Mathematics 133 -- Intensive Calculus for Science 1

Exam 1 -- Things to Know

September 21, 2001

General Information

The first full-period exam of the semester will be given in class on Friday, September 28. There will be seven or eight questions (maybe grouped together as parts of larger questions) similar to problems from the quizzes so far. I will let you use a graphing calculator on this exam, but calculators like the TI 89 or 92 with symbolic manipulation are not allowed on this or any other exam.

We will review for the exam in class on Thursday, September 27. If there is interest I can also see if Kathryn Blaisdell is available for an evening ``last minute question'' session on Thursday.

Material To Know

You should know the following material.

• The material on rules for exponents, fractions, etc. that we reviewed the first week.
• Functions, linear functions and their properties (Section 1.1)
  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
• Exponential functions and their properties (Section 1.2)
  The general formula for exponential functions f(x) = ca^x (or using different letters, P(t) = P₀ a^t, as on page 11 of the text).
  1. Exponential growth versus exponential decay (which values of a give which case)
  2. Be able to determine an equation for an exponential function, given a graph or a table of values.
  3. How to tell exponential functions apart from linear functions
• New functions from old, via horizontal and vertical shifting, stretching/shrinking (Section 1.3)
• Inverse functions. (Section 1.3) 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.
• The logarithm functions f(x) = log_a(x) and their properties (Section 1.4)
  1. g(x) = log_a(x) is the inverse function of the exponential function f(x) = a^x.
  2. Formulas for logs of products, quotients, powers and how to apply them
  3. The shapes of the graphs y = log_a(x)
  4. Using logarithms to solve equations involving exponentials
  5. The natural logarithm function f(x) = ln(x) (the logarithm function with base a = e = 2.71828...)
• Trigonometric functions. 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.

Good Review Problems:

From the Review problems at the end of Chapter 1: 1, 2, 6, 7, 8, 11, 14, 22, 23, 26, 27, 31, 33, 35, 37, 38.

Also see the Sample Exam 1.