Mathematics 131 -- Calculus for Physical and Life Sciences 1

Exam 1 -- Things to Know

September 17, 2004

General Information

The first exam of the semester will be given on Wednesday evening, September 22 at XXX in YYY. This exam will cover the material we have studied since the start of the semester -- sections 1 - 6 of Chapter 1 in the text. (See below for a more detailed breakdown of the topics to know.) A basic scientific (non-graphing) calculator will be provided for your use on the exam. Some questions will ask you to draw graphs of functions by hand, and/or determine possible formulas for given graphs, based on the properties of the ``library of functions'' we have studied in class. Be prepared for questions of both these types.

We will review for the exam in class on Wednesday, September 22 or possibly Tuesday, September 21 if people prefer.

Material To Know

You should know the following material.

• 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)
  1. 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).
  2. Exponential growth versus exponential decay (which values of a give which case)
  3. Be able to determine an equation for an exponential function, given a graph or a table of values.
  4. How to tell exponential functions apart from linear functions
• New functions from old via horizontal and vertical shifting, or 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 (Section 1.5). 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.
• Power, polynomial, and rational functions (Section 1.6) Know:
  1. How to find x and y-axis intercepts, ``end behavior'', etc. from the formula
  2. How to to find a formula for a polynomial or a ``simple'' rational function, given the graph.

Good Review Problems:

From the Review problems at the end of Chapter 1: 1, 2, 6, 7, 8, 11, 15, 22, 23, 26, 27, 31, 33, 35, 37, 38.