DSST Mathematics 2

Question 1

What is the derivative of f(x) = 3x⁴ - 2x² + 5x - 7?

Accepted Answer

12x³ - 4x + 5

Answer

Using the power rule, the derivative is 12x³ - 4x + 5; the constant -7 drops to zero.

Question 2

Which of the following is the solution set of |2x - 3| < 7?

Accepted Answer

-2 < x < 5

Answer

Solving -7 < 2x - 3 < 7 gives -4 < 2x < 10, so -2 < x < 5.

Question 3

A savings account earns 4% annual interest compounded quarterly. What is the effective annual rate (APY)?

Accepted Answer

Approximately 4.06%

Answer

APY = (1 + 0.04/4)⁴ - 1 ≈ 1.0406 - 1 = 4.06%.

Question 4

If sin θ = 3/5 and θ is in the first quadrant, what is tan θ?

Accepted Answer

3/4

Answer

With sin θ = 3/5, cos θ = 4/5 (Pythagorean theorem), so tan θ = sin/cos = 3/4.

Question 5

What is the sum of the infinite geometric series 8 + 4 + 2 + 1 + ...?

Accepted Answer

16

Answer

The common ratio is 1/2, so S = a/(1-r) = 8/(1 - 1/2) = 16.

DSST - DANTES Subject Standardized Tests Practice Test