Gaokao Exam Gaokao Mathematics: Functions and Calculus 4

Question 1

If f(x) = x² - 3x + 2 and g(x) = f(f(x)), find g'(0).

Accepted Answer

9

Answer

12

Answer

6

Answer

3

Question 2

The range of f(x) = 2sin(x) + 1 for x ∈ [0, π] is:

Accepted Answer

[1, 3]

Answer

[-1, 3]

Answer

[0, 3]

Answer

[-2, 3]

Question 3

For f(x) = ln(x² - 4x + 3), what is the domain of f?

Accepted Answer

(-∞, 1) ∪ (3, +∞)

Answer

(1, 3)

Answer

all real numbers

Question 4

Which statement about the function f(x) = x + 1/x (x ≠ 0) is correct?

Accepted Answer

f is odd and has a local minimum at x = 1

Answer

f is even and increasing on (0, +∞)

Answer

f is odd and decreasing on (0, 1)

Answer

f is even and has a local maximum at x = -1

Question 5

Evaluate ∫₀^π/2 cos²(x) dx.

Accepted Answer

π/4

Answer

π/2

Answer

1

Answer

1/2

Question 6

The function f(x) = (x-a)²(x-b) has a local maximum at x = a and a local minimum at x = b if:

Accepted Answer

a > b

Answer

a < b

Answer

a = b

Answer

a = 2b

Question 7

If the equation x² + mx + n = 0 has roots α and β, and α² + β² = 5 with αβ = 2, find m² - 2n.

Accepted Answer

9

Answer

5

Answer

7

Answer

3