with  $\begin{align*}n\ge 1\end{align*}$ . 

  Power Reducing Identity:

  Relates the power of a trigonometric function containing a given argument to a set of trigonometric functions, each containing the original argument.

  Probability:

  The chance that something will happen. It can be written as a fraction, decimal, or percent.

  Product Property of Logarithms:

  States that as long as  $\begin{align*}b \ne 1\end{align*}$ , then $\begin{align*}\log_b xy=\log_b x + \log_b y.\end{align*}$   

  Proof:

  A series of true statements leading to the acceptance of truth of a more complex statement.

  Pythagorean Identity:

  A relationship showing that the sine of an angle squared plus the cosine of an angle squared is equal to one.

  Pythagorean Theorem:

  A mathematical relationship between the sides of a right triangle, given by  $\begin{align*}a^2 + b^2 = c^2,\end{align*}$ where $\begin{align*}a\end{align*}$  and  $\begin{align*}b\end{align*}$  are legs of the triangle and  $\begin{align*}c\end{align*}$  is the hypotenuse of the triangle. 

  Pythagorean Triple:

  A set of three whole numbers  $\begin{align*}a\end{align*}$ , $\begin{align*}b\end{align*}$ , and $\begin{align*}c\end{align*}$  that satisfy the Pythagorean Theorem, $\begin{align*}a^2 + b^2 = c^2\end{align*}$ .    

   

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  Quadrantal Angle:

  An angle that has its terminal side on one of the four lines of axis: positive x, negative x, positive y, or negative y.

  Quadratic Function:

  A function that can be written in the form  $\begin{align*}f(x)=ax^2 + bx + c\end{align*}$ , where $\begin{align*}a\end{align*}$ , $\begin{align*}b\end{align*}$ , and $\begin{align*}c\end{align*}$  are real constants and  $\begin{align*}a \ne 0\end{align*}$ .    

  Quantitative Variable:

  A variable that takes on numerical values that represent a measurable quantity. Examples of quantitative variables are the height of students or the population of a city.

  Quartile:

  Each of four equal groups that a dataset can be divided into.

  Quotient Property of Logarithms:

  States that as long as  $\begin{align*}b \ne 1\end{align*}$ , then $\begin{align*}\log_b \tfrac{x}{y}=\log_b x - \log_b y.\end{align*}$   

   

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  Radian:

  A unit of angle that is equal to the angle created at the center of a circle whose arc is equal in length to the radius.

  Radius:

  Of a circle, the distance from the center of the circle to the edge of the circle.

  Range:

  Of a function, the set of y-values for which the function is defined.

  Rank:

  Of an observation, the number of observations that are less than or equal to the value of that observation.

  Rational Function:

  Any function that can be written as the ratio of two polynomial functions.

  Rational Inequality:

  Ratio of two polynomials, specified to be greater or less than a given value.

  Rational Zero Theorem:

  States that for a polynomial,  $\begin{align*}f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0,\end{align*}$  where $\begin{align*}a_n, a_{n-1}, \cdots a_0\end{align*}$  are integers, the rational roots can be determined from the factors of $\begin{align*}a_n\end{align*}$  and  $\begin{align*}a_0\end{align*}$ . More specifically, if $\begin{align*}p\end{align*}$  is a factor of $\begin{align*}a_0\end{align*}$  and $\begin{align*}q\end{align*}$  is a factor of $\begin{align*}a_n\end{align*}$ , then all the rational factors will have the form $\begin{align*}\pm \frac{p}{q}\end{align*}$ .     

  Recursive:

  The recursive formula for a sequence allows you to find the value of the nth term in the sequence if you know the value of the (n - 1)th term in the sequence.

  Reduced Row Echelon Form:

  A matrix is in reduced row echelon form if it has a leading one at the start of every non-zero row, zeros below every leading one, all rows containing only zeros at the bottom of the matrix, and only zeros to the right of leading ones in rows with leading ones.

  Reference Angle:

  The angle formed between the terminal side of the angle and the closest of either the positive or negative x-axis.

  Relative Extrema:

  Of a function, the points of the function with y-values that are the highest or lowest of a local neighborhood of the function.

  Remainder Theorem:

  States that if  $\begin{align*}f(k) = r\end{align*}$ , then $\begin{align*}r\end{align*}$  is the remainder when dividing  $\begin{align*}f(x)\end{align*}$  by  $\begin{align*}(x-k)\end{align*}$ . 

  Restricted Domain:

  Refers to the fact that when creating an inverse, you sometimes must cut off the domain of most of the function, saving the largest possible portion so that when the inverse is created, it is also a function.

  Resultant:

  A vector representing the sum of two or more vectors.

  Riemann Sum:

  An approximation of the area under a curve, calculated by dividing the region up into shapes that approximate the space.

  Right-Hand Rule:

  Used to indicate the direction of a cross product. Position the thumb and index finger of our right hand with the 1st vector along your thumb and the 2nd vector along your index finger. Your middle finger, when extended perpendicular to your palm, will indicate the direction of the cross product of the two vectors. 

  Roots:

  Of a function, the values of x that make y equal to zero.

  Row Echelon Form:

  A matrix is in row echelon form if it has a leading one at the start of every non-zero row, zeros below every leading one, and all rows containing only zeros at the bottom of the matrix.

  Row Operations:

  Include swapping rows, adding a multiple of one row to another, or scaling a row by multiplying through by a scalar.

