Gaokao Exam Gaokao Mathematics: Functions and Calculus 2

Question 1

If f(x) = x³ + x, then f(x) is:

Accepted Answer

Odd function only

Answer

Even function only

Answer

Both even and odd

Answer

Neither even nor odd

Question 2

Find all local extrema of g(x) = x⁴ - 8x² + 3.

Accepted Answer

Local max at x = 0; local min at x = ±2

Answer

Local min at x = 0; local max at x = ±2

Answer

Local min at x = ±2 only

Answer

Local max at x = 0 only

Question 3

The domain of f(x) = √(1 - x²) / ln(x + 2) is:

Accepted Answer

(-2, -1) ∪ (-1, 1)

Answer

[-1, 1]

Answer

(-1, 1)

Answer

(-2, 1]

Question 4

Given f'(x) = 3x² - 6x, identify all intervals on which f is concave up.

Accepted Answer

(1, +∞)

Answer

(-∞, 0) ∪ (2, +∞)

Answer

(0, 2)

Answer

(-∞, 1)

Question 5

Evaluate ∫₁^e (1/x + x) dx.

Accepted Answer

1 + (e²-1)/2

Answer

1 + e²/2

Answer

(e²+1)/2

Answer

e - 1 + e²/2

Question 6

If f(x) = 2^x and g(x) = log₂(x), find f(g(8)).

Accepted Answer

8

Answer

3

Answer

6

Answer

16

Question 7

The function f(x) = kx + b is the derivative of F(x) = x² + 2x - 5. Find k + b.

Accepted Answer

3

Answer

1

Answer

2

Answer

4