# Free Test Online

## Standardized Tests Math and Science Practice

• Question #1: The function given by:

is differentiable at x=0. What is the value of f(n-m)?

(a) 2+e

(b) 3+e2

(c) e2

(d) 2e

(e) e3

Solution: Since f(x) is differentiable at x = 1, it must be continuous there, which means that

f(0) = n+1

n + 1 = 4, and n = 3

Now we can determine m from the fact that f(x) is differentiable at x = 0.

The right-hand branch slope is

and f'(0) = 2.
The left-hand branch slope is f'(0) = m.

m = 2

At this point we can calculate n – m = 1

f(1) = 3+e2

• Question #2: If y = sin(x3), what is dy/dx?
(a) 3x2cos(x3)

(b) -3x2cos(x3)

(c) x2cos(32)

(d) -x2cos(32)

(e) cos(x3)

u(x) = x3

du/dx = 3x2

y(u) = sin(u)

dy/du = cos(u)

dy/dx = (dy/du)(du/dx) = cos(x3)·3x2

dy/dx = 3x2cos(x3)

• Question #3:

(a) -1

(b) 1/5

(c) 1

(d) -1/3

(e) 1/3

• Question #4: What is the value of a, if:

(a) ¶

(b) 1

(c) 1 + ¶

(d) √2

(e) 1 + e

Answer: u = 2 + sin(ax)

du/dx = a·cos(ax)

ln(3/2) = (1/a)ln(3/2) and a = 1.

• Question #5: Which of the following are antiderivatives of f(x) = 2x?

(a) 2x/ln(2) + ln(2)

(b) 22x/ln(2) + ln(2)

(c) x2/ln(2) + 1/ln(2)

(d) x + 2ln(2)

(e) 2x + ln(2)