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本文编辑于2019年12月22日

AP, Advanced Placement。是加拿大和美国优秀高中生必备的学习课程。对多数加拿大和美国名牌大学，已经成为入学（尤其是申请热点专业和/或奖学金）的基本要求。

本文所涉及的知识点，不在国内高中教学阶段范围。本系列文章，仅作为中学师生和家长的参考材料。也可作为对部分有兴趣了解北美高中教学（数学）、国内外大学一年级高等数学教学的参考材料。

微分-应用

1. The slope of the curve y² -xy - 3x = 1 at the point(0, -1) is

1. -1
2. -2
3. 1
4. 2
5. -3

2. The equation of the tangent to the curve y = x at the point (π/2, π/2) is

1. y = x - π
2. y = π/2
3. y = π - x
4. y = x + π/2
5. y = x

3. The tangent to the curve of y = xe^-x is horizontal when x is equal to

1. 0
2. 1
3. -1
4. 1/e
5. none of above

4. The tangent to the curve y² -xy + 9 = 0 is vertical when

1. y = 0
2. y = ±3^1/2
3. y = 1/2
4. y = ±3
5. none of above

5. The best approximation, in cubic centimeters, to the increase in volume of a sphere when the radius is increased from 3 to 3.1 cm is

1. 0.04π/3
2. 0.04π
3. 1.2π
4. 3.6π
5. 36π

6. If the side e of a square is increased by 1%, then the area is increased approximately

1. 0.02e
2. 0.02e²
3. 0.01e²
4. 1%
5. 0.01e

7. The edge of a cube has length 10 cm, with a possible error of 1%, The possible error, in cubic cm, in the volume of the cube is

1. 3
2. 1
3. 10
4. 30
5. none of above

Question 8 ~ 9 are based on the fig.1 as following

8. For which curve (A, B, C, D, E) shown on fig.1 are both f' and f'' negative?

9. For which curve (A, B, C, D, E) shown on fig.1 is f'' positive but f' negative?

10. If a particle moves along a line according to the law s = t⁵ + 5t⁴, then the number of times it reverses direction is?

1. 0
2. 1
3. 2
4. 3
5. 4

11. The point(s) on the curve x² - y² = 4 closest to the point (6, 0) is (are)?

1. (2, 0)
2. (5^½, ±1)
3. (3, ±5^½)
4. (13^½, ±3^½)
5. None of above

12. The first-quadrant point on the curve y²x = 18 that is closest to the point (2, 0) is?

1. (2, 3)
2. (6, 3^½)
3. (3, 6^½)
4. (1, 18^½)
5. None of above

参考答案

1、A； 2、E； 3、B； 4、D； 5、D； 6、B；

7、D； 8、E； 9、B； 10、C； 11、C； 12、C;

注：本文参考参考《AP Calculus -- by David Bock, M.S.》。本网站推荐大家使用原版教材。网上信息仅限于个人学习使用，请勿用于任何商业用途。