12th Grade Math Flashcard

Front

Solve the equation: 2x + 5 = 15

Back

x = 5

Front

Find the limit of the function f(x) = (x^2 - 4) / (x - 2) as x approaches 2

Back

4

Front

What is the integral of f(x) = 2x + 3?

Back

The integral of f(x) = 2x + 3 is x^2 + 3x + C

Front

What is the derivative of f(x) = 3x^2 + 2x - 5?

Back

f'(x) = 6x + 2

Front

Solve the equation: 3sin(x) = 1

Back

x = sin^-1(1/3)

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

Define a function's limit.

Back

The limit of a function is the value that the function approaches as the input approaches a certain point.

Front

What is the Fundamental Theorem of Calculus?

Back

It links the concept of differentiation and integration, stating that if F is an antiderivative of f on an interval [a, b], then ∫_a^b f(x)dx = F(b) - F(a).

Front

What is the Pythagorean theorem?

Back

In a right triangle, a² + b² = c², where c is the hypotenuse.

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.