Integrated 3 Fall Final

Front

What is the formula for the perimeter of a parallelogram?

Back

The perimeter (P) of a parallelogram is given by the formula P = 2(a + b), where 'a' and 'b' are the lengths of the two different sides.

Front

How do you calculate the volume of a cylinder?

Back

The volume (V) of a cylinder is calculated using the formula V = πr²h, where 'r' is the radius and 'h' is the height.

Front

What does the ordered pair (0, -2) represent on a graph?

Back

The ordered pair (0, -2) represents the y-intercept of the graph, where the line crosses the y-axis.

Front

How do you simplify the expression (7x² + 4x - 5) - (3x² - 2x + 6)?

Back

To simplify, combine like terms: (7x² - 3x²) + (4x + 2x) + (-5 - 6) = 4x² + 6x - 11.

Front

What is the solution to the equation 25x² = 100 by taking the square root?

Back

The solution is x = ±2, since taking the square root of both sides gives x = ±√(100/25) = ±√4 = ±2.

Front

What is the area of a rectangle?

Back

The area (A) of a rectangle is calculated using the formula A = length × width.

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the solutions (roots) of a quadratic equation in the form ax² + bx + c = 0, given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

How do you find the slope of a line given two points (x₁, y₁) and (x₂, y₂)?

Back

The slope (m) is calculated using the formula m = (y₂ - y₁) / (x₂ - x₁).

Front

What is the formula for the circumference of a circle?

Back

The circumference (C) of a circle is given by the formula C = 2πr, where 'r' is the radius.