MATH 255A, Review Sheet for Test 1

Test topics

1. Graphical differentiation (3.5).
2. Definition of the derivative. Equation of the tangent line (3.3-3.4)
3. Limits. Continuity (3.1-3.2)
4. Exponential growth (word problems) (2.3)
5. Exponential, logarithmic, trigonometric functions (2.1,2.2,2.4)
6. Graphs of linear, quadratic functions (1.1,1.4)
7. Functions, domains, ranges (1.3)

Formulas/facts you need to know for the test

• Definitions: limit, right/left limit, continuity, derivative
• Graphs of elementary functions (linear, quadratic, rational, power, exponential, logarithmic, trigonometric)
• Properties of the exponential/logarithmic functions
• Radian measure. Values of trigonometric functions for typical angles (0, pi/6, pi/4, pi/3, pi/2, etc.)
• Formula for the exponential growth/decay
• Equation of the tangent line

Practice tests

Here are two examples of practice tests compiled of problems from the textbook. They do not cover all possible types of questions on the test, but are representative of how many quastions you are expected to answer in one hour. For more practice pick problems from the range given in the homework.

1.R: 39, 2.2: 49, 2.3: 23, 2.4: 63, 3.1: 41, 3.4: 19, 3.R: 31, 3.R: 43

1.R: 44, 3.1: 49, 2.3: 25, 2.4: 97, 3.5: 13, 3.1: 79, 2.2: 61, 3.4: 18.

General rules

Tests are closed books/notes. Simple scientific calculator (example: TI-30XII) is allowed on the test. Graphing calculators (example: TI-83, 84, 89) cannot be used. Calulator is not required to answer the questions. You should justify all answers properly. Partial credit will be given depending on how well you explain your solutions. Correct answers without explanations will receive zero points.