Math 10A: Calculus

Listed below are the key concepts from sections 2.1 through 3.9 in Hughes-Hallett. You are responsible for familiarity with all of these concepts, and comptenece in applying them is critical in performing well on the second midterm; in addition, you are expected to retain knowledge of significant concepts from the first midterm. Next to each concept, several practice problems have been listed to help give you a familiarity with the material and expectations. Note that some questions appear in several categories: these questions test your ability to synthesize several concepts within a single response.

• Numerical determination of the derivative:
  • Sketching and estimating derivatives from graphs: 2.1.5, 2.1.6, 2.1.14, 2.1.15, 2.2.8, 2.2.9, 2.3.3, 2.3.5, 2.3.7, 2.3.9, 2.3.31, 2.3.33
  • Instantaneous vs. average rates of change: 2.1.14, 2.1.15, 2.1.17, 2.2.3, 2.2.19
  • Approximation of instantaneous rates of change: 2.1.3, 2.2.1
• Interpretation and use of the derivative:
  • First derivative sign: 2.3.41, 2.3.42, 2.5.1, 2.5.3, 2.5.19, 2.5.21
  • Second derivative sign: 2.5.1, 2.5.3, 2.5.5, 2.5.19, 2.5.21, 3.3.45
  • Differentiability: 2.6.13, 2.6.15, 2.6.17
  • Tangent lines: 2.2.13, 2.2.19, 2.2.39, 3.1.53, 3.2.41
  • Function approximation with derivatives: 2.2.11, 3.9.1, 3.9.3, 3.9.5, 3.9.19
  • Real-world interpretations: 2.3.5, 2.3.39, 2.4.1, 2.4.3, 2.4.9 2.4.17
• Symbolic manipulation of derivatives:
  • Solution with the difference quotient: 2.1.19, 2.2.29, 2.2.33, 2.2.37, 2.3.15
  • Power rule: All of 3.1 is good drill; particularly interesting problems are 3.1.7, 3.1.17, 3.1.25, 3.1.29, 3.1.35, 3.1.51, 3.1.53, 3.3.21, 3.3.23.
  • Exponential rule: All of 3.2 is good drill; particularly interesting problems are 3.2.11, 3.2.13, 3.2.19, 3.2.21, 3.2.23, 3.2.41
  • Trig functions: All of 3.5 is good drill; particularly interesting problems are 3.5.11, 3.5.13, 3.5.23, 3.5.31, 3.5.37
  • Product rule: 3.3.1, 3.3.3, 3.3.5, 3.3.7, 3.3.9, 3.5.23
  • Quotient rule: 3.3.11, 3.3.13, 3.3.15, 3.3.21, 3.3.29, 3.3.45, 3.4.31, 3.4.35
  • Chain rule: All of 3.4 is good drill; particularly interesting problems are 3.4.9, 3.4.33, 3.4.45, 3.4.47, 3.5.11, 3.6.13, 3.6.15
  • Inverse functions: All of 3.6 is good drill; particularly interesting problems are 3.6.3, 3.6.13, 3.6.15, 3.6.17, 3.6.29
  • Implicit derivatives: All of 3.7 is good drill.
  • Rule synthesis: 3.4.29, 3.4.37, 3.4.43, 3.5.13, 3.5.31, 3.5.37, 3.6.29, 3.6.33