# 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) 2sin^{2}(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: A_{n }= a_{1} + (n-1)d

Where A_{n} is the n^{th} term in the sequence, a_{1} is the first term, n is the term to be found and d is the difference between consecutive terms

Geometric: A_{n} = a_{1}(r^{n-1})

Where A_{n} is the n^{th} term in the sequence, a_{1} is the first term, n is the term to be found and r is the multiple difference between consecutive terms.

Summation Notation: S_{1}^{n} A_{n }reads: Summation from 1 to n of the series, A_{n }

**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, e
^{x}, ln(x) ect. - *Stress notation here as-well:
- With time remaining, briefly review all material covered