# 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