Math 10A: Calculus

Listed below are the key concepts from sections 1.1 through 1.8 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 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.

• Function properties:
  • Domain and range: 1.1.15, 1.1.17, 1.1.19, 1.1.21
  • Increase and decrease: 1.2.11
  • Concavity: 1.2.7, 1.2.9, 1.2.11, 1.2.35
  • Even and odd functions: 1.3.31, 1.3.33, 1.3.35, 1.3.37, 1.3.54
  • Invertibility: 1.3.25, 1.3.27, 1.3.39, 1.3.41, 1.3.53
• Function transformations: 1.3.3, 1.3.5, 1.3.7, 1.3.9, 1.3.29
• Linear functions:
  • Identifying properties of linear functions: 1.1.7, 1.1.9, 1.1.11
  • Constructing linear models: 1.1.29, 1.1.33, 1.1.35
• Exponential functions and logarithms:
  • Identifying growth and decay: 1.2.1, 1.2.3, 1.2.23, 1.2.25
  • Matching functions to known data: 1.2.17, 1.2.19, 1.2.21
  • Interconverting forms: 1.2.23, 1.2.25, 1.4.25, 1.4.27
  • Constructing exponential models: 1.2.31, 1.2.39, 1.4.35
  • Manipulating logarithms: 1.4.3, 1.4.5
  • Solving exponential equations: 1.4.11, 1.4.13, 1.4.21, 1.4.29, 1.4.35
• Trigonometric functions:
  • Angle identification: 1.5.1, 1.5.3, 1.5.5, 1.5.7, 1.5.9
  • Determining properties of functions: 1.5.15, 1.5.17
  • Matching functions to known data: 1.5.21, 1.5.23, 1.5.25
  • Constructing trigonometric models: 1.5.35, 1.5.38, 1.5.43
  • Solving trigonometric equations: 1.5.29, 1.5.31, 1.5.33
• Polynomial and rational functions:
  • Polynomial properties: 1.6.5, 1.6.7, 1.6.9, 1.6.25
  • Polynomial roots and multiplicity: 1.6.7, 1.6.9, 1.6.26
  • Rational function zeroes and vertical asymptotes: 1.6.14, 1.6.25, 1.6.29
  • Rational function long-term behavior: 1.6.6, 1.6.14, 1.6.29
• Continuity and limits:
  • Finding discontinuities: 1.7.1, 1.7.3, 1.7.15
  • Continuity in piecewise functions: 1.7.17, 1.7.18, 1.7.19, 1.7.20
  • Intermediate value theorem: 1.7.11, 1.7.13
  • Evaluation of limits: 1.8.1, 1.8.7, 1.8.13, 1.8.19, 18.31, 1.8.33, 1.8.41