Pre-Cal Midterm 24'

Front

What is the period of the function y = 4cos(1/2x + π)?

Back

The period is 4π.

Front

Simplify the expression (3y⁴)².

Back

The simplified expression is 9y⁸.

Front

Simplify the exponential expression: 10x⁻².

Back

The simplified expression is 2x².

Front

A hawk swoops down toward a mouse at an angle of 30 degrees. If the mouse is 15 feet from the base of the tree, what is the distance from the tree branch to the mouse?

Back

The distance is 30 feet.

Front

Factor by grouping: 5n³ - 10n² + 3n - 6.

Back

The factored form is (5n² + 3)(n - 2).

Front

What is the amplitude of the function y = 4cos(1/2x + π)?

Back

The amplitude is 4.

Front

What is the general form of a cosine function?

Back

The general form is y = A cos(Bx + C) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

Front

How do you find the period of a cosine function?

Back

The period is found using the formula: Period = 2π / |B|, where B is the coefficient of x.

Front

What is the result of (x² + 2x + 1)²?

Back

The result is x⁴ + 4x³ + 4x².

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse.