Lesson #71
Review for Semester Exam
Quote:
"The more you know, the less sure you are." -- Voltaire
Objectives:
The student will review all concepts covered in the first semester.
1. Discuss exam review sheets and other questions.
Outline of A.P. Calculus Semester 1 Exam
Day 1:
Part I With a Calculator
Multiple Choice
Free Response
Day 2:
Part II Without a Calculator
Multiple Choice
Free Response
To do well on this exam, you should do the following:
1. Study your notes - study methods used in proofs and problems.
Learn definitions in your notes.
2. Rework problems that I assigned for homework.
3. Rework problems on tests and quizzes and Mini exams.
4. Work all the problems on the review sheets.
5. Study the list of Derivatives.
Outline of Exam by Topics:
I. Chapter 1 - Functions
A. Properties of functions --Definition, Domain, and Range
B. Graphing Functions
C. Parametric Equations
D. Greatest Integer Function
E. Inverse Trig Functions
F. Logarithmic and Exponential Functions (Log and exponential equations)
G. Symmetry
II. Chapter 2 - Limits and Continuity
A. Limits - Intuitive (and infinite geometric series)
B. Limits - Definition (including the definition)
C. Limits - Computations
D. Continuity
III. Chapter 3 - Differentiation
A. Definition of Derivative, Graph of derivative, Rates of Change (Avg, Inst.)
B. Tangent and Normal Lines
C. Derivative Formulas
(Chain Rule, Trig., Tables, Product, Power, Sum, Quotient, Parametric Eq.)
D. Derivatives of trig functions
E. Differentials
F. Velocity, Acceleration
G. Related Rates
IV. Chapter 4 - Logarithmic and Exponential Functions
A. Inverse Functions
D. Implicit Differentiation
E. Derivatives of logarithmic and exponential functions
F. Derivatives of Inverse Trigonometric Functions
G. L'Hopital's Rule
V. Chapter 5 - Curve Sketching
A. Increasing, Decreasing, Concavity
B. Relative Extrema - Maxima, Minima, Points of Inflection
C. Absolute Extrema
D. Applied Maxima Minima Problems
VI. Appendix A - Trigonometry
A. Trig Functions
B. Trig Identities
C. Trig Equations
VII. Appendix B -Solving Polynomial Equations
A. Remainder Theorem
VIII. Appendix D - Real Numbers, Intervals, and Inequalities
A. Express repeating decimals as ratios of integers
B. Interval Notation
C. Solving inequalities
IX. Appendix E - Absolute Value
X. Appendix F - Coordinate Planes and Lines
A. Slope of a line and Angle of inclination
B. Equations of lines
XI. Appendix G - Distance and Circles
A. Distance
B. Circles