Gaokao Exam Gaokao Mathematics: Functions and Calculus 5

Question 1

Let h(x) = f(x)·g(x) where f(x) = x² and g(x) = e^x. Find h''(0).

Accepted Answer

2

Answer

0

Answer

1

Answer

4

Question 2

The function f(x) = x³ - 3x has how many real roots for the equation f(x) = 2?

Accepted Answer

1

Answer

0

Answer

2

Answer

3

Question 3

Using the substitution u = x², evaluate ∫₀² x·e^(x²) dx.

Accepted Answer

(e⁴-1)/2

Answer

e⁴-1

Answer

(e⁴+1)/2

Answer

2e⁴

Question 4

For f(x) = arctan(x), which of the following is true?

Accepted Answer

f is an odd function with horizontal asymptotes at y = ±π/2

Answer

f is decreasing on ℝ

Answer

f is an even function

Answer

f has a vertical asymptote at x = 0

Question 5

Let f(x) = {x² + 1, x ≤ 0; e^x, x > 0}. Find f(f(-1)).

Accepted Answer

e²

Answer

e + 1

Answer

e

Answer

5

Question 6

If f(x) = x³ - 3x, the maximum value of f on [-2, 3] is:

Accepted Answer

18

Answer

2

Answer

9

Answer

20

Question 7

The area bounded by y = x² and y = x is:

Accepted Answer

1/6

Answer

1/3

Answer

1/2

Answer

1/4