Free GRE Mathematics Test Exam Questions and Answers

Let C denote an arbitrary constant. ∫ e^(ex) dx =

• AA. e^(ex−1) + C
• BB. e^(ex) + C
• CC. e^(ex+1) + C
• DD. x e^(ex) + C
• EE. e^(ex+1)/(ex + 1) + C

Σ (n=0 to ∞) (3 log 2)ⁿ/n! =

• AA. 1
• BB. 2
• CC. 3
• DD. 6
• EE. 8

Let r and A be the radius and the area, respectively, of a circle. If r increases by 40 percent, by what percent will A increase?

• AA. 40%
• BB. 49%
• CC. 80%
• DD. 96%
• EE. 130%

If a differentiable function y(x) satisfies the equation x + y⁴ = 10 for y ≠ 0, then dy/dx =

• AA. −1/(4y³)
• BB. −1/y⁴
• CC. −x/(4y³)
• DD. 9/(4y³)
• EE. (10 − x)/y⁴

Let g be a differentiable function on ℝ, and let h be the function defined by h(x) = ∫ from 0 to x² of g(t) dt for all x ∈ ℝ. Which of the following is equal to h′(x) for all x ∈ ℝ ?

• AA. g(x²)
• BB. 2xg′(x²)
• CC. 2xg(x²)
• DD. g′(x²) − g′(0)
• EE. 2xg(x²) − g(0)

Let f be a real-valued function such that f(f(x)) = x for all real numbers x in the domain of f. Which of the following could be the graph of f in the xy-plane?

• AA. (graph F1)
• BB. (graph F2)
• CC. (graph F3)
• DD. (graph F4)
• EE. (graph F5)

If a and b are positive numbers, then lim (x→0) (1 + x/a)^(b/x) =

• AA. e^(ab)
• BB. e^(b/a)
• CC. e^(a/b)
• DD. 1
• EE. ∞

If the function f is defined by f(x) = log x/(x² − 1) for all positive numbers x except x = 1, and if f(1) = a, for what value of a is f continuous at x = 1 ?

• AA. 0
• BB. 1/2
• CC. 1
• DD. 2
• EE. There is no such value.

Of the 10 lightbulbs in a box, 3 are defective. If 2 lightbulbs are to be chosen from the box at random and without replacement, what is the probability that at least 1 of the 2 lightbulbs will be defective?

• AA. 3/10
• BB. 7/15
• CC. 8/15
• DD. 19/30
• EE. 7/10

In the power series expansion Σ (n=0 to ∞) aₙxⁿ of 1/(1 − x)², where |x| < 1, what are the coefficients a₀, a₁, and a₂, respectively?

• AA. 1, 1, and 1
• BB. 1, 2, and 3
• CC. 1, 2, and 6
• DD. 2, 4, and 6
• EE. 1, 1/2, and 1/6