JEOPARDY ROOM
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Pre-Calculus Jeopardy

Pre-Calculus. Project the board, share one room code, and keep the class on the same review.

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Check the clues and answers for your group. Answers stay hidden during live play until the host reveals them.

Round 1

Function Basics

$200
The set of all possible input values for a given function.
$400
The specific value of a function's output when the input is removed from a point of discontinuity.
$600
The notation used to represent the composition of function f with function g.
$800
A function that passes the horizontal line test and has a unique inverse.
$1000
The type of function where f of negative x equals negative f of x, exhibiting symmetry about the origin.

Trig Identities

$200
The reciprocal function of the cosine function.
$400
The expression for tangent in terms of sine and cosine.
$600
The sine double-angle identity is expressed by this product.
$800
The Pythagorean identity that relates tangent squared plus this value to secant squared.
$1000
The identity stating that sine squared plus cosine squared equals this constant.

Logarithms

$200
The value of log base b of b.
$400
The name of the logarithm with a base of ten.
$600
The mathematical constant e is the base for this specific type of logarithm.
$800
The result of taking the log of a product is equal to this operation on the logs of the factors.
$1000
The property that allows the exponent of a log argument to be moved to the front as a multiplier.

Conic Sections

$200
The fixed point inside a parabola used in its formal definition.
$400
The locus of points in a plane equidistant from a fixed center point.
$600
The conic section formed by slicing a cone parallel to its slant height.
$800
The shape defined by the set of all points where the sum of distances to two foci is constant.
$1000
The shape defined by the set of all points where the absolute difference of distances to two foci is constant.

Sequences

$200
The symbol used to represent the sum of a series.
$400
The formula that defines a sequence term based on its position n.
$600
The type of series that continues indefinitely without approaching a finite sum.
$800
A sequence where each term is found by multiplying the previous term by a fixed ratio.
$1000
A sequence where the difference between consecutive terms is constant.

Matrices

$200
The process of interchanging rows and columns of a matrix.
$400
A matrix with the same number of rows and columns.
$600
The value calculated for a square matrix that determines if it is invertible.
$800
A square matrix with ones on the main diagonal and zeros elsewhere.
$1000
This square matrix has ones on its main diagonal, zeros elsewhere, and acts as the multiplicative identity.

Double Jeopardy

Function Basics

$400
The point where a function changes from concave up to concave down.
$800
The specific type of function defined by the ratio of two polynomials.
$1200
The value of a function as the input approaches infinity, often describing a horizontal asymptote.
$1600
The test used to determine if a function is even or odd by substituting negative x.
$2000
The theorem stating that every polynomial of degree n has exactly n roots in the complex plane.

Trig Identities

$400
The Law of Cosines relates side lengths to the cosine of this component.
$800
The identity relating the difference of two sines to a product of sine and cosine.
$1200
The identity that defines the period of the tangent function as pi divided by this coefficient.
$1600
The identity that expresses cosine of alpha plus beta in terms of individual angles.
$2000
The identity used to reduce the power of sine squared to a first-degree cosine expression.

Logarithms

$400
The value to which a base must be raised to produce the argument.
$800
The growth rate modeled by the constant e in continuous compound interest.
$1200
The formula used to convert a logarithm of an arbitrary base into a natural log.
$1600
The function that serves as the reflection of the exponential function over the line y equals x.
$2000
A logarithmic equation where the variable is found in the exponent of the argument.

Conic Sections

$400
The parameter that determines how 'flat' an ellipse is, ranging from zero to one.
$800
The lines that a hyperbola approaches as the variables approach infinity.
$1200
The transformation used to remove the xy-term from a conic equation.
$1600
The general second-degree equation form used to classify all conic sections.
$2000
The chord passing through the focus of an ellipse perpendicular to the major axis.

Sequences

$400
The notation used to find the nth term based on the previous term.
$800
The name of the sequence where each term is the sum of the two preceding terms.
$1200
The method of proving statements for all natural numbers using a base case and inductive step.
$1600
The term for a partial sum of a sequence as the number of terms approaches infinity.
$2000
The type of series that converges if the absolute value of the common ratio is less than this threshold.

Matrices

$400
The dimension of a matrix described by rows by columns.
$800
The values lambda for which the equation A times v equals lambda times v holds.
$1200
The method of solving a linear system by multiplying by the inverse coefficient matrix.
$1600
The technique of using row operations to reach a matrix with zeros below the main diagonal.
$2000
The rule stating the determinant of the product is the product of these values.

Final Jeopardy · Complex Numbers

This formula relates complex exponentials to trigonometric functions using the constant i.
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