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本文编辑于2019年12月19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。

函数-练习

1. If f(x) = x3 + Ax2 + Bx - 3 and if f(1) = 4 and f(-1) = -6, what is the value of 2A + B?

  1. 10
  2. 8
  3. 0
  4. None of above
  5. It can not be determined by given information

2. Which of the following equations has a graph that is symmetric with respect to the origin?

  1. y = (x - 1)x-1
  2. y = 2x4 + 1
  3. y = x3 + 2x
  4. y = x3 + 2
  5. y = x(x3 + 1)-1

3. If y = f(x) = sin(arctan x). Then the range of f is?

  1. {y | 0 < y ≤ 1}
  2. {y | -1 < y < 1}
  3. {y | -1 ≤ y ≤ 1}
  4. {y | -π/2 < y < π/2}
  5. {y | -π/2 ≤ y ≤π/2}

4. The roots of the equation f(x) = 0 are 1 and -2. The roots of f(2x) = 0 are?

  1. 1 and -2
  2. 1/2 and -1
  3. -1/2 and 1
  4. 2 and -4
  5. -2 and 4

5. The set of zeros of f(x) = x³ + 4x² + 4x?

  1. {-2}
  2. {0, -2}
  3. (0, 2}
  4. {2}
  5. {-2, 2}

6. The function whose graph is a reflection in the y-axis of the graph of f(x) = 1 - 3x is?

  1. g(x) = 1 - 3-x
  2. g(x) = 1 + 3x
  3. g(x) = 3x - 1
  4. log3(x-1)
  5. g(x) = log3(1 - x)

7. The range of y = f(x) = ln(cos x) is ?

  1. {y | -∞ < y ≤ 0}
  2. {y | 0 < y ≤ 1}
  3. {y | -1 ≤ y ≤ 1}
  4. {y | -π/2 < y < π/2}
  5. {y | 0 ≤ y ≤ 1}

8. The smallest positive x for which the function f(x) = sin(x/3) - 1 is a maximum is?

  1. π/2
  2. π
  3. 3π/3
  4. 3π
  5. 6π

9. Suppose that f(x) = ln x for all positive x and g(x) = 9 - x² for all real x. The domain of f(g(x)) is?

  1. {x | x ≤ 3}
  2. {x | |x| ≤ 3}
  3. {x | |x| ≥ 3}
  4. {x | |x| < 3}
  5. {x | 0 < x < 3}

10. Suppose that f(x) = ln x for all positive x and g(x) = 9 - x² for all real x (as Question 9). The range of y = f(g(x)) is?

  1. {y | y > 0}
  2. {y | 0 < y ≤ ln 9}
  3. {y | y ≤ ln 9}
  4. {y | y > 0}
  5. None of above

11. The curve defined parametrically by x(t) = t² + 3 and y = t² + 4 is part of a(n)?

  1. line
  2. ellipse
  3. circle
  4. hyperbola
  5. parabola

12. Which equation includes the curve defined parametrically by x(t) = cos²(t) and y(t) = 2sin(t)?

  1. x² + y² = 4
  2. x² + y² = 1
  3. 4x² + y² = 4
  4. 4x; + y² = 4
  5. x; + 4y² = 1

参考答案

1、B； 2、C； 3、B； 4、B； 5、B； 6、A；

7、A； 8、C； 9、D； 10、C； 11、A； 12、D。

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。