Mathematics 133 -- Calculus with Fundamentals 1

Exam 1 -- Things to Know

September 15, 2015

General Information

The first full-period exam of the semester will be given in class on Thursday, September 24. It will cover the material from sections 1 - 6 of Chapter 1. There will be eight or nine questions (maybe grouped together as parts of larger questions) similar to problems from the quizzes, problem sets, and in-class practice problems so far. Graphing calculators will not be allowed on this exam.

Lauren will run a review session for the exam on Wednesday evening, September 23.

Material To Know

You should know the following material.

• The material on intervals and absolute values (Section 1.1)
• Functions, domains and ranges (Section 1.1)
• New functions from old, via horizontal and vertical shifting, stretching/shrinking (Section 1.1)
• Linear functions (Section 1.2)
  1. The slope-intercept (y = mx + b) and point-slope (y - y₀ = m(x - x₀)) forms for linear functions
  2. The meaning of the slope and how to determine it from either a formula for the function, or from a table of values
• Quadratic functions, completing the square, determining max/min values, plotting (Section 1.2)
• Piecewise-defined functions (Section 1.3)
• Operations on functions (especially composition) (Section 1.3)
• Trigonometric functions (Section 1.4). Know:
  1. Radian measure for angles and how to determine the values of sin(t), cos(t), tan(t) for an angle t in radians
  2. How to sketch graphs for sinusoidal oscillations y = A sin(Bx) + C or y = A cos(Bx) + C and the meanings of A,B,C
  3. How to find a formula for a sinusoidal oscillation, given the graph.
• Inverse functions (Section 1.5). Know:
  1. How to tell whether or not a function is invertible from its graph,
  2. How to derive a formula for the inverse function f^{-1} from a formula for f,
  3. How to sketch the graph of the inverse function from the graph of f.
• Exponential, logarithm functions and their properties (Section 1.6)
  1. The general formula for exponential functions f(x) = b^x. Exponential growth versus exponential decay (which values of b give which case)
  2. The natural logarithm function f(x) = ln(x) and its properties (Section 1.6)
  3. g(x) = ln(x) is the inverse function of the exponential function f(x) = e^x.
  4. Formulas for logs of products, quotients, powers and how to apply them
  5. The shape of the graph y = ln(x)
  6. Using logarithms to solve equations involving exponentials

Good Review Problems:

There is an online e-book version of the Chapter 1 Review Problems from our book posted on LaunchPad (with answers for the odd-numbered problems). I suggest you try the odd numbered problems on paper, then check your answers. (You can omit 15, 29, 49).

Also see the sample exam questions posted on the course homepage.