嘉定一中AP选修课
AP Calculus BC
课程概览
Microeconomics
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Midterm Test 1
Midterm Test 1
期中测试1 (Units 1-4)
期中测试，覆盖极限、求导、导数应用等Units 1-4的内容
✍️ 8 题
1. lim(x→0) sin(x)/x = ?
A. 1
B. 0
C. ∞
D. Does not exist
2. If f(x) = |x - 2|, at which point is f not differentiable?
A. x = 2
B. x = 0
C. x = -2
D. Nowhere
3. Find f'(x) if f(x) = x²·sin(x)
A. 2x·sin(x) + x²·cos(x)
B. 2x·cos(x)
C. x²·cos(x)
D. 2x·sin(x) - x²·cos(x)
4. Find the derivative of f(x) = tan⁻¹(x)
A. 1/(1+x²)
B. 1/(1-x²)
C. sec²(x)
D. -1/(1+x²)
5. If a particle moves with position s(t) = t³ - 6t² + 9t, when is it moving to the right?
A. t ∈ (0,1) ∪ (3,∞)
B. t ∈ (1,3)
C. t > 3
D. t < 1
6. Using linear approximation, estimate √(4.1)
A. 2.025
B. 2.05
C. 2.1
D. 2.0
7. If f'(x) > 0 and f''(x) < 0 on an interval, then f is:
A. Increasing and concave down
B. Decreasing and concave down
C. Increasing and concave up
D. Decreasing and concave up
8. A box with a square base has volume 1000 cm³. Find the minimum surface area.
A. 600 cm²
B. 500 cm²
C. 400 cm²
D. 300 cm²
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