AS Associate Of Science In Mathematics

Question 1

What is the value of the derivative of f(x) = 3x² + 5x − 2 at x = 2?

Accepted Answer

17

Answer

The derivative f'(x) = 6x + 5; at x = 2, f'(2) = 6(2) + 5 = 12 + 5 = 17.

Question 2

Which of the following is the correct definition of a limit in calculus?

Accepted Answer

The value a function approaches as the input approaches a given value

Answer

A limit describes the value that a function approaches (but does not necessarily reach) as the input approaches a specified value.

Question 3

What is the solution to the system of equations: 2x + y = 7 and x − y = 2?

Accepted Answer

x = 3, y = 1

Answer

Adding the equations eliminates y: 3x = 9, so x = 3; substituting back gives y = 7 − 2(3) = 1.

Question 4

What is the formula for the area of a circle with radius r?

Accepted Answer

πr²

Answer

The area of a circle is given by A = πr², where r is the radius of the circle.

Question 5

Which of the following correctly states the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides: a² + b² = c².

AS - Associate In Science Degrees Practice Test

AS - Associate In Science Degrees Practice Test

AS Associate Of Science In Mathematics