Gaokao Exam Gaokao Mathematics: Functions and Calculus 3

Question 1

The curve y = x³ - x has horizontal tangent lines at which x-values?

Accepted Answer

x = ±1/√3

Answer

x = 0 only

Answer

x = ±1

Answer

x = 0 and x = ±1

Question 2

Given f(x) = x·e^x, find f''(1).

Accepted Answer

3e

Answer

e

Answer

2e

Answer

e + 1

Question 3

The inverse function of f(x) = (x-1)/(x+1) (x ≠ -1) is:

Accepted Answer

f⁻¹(x) = (1+x)/(1-x)

Answer

f⁻¹(x) = (x+1)/(x-1)

Answer

f⁻¹(x) = (1-x)/(1+x)

Answer

f⁻¹(x) = x

Question 4

Which of the following functions is NOT differentiable at x = 0?

Accepted Answer

f(x) = |x|

Answer

f(x) = x²

Answer

f(x) = x³

Answer

f(x) = sin(x)

Question 5

∫₀¹ x·e^x dx equals:

Accepted Answer

e - 2

Answer

e - 1

Answer

1

Answer

2 - e

Question 6

Let f(x) = x² - 2|x| + 1. The minimum value of f(x) is:

Accepted Answer

0

Answer

1

Answer

-1

Answer

2

Question 7

The graph of y = f(x) passes through (1, 2). If g(x) = f(2x - 1) + 3, what point does g pass through?

Accepted Answer

(1, 5)

Answer

(1, 2)

Answer

(2, 5)

Answer

(0, 5)