AS Associate Of Science In Mathematics 2

Question 1

What is the integral of f(x) = 4x³?

Accepted Answer

x⁴ + C

Answer

Using the power rule for integration: ∫4x³ dx = 4 · (x⁴/4) + C = x⁴ + C.

Question 2

Which property states that a(b + c) = ab + ac?

Accepted Answer

Distributive property

Answer

The distributive property states that multiplying a number by a sum is the same as multiplying it by each addend and then adding the products.

Question 3

What is the standard form of the equation of a circle with center (h, k) and radius r?

Accepted Answer

(x − h)² + (y − k)² = r²

Answer

The standard form equation of a circle is (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.

Question 4

If a data set has values 4, 7, 7, 9, 13, what is the median?

Accepted Answer

7

Answer

The median is the middle value of an ordered data set; with 5 values, the middle (3rd) value is 7.

Question 5

What does a negative discriminant (b² − 4ac < 0) indicate about a quadratic equation?

Accepted Answer

Two complex (non-real) roots

Answer

A negative discriminant means the quadratic has no real roots; instead, it has two complex conjugate roots.

AS - Associate In Science Degrees Practice Test