ACAP SE 8th Grade (12 questions)

Front

What is an exponent?

Back

An exponent is a number that indicates how many times to multiply the base by itself. For example, in 5^3, 5 is the base and 3 is the exponent, meaning 5 x 5 x 5.

Front

What is the formula for the volume of a sphere?

Back

The volume V of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

What does it mean for one volume to be 'twice' another?

Back

If one volume is twice another, it means that the larger volume is equal to two times the smaller volume.

Front

How do you simplify expressions with exponents?

Back

To simplify expressions with exponents, use the laws of exponents, such as a^m * a^n = a^(m+n) and (a^m)^n = a^(m*n).

Front

What is scientific notation?

Back

Scientific notation is a way of expressing numbers as a product of a number between 1 and 10 and a power of 10, e.g., 5 x 10^3.

Front

How do you compare two numbers in scientific notation?

Back

To compare two numbers in scientific notation, compare their exponents first. If the exponents are the same, compare the coefficients.

Front

What is the relationship between the radius and volume of a sphere?

Back

The volume of a sphere increases with the cube of the radius. If the radius doubles, the volume increases by a factor of 2^3 = 8.

Front

What is the slope of a line with a positive slope?

Back

A line with a positive slope rises from left to right, indicating that as x increases, y also increases.