HHS Pre-Calculus

Reference Book

Purpose: To create a reference book to review topics for your final exam and to prepare you for Calculus.

Instructions: Students are to compose a reference book containing information and examples of the graphs of common functions and concepts. The topics are listed below. Your book should contain detailed information and examples. Use color neatly for illustration purposes, if you desire. If you are unsure about the depth of any topic, please see your teacher for clarification.

General Layout: 2 point deduction for any structural errors.

  • A title page at the front of the book is required.
  • Include a table of contents with topics and page numbers.
  • All work is to be done on lineless paper using colored or black ink (NO PENCIL). Computer graphics CAN NOT BE USED.
  • Each numbered topic should be a new chapter
  • All work (except for headings) should be handwritten

Checkpoints:

  • Wednesday, September 30 – Through Chapter 2
  • Monday, November 2 – Through Chapter 4
  • Monday, December 14 – Entire Reference Book Due

Late Fees:

  • Planned absence on Monday, December 14 will require an early submission of the reference book.
  • 5 points will be deducted per day if the reference book is turned in after December 14.
  • 30 points will be deducted if turned in after Winter Break.

Topics to be included in your reference book: (145 points total)

  1. Functions and Graphs (33 points)
  2. 12 Basic Functions (include Domain, Range, Symmetry, Interval Increasing, Interval Decreasing, Continuity, Boundedness, End Behavior (Limits), and a graph for EACH).
  3. Linearv. Logarithmicix. Greatest Integer
  4. Quadraticvi. Exponentialx. Sine
  5. Cubicvii. Absolute Valuexi. Cosine
  6. Square Rootviii. Reciprocalxii. Logistic
  7. Graphical Transformations (Explain and graph the transformations)
  8. f(x)= -f(x) and f(x) = f(-x)
  9. f(x)=f(x + c) and f(x)=f(x – c)
  10. f(x)=f(x) + c and f(x)=f(x) – c
  11. f(x) = a  f(x) where a>1 and 0<a<1
  12. f(x) = f(x/c) where c>1 and 0<c<1
  13. Function Composition and Inverses – Given f(x) and g(x), find the equation of the new function and domain of:
  14. f(g(x))
  15. g(f(x))
  16. f-1(x)
  17. g-1(x)
  1. Polynomial, Power, and Rational Functions (15 points)
  2. Quadratic Functions
  3. Standard Form
  4. Vertex Form
  5. Converting from Standard Form to Vertex Form using Completing the Square
  6. Power Functions – given an equation find the degree and constant of variation:
  7. Direct Variation
  8. Indirect Variation
  9. Polynomial Functions
  10. Multiplicity relative to an equation and a graph
  11. Given the zeros, find the function
  12. Given the function, find the zeros (rational, irrational, and complex)
  13. Long Division vs Synthetic Division
  14. Examples of both
  15. When to use one vs the other
  16. Solving Inequalities with Sign Charts
  1. Exponential and Logarithmic Functions (19 points)
  2. SolvingExponential and Logarithmic Functions
  3. Modeling with Exponential and Logistic Functions
  4. Properties of Logs
  5. Example of expanding
  6. Example of condensing
  7. Partial Fraction Decomposition
  8. Sequences and Series
  9. Recursive and Explicit Formulas for Arithmetic Sequences
  10. Recursive and Explicit Formulas for Geometric Sequences
  11. Convergent vs Divergent Sequences
  12. Sum of Finite Series
  13. Partial Sum of Infinite Series
  14. Sum of Convergent Infinite Series
  1. Trigonometric Functions (26 points)
  2. Radians
  3. Radians to Degrees
  4. Degrees to Radians
  5. Unit Circle
  6. Graphs of Sine, Cosine, and Tangent
  7. Graphs of Cosecant, Secant, and Cotangent
  8. Graphs of Inverse Sine, Inverse Cosine, and Inverse Tangent
  9. Evaluating Trigexpressions using Unit Circle
  10. Sine, Cosine, and Tangent examples (examples must be negative angles)
  11. Cosecant, Secant, and Cotangent examples (examples must be in radians)
  12. Inverse Sine, Inverse Cosine, and Inverse Tangent examples (examples must be in degrees)
  13. Sinusoidal Functions (show original and transformed graphs)
  14. Amplitude – Vertical Stretch/Shrink
  15. Period – Horizontal Stretch/Shrink
  16. Phase Shift – Horizontal Shift
  17. Midline – Vertical Shift
  18. Reflections – Over x/y axis
  1. Analytic Trigonometry (formulas ONLY for #A-E)(12 points)
  2. Reciprocal Identities and Quotient IdentitiesH. Proving Trig Identities
  3. Pythagorean IdentitiesI. Law of Sines
  4. Double Angle IdentitiesJ. Law of Cosines
  5. Half Angle IdentitiesK. Area of a Triangle (SAS and SSS)
  6. Power-Reducing Identities
  7. Simplifying Trig Functions
  8. Solving Trig Equations
  1. Applications of Trigonometry (20 points)
  2. Vectors
  3. Component Form
  4. Standard Form (using i and j)
  5. Trig Form
  6. Unit Vector
  7. Dot Product
  8. Finding the angle between vectors
  9. Parametric Equation
  10. Eliminating the Parameter (one trig example and one non-trig example)
  11. Finding Restrictions on the Domain and Range
  12. Projectile Motion
  13. Polar Coordinates
  14. Plotting Polar Coordinates
  15. Converting points from polar to rectangular and vice versa
  16. Converting equations from polar to rectangular and vice versa
  17. Graphs and Equations of Polar Relations
  18. Rose curves
  19. Limacons
  20. Lemniscates
  21. Spiral of Archimedes
  1. Conic Sections (include standard forms of the equations and graphs of the figures) (20 points)
  2. Parabola
  3. Vertex
  4. Focus
  5. Directrix
  6. Focal Length/Width
  7. Direction of opening
  8. Ellipse
  9. Center
  10. Vertices
  11. Foci
  12. Wide vs Tall
  13. Hyperbola
  14. Center
  15. Vertices
  16. Foci
  17. Asymptotes
  18. Left/Right vs Up/Down