EOC Math 3 Review 3

Front

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

Back

The volume V of a solid of revolution can be calculated using the disk method or the washer method, depending on the shape. For a function y = f(x) rotated around the x-axis, the volume is given by: V = π∫[a,b] (f(x))^2 dx.

Front

What is an isosceles trapezoid?

Back

An isosceles trapezoid is a quadrilateral with one pair of parallel sides (the bases) and the non-parallel sides (the legs) are of equal length.

Front

How do you calculate the area of an isosceles trapezoid?

Back

The area A of an isosceles trapezoid can be calculated using the formula: A = (1/2) * (b1 + b2) * h, where b1 and b2 are the lengths of the bases and h is the height.

Front

What is the relationship between sample size and margin of error in statistics?

Back

Increasing the sample size decreases the margin of error, leading to more precise estimates of the population parameter.

Front

What is the formula for the mean of a data set?

Back

The mean (average) of a data set is calculated by summing all the values and dividing by the number of values: Mean = (Σx) / n.

Front

What is the definition of standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.

Front

How do you solve a problem involving combined work rates?

Back

To solve combined work rate problems, add the individual rates of work together. If A can complete a task in t1 hours and B in t2 hours, their combined rate is: 1/t = 1/t1 + 1/t2.

Front

What is the definition of an inequality?

Back

An inequality is a mathematical statement that indicates one quantity is less than, greater than, less than or equal to, or greater than or equal to another quantity.

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What is the formula for the volume of a cone?

Back

The volume V of a cone is given by the formula: V = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height.