M3 EOC Review Starter Flashcard #5 Fall24

Front

What is the formula for the volume of a solid of revolution when rotating a shape around a line?

Back

The volume V can be calculated using the formula: V = π ∫[a,b] (f(x))^2 dx, where f(x) is the function being rotated.

Front

What is a polynomial function?

Back

A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

What does it mean for a polynomial to have a 'lead coefficient'?

Back

The lead coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x for which the polynomial evaluates to zero.

Front

What is the significance of the multiplicity of a zero?

Back

Multiplicity indicates how many times a particular zero is repeated in the polynomial. A zero with multiplicity greater than one indicates that the graph touches the x-axis at that point.

Front

How do you determine the number of real and imaginary roots of a polynomial?

Back

Use the discriminant (b^2 - 4ac) for quadratic polynomials, or apply the Fundamental Theorem of Algebra for higher degree polynomials.

Front

What is the formula for margin of error in statistics?

Back

Margin of error = 2 * (s / √n), where s is the sample standard deviation and n is the sample size.

Front

How do you calculate the sample size needed for a specific margin of error?

Back

Rearranging the margin of error formula gives n = (2s / margin of error)^2.

Front

What is the relationship between standard deviation and margin of error?

Back

A smaller standard deviation results in a smaller margin of error for a given sample size.

Front

What is the definition of a rectangle in geometry?

Back

A rectangle is a quadrilateral with four right angles and opposite sides that are equal in length.