Mathematics 135 -- Calculus 1

Exam 1 -- Things to Know

September 14, 2016

General Information

The first full-period exam of the semester will be given in class on Friday, September 23. 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.
• Use of cell phones, I-pods, tablet computers, and any other electronic devices besides a basic calculator will not be allowed during the exam. Please leave such devices in your room or put them away in your backpack (make sure cell phones are turned off).

If there is interest, I would be happy to run a review session. Because of other commitments I have, though, this would almost have to be Thursday evening. Don't wait to start studying until then!

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 a big OPTIONAL review assignment on Chapter 1 in WebAssign. This is not a graded assignment for the course, but doing at least some of these will be a good way to practice and prepare for the exam.

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