Pre-Calculus Curriculum Framework Committee

Suggested Block Schedule Pacing Guide – Semester Two

Week / Topics / Assessable Specifications / Committee Key Targets
10 / Trig Review
Basic identities/Unit Circle
 Determine the trigonometric ratios for basic angles [0, /6, /4, /3, /2, ] and their multiples
 Graphically represent, in the appropriate quadrant, basic trigonometric ratios and relationships
 Verify trigonometric identities with particular emphasis on the Pythagorean identities
 Solve trigonometric equations determining all possible solutions 0  2 / 3, 4
11 / Trig Graphs
Inverse Trig Functions
 Translate and transform graphs of sine and cosine determining the period, amplitude and phase shift
 Transform graphs of sine and cosine functions into their respective cosecant and secant functions determining asymptotes and points of tangency
 Translate and transform functions of tangent and cotangent determining period, asymptotes, roots and phase shift
 Given any trigonometric function, graphically represent its inverse and an appropriate domain interval for which that inverse exists / 1, 3
12 / Complex numbers in trigonometric form
Operations with complex numbers
 Re-express complex numbers from standard form to trigonometric form
 Demonstrate the graphical representations of complex numbers in standard and trigonometric forms
 Apply DeMoivre’s Theorem to determine complex roots of an upper degree function and to graphically display these roots / 2
13 / Matrices and Systems of Equations
 Use substitution and/or elimination to solve a system or to isolate a variable
 Justify solutions numerically and/or graphically through the use of a table, inspection or technology
 Translate any linear system into matrix form and solve by applying the inverse matrix
 Solve a two or three variable system using matrices and/or Cramer’s Rule
 Create a solution model given a real-world application using systems of equations
 Determine specific x and y values as solutions using either the TABLE command or VALUE command
 Locate points of intersection / 5, 8
14 / Conic Sections
 Classify and justify conic sections based on implicitly defined equations
 Perform all algebraic manipulations in order to determine the appropriate characteristics [center/vertex, major/minor axes, axes of symmetry, focal distance, equations of asymptotes]
 Graphically represent each conic section, labeling each appropriate characteristic
 Model each type of function using a graphing calculator, setting an appropriate viewing window using domain and range with proper scaling of axes
 Apply concepts of domain and range to set an appropriate viewing window
 Determine local extreme points and/or changes in direction / 6, 8
15-16 (as time allows) / * Probability/Statistics, Further Geometry
*Sequence/Series, Further Vectors / OPTIONS
17 / Calculus Preview
Limits
Difference Quotients
18 / Final Review

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the National Science Foundation under Grant No. 0314898.