Mathematics 135 -- Calculus 1

Exam 1 -- Things to Know

September 19, 2019

General Information

The first full-period exam of the semester will be given in class on Friday, September 27. It will cover the material from sections 1 - 6 of Chapter 1 and sections 1 - 3 of Chapter 2. About 60% of the points will be devoted to questions from Chapter 1 topics and about 40% of the points will come from Chapter 2 topics. This is the same as the material from Problem Sets 1 and 2, plus the material from class on Friday, September 20. 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 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).

Material To Know

You should know the following material.

• 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, solving by factoring or the quadratic formula. (I will not ask you to complete the square and use that to plot or analyze a quadratic function in other ways.)
• There won't be anything specifically from Section 1.3 (we'll review some of that when we get to Chapter 3 and we need to use it).
• 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
• Average and instantaneous rates of change (Section 2.1)
• Limits graphically and numerically (Section 2.2)
• The Basic Limit Laws (Section 2.3) I won't ask you to state them; know how to recognize when they do or do not apply, and be able to use them to compute limits.

How to Review

See the sample exam questions posted on the course homepage.

For additional review problems, try a good selection of the odd-numbered problems in the book (by hand). Check your answers against the answer key in the back.