Precalculus

Session I: Algebra II Review

  • Review all Algebra II, Trigonometry concepts such as: graphing functions, manipulating equations, solving complex (xy) equations, systems of equations.
  • Trig functions’ concepts, graphs of parent functions (sin, cos, tan) special right triangles, unit circle values,
  • Converting between radian and degrees,
  • Properties of logs and exponential functions.

Session II: Trig functions and Identities

  • Begin trig identities. Cover all the identities of the 6 main trig functions, verify identities with equations
  • Teach how to graph all trig functions with adjustments, amplitude, period, asymptotes, ect.

Ex) Graph: 2sin(3x+ pi)

Session III: Solving Trig Functions and Identities

  • Teach solving trig functions for values of x/q using unit circle
  • Find exact values of trig functions
  • Use sum and difference and product to sum formulas to solve for exact values

Ex) cos(x+p) = ?
Ex)  sin(195°) = ?
Ex) 2sin2(x) +sqrt(3) = sinx

Session IV: PFD

  • Teach Partial Fraction Decomposition. *Needs a whole lesson due to complexity of topic.

Session V: Mid-Summer Review

  • Review Partial Fraction Decomp. with many examples, review or introduce long division of polynomials (should be review because the material should have been taught in Algebra II)
  • Review all properties and rules of Logarithmic and exponential functions and do many algebraic examples,
  • Finally, if there is time remaining, introduce the topic of Sequences, Series, and Summations.

Session VI: Sequences, Series, and Summations

  • Introduce Sequences, Series and Summations:
  • Distinguish arithmetic and geometric, provide formulas, express notation (extremely important to correctly understand and use notation)

Arithmetic: An = a1 + (n-1)d

Where An is the nth term in the sequence, a1 is the first term, n is the term to be found and d is the difference between consecutive terms

Geometric: An = a1(rn-1)

Where An is the nth term in the sequence, a1 is the first term, n is the term to be found and r is the multiple difference between consecutive terms.

Summation Notation: S1n Areads: Summation from 1 to n of the series, An

Session VII: Limits

  • Begin the concept of Limits. What a limit is, how it works, why it is useful.
  • Explain the concept of continuity, asymptotes, holes and how a limit ties in with those less abstract concepts.
  • Introduce how to evaluate a limit of a function and discuss methods for different functions, proper and improper.

Session VIII: Derivatives and Review

  • Introduce the Derivatives of functions.
  • Provide physics background, position, velocity, acceleration as a explanation of a derivative and what it does/how it works.
  • Relate to rates of change previously learned, tangent lines.
  • Explain basic rules: chain rule, product, quotient.
  • Give known derivatives of functions that have already been taught: sin, cos, tan, ex, ln(x) ect.
  • *Stress notation here as-well:
  • With time remaining, briefly review all material covered

 

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