Semester 1 Review PreAP - Part 1

Front

What is the inverse of the function f(x) = 5x - 8?

Back

The inverse is f^{-1}(x) = \frac{1}{5}x + \frac{8}{5}.

Front

How do you find the height of a kite when 100 m of string is released at an angle of 67°?

Back

Use the sine function: height = 100 * sin(67°) = 92.050 ft.

Front

What does the 73rd partial sum mean in a sequence?

Back

It refers to the sum of the first 73 terms of the sequence.

Front

What is the value of x if x = 30.256°?

Back

x = 30.256°.

Front

How do you identify intervals where the function f(x) = |x + 2| + |x - 6| is increasing, decreasing, or constant?

Back

Increasing on (6, ∞); decreasing on (-∞, -2); constant on (−2, 6).

Front

Define the term 'function'.

Back

A function is a relation that assigns exactly one output for each input.

Front

What is the definition of an inverse function?

Back

An inverse function reverses the operation of the original function.

Front

How do you calculate the sine of an angle in a right triangle?

Back

Sine is calculated as the ratio of the length of the opposite side to the hypotenuse.

Front

What is the formula for the sum of an arithmetic series?

Back

The sum S_n of the first n terms is given by S_n = \frac{n}{2}(a + l), where a is the first term and l is the last term.

Front

What is the difference between increasing and decreasing functions?

Back

An increasing function has a positive slope, while a decreasing function has a negative slope.