   

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  Sample:

  A specified part of a population, intended to represent the population as a whole. 

  Scalar Projection:

  Of a vector onto another vector, equal to the length of the projection of the 1st vector onto the 2nd vector.

  Scatter Plot:

  A plot of the dependent variable versus the independent variable, used to investigate whether or not there is a relationship or connection between two sets of data.

  Secant:

  Of an angle in a right triangle, the value found by dividing the length of the hypotenuse by the length of the side adjacent to the given angle. The secant ratio is the reciprocal of the cosine ratio.

  Secant Line:

  A line that joins two points on a curve.

  Second Quartile:

  Also known as  $\begin{align*}Q_2\end{align*}$ , the median of the data. 

  Sector:

  A portion of a circle contained between two radii of the circle. Sectors can be measured in degrees.

  Sector Area Formula:

  Used to calculate how many degrees of the circle should be allocated to a given value, calculated by dividing the frequency of the data in the sector by the total frequency of the data all multiplied by 360.

  Sequence:

  An ordered list of numbers or objects.

  Series:

  The sum of the terms of a sequence.

  Sigma Notation:

  Also known as summation notation, a way to represent a sum of numbers. It is especially useful when the numbers have a specific pattern or would take too long to write out without abbreviation.

  Sine:

  Of an angle in a right triangle, a value found by dividing the length of the side opposite the given angle by the length of the hypotenuse. 

  Square Matrix:

  A matrix in which the number of rows equals the number of columns.

  Standard Deviation:

  The square root of the variance. Standard deviation is one way to measure the spread of a set of data.

  Standard Form:

  Of a line,  $\begin{align*}Ax+By=C\end{align*}$ , where $\begin{align*}A\end{align*}$ , $\begin{align*}B\end{align*}$ , and $\begin{align*}C\end{align*}$  are real numbers. The standard form of a quadratic function is $\begin{align*}f(x)=ax^{2}+bx+c\end{align*}$ .     

  Standard Normal Distribution:

  $\begin{align*}\phi(x)=\frac{1}{\sqrt{2 \pi}}e^{- \frac{1}{2}x^2},\end{align*}$  a normal distribution with mean of 0 and a standard deviation of 1.

  Standard Position:

  Of an angle, measures an angle starting from the positive x-axis and going counter-clockwise. It is the typical method for drawing and measuring an angle. 

  Subtended Arc:

  The part of the circle between the two rays that make the central angle.

  Symmetrical about the Origin:

  A point (x, y) is symmetric about the origin  when (-x, -y) is also on the graph.

  Symmetrical about the y-axis:

  A point (x, y) is symmetric about the y-axis when (-x, y) is also on the graph. 

  Symmetric Matrix:

  A square matrix with reflection symmetry across the main diagonal.

  Synthetic Division:

  A shorthand version of polynomial long division, where only the coefficients of the polynomial are used.

  System of Equations:

  A set of two or more equations.

   

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  Take the Log of Both Sides:

  Take the log of both the entire right-hand side of the equation and the entire left-hand side of the equation. As long as neither side is negative or equal to zero, it maintains the equality of the two sides of the equation.

  Tangent:

  Of an angle in a right triangle, a value found by dividing the length of the side opposite the given angle by the length of the side adjacent to the given angle.

  Tangent Line:

  A line that "just touches" a curve at a single point and no others.

  Theta (θ):

  A Greek letter used in math to stand for an unknown angle.

  Third Quartile:

  Also known as  $\begin{align*}Q_3\end{align*}$ , the median of the upper half of the data. 

  Transcendental Number:

  A number that is not the root of any rational polynomial function. Examples include  $\begin{align*}e\end{align*}$  and  $\begin{align*}\pi\end{align*}$ .

  Transformation:

  Moves a figure in some way on the coordinate plane.

   

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  Unit Circle:

  A circle of radius one, centered at the origin.

  Unit Normal Vector:

  A vector with a magnitude of one that is perpendicular to the unit tangent vector and the curve. 

  Unit Vector:

  A vector with a magnitude of one.

   

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  Variance:

  A measure of the spread of the dataset equal to the mean of the squared variations of each data value from the mean of the dataset.

  Vector:

  A mathematical quantity that has both a magnitude and a direction.

  Vector Projection:

  Of a vector onto a given direction, a vector with a magnitude equal to the scalar projection. The direction of the vector projection is the same as the unit vector of that given direction.

  Vertex:

  The highest or lowest point on the graph of a parabola. The vertex is the maximum point of a parabola that opens downward and the minimum point of a parabola that opens upward.

  Vertex Form:

  Of a parabola,  $\begin{align*}(x-h)^2=4p(y-k)\end{align*}$  or $\begin{align*}(y-k)^2=4p(x-h),\end{align*}$  where $\begin{align*}(h, k)\end{align*}$  is the vertex.  

  Vertical Line Test:

  Says that if a vertical line drawn anywhere through the graph of a relation intersects the relation in more than one location, then the relation is  not  a function.

  Vertical Shift:

  The result of adding a constant term to the value of a function. A positive term results in an upward shift and a negative term in a downward shift.

   

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  Weighted Average:

  An average that multiplies each component by a factor representing its frequency or probability.

   

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  Zeros:

  Of a function  $\begin{align*}f(x)\end{align*}$ , the values of x that cause  $\begin{align*}f(x)\end{align*}$  to be equal to zero.