I will operate under the assumption that you know all of ...



Instructors will operate under the assumption that you know all of the following concepts. If you do not know them, it is your responsibility to review them and get help on anything that gives you trouble.

← Absolute value

← How to solve multi-step equations

← Properties: Associative, Commutative, Distributive, Reflexive, Symmetric, Transitive

← How to add, subtract, multiply, and divide fractions

← Properties of, and how to simplify radicals

← Properties of exponents

← Rational exponents

← How to multiply binomials and trinomials

← How to factor binomials

← How to find roots (zeros) of a function

← How to graph lines

← How to write linear equations

← Horizontal and vertical lines

← Parallel and perpendicular lines

← How to find the vertex of a quadratic function

← How to graph quadratics

← How to solve a system of equations

← How to graph inequalities

← How to solve inequalities

← Basic trigonometric functions and their relationships to right triangles

← Distance

← Midpoint

← Domain and Range

← How to add/subtract polynomials

← Coefficient

← Constant

← Term

← Degree of a polynomial

← How to use your graphing calculator

← Percents

← Perimeter

← Area

← Y-intercept

←

The following are the concepts that you will learn in preparation for Calculus. The most important concepts and skills for determining whether or not you are ready for calculus are a) trig functions, b) trig identities, c) factoring, d) ability to identify what a graph looks like given its equation, and e) your ability to apply your knowledge to new situations/problems.

Unit 1:

← Functions vs Relations

← Function notation

← Evaluating functions

← Domain/Range

← Independent vs Dependent variables

← Increasing vs decreasing functions

← Even vs odd functions

← Key point

← Local Max/Min values

Unit 2:

← 2.1

← Zeros, roots, x-intercepts

← 2.2

← Standard Form of a quadratic

← Completing the square

← Quadratic formula

← Solving by factoring

← Discriminant

← 2.3

← Solving absolute value eqs

← Solving radical equations

← Extraneous solutions

← Solving inequalities

← 2.4

← +, -, (, ( functions

← Composite functions

← 2.5

← Parametric functions

← 2.6

← Transformations

← Reflections

← 2.7

← Inverses

Unit 3:

← 3.1

← Polynomial functions

← Graphing functions of degree 2 or higher

← Introduction to derivatives

← Transformations

← 3.2

← Max/min points

← Limits [pic]

← Finding zeros

← 3.3

← Factors and long division

← Synthetic division

← Remainder theorem

← Factor theorem

← 3.4

← Descartes rule of signs

← Upper and lower bounds

← Rational root theorem

← 3.5

← i

← +, -, (, ( complex numbers

← Conjugates

← Graphing complex numbers

← 3.6

← Fundamental Theorem of Algebra

← Using conjugates in factoring

← Finding all roots (zeros)

← Factoring completely

Unit 4:

← 4.1

← Base

← Exponent

← e

← Power functions

← Exponential functions

← Graphing exponential and power functions

← 4.2

← log vs ln

← Log graphs

← How to know when to use e

← 4.3, 4.4, and 4.5

← Solving exponential and logarithmic functions

← Properties of exponents

← Properties of logs

← Logistic growth functions

← Applying exponential and logarithmic functions

Unit 5:

← 5.1

← Rational functions

← Vertical asymptotes

← Horizontal asymptotes

← Limits [pic]

← 5.2

← Graphing rational functions where:

o Numerator smaller degree than denominator

o Same degree numerator and denominator

← Transformations

← 5.3

← Graphing rational functions where numerator is higher degree than denominator

← Slant asymptotes

← Intermediate behavior

o [pic]

o [pic]

← Roots

← Y-intercepts

← 5.4

← Solving rational equations

← Finding common denominator

← Factoring

← Extraneous solutions (can’t divide by zero!)

← Solving rational inequalities

← Finding intervals to test

← 5.5

← Partial fraction decomposition

← Factoring

← Writing system and solving systems of eqs.

Unit 6:

← 6.1

← Angles

← Degree measure

← Radians

← Arc length

← Special angles

← Complements

← Supplements

← Bearing vs Heading

← Angular and linear speeds

← 6.2

← Right triangle trig

← Sin, cos, tan, sec, csc, cot

← Trig identities

← Solving right triangles

← 6.3

← Memorize the 6 trig functions for the special angles in radians and degrees

← Unit circle and trig

← Reference angles

← Angles and quadrants

← 6.4

← Graphing sine and cosine

← Domain/range

← Transformations

← Odd/even functions

← Period

← Amplitude

← Periodic functions

← Shifts

← Axis of wave (midline)

← 6.5

← Graphs of the other four trig functions

← Domain/range

← Asymptotes

← Even/odd

← Period

← 6.6

← Graphing sums and differences of sinusoids

← Damped functions

← Oscillating springs

← 6.7

← Inverse trig functions

← Domain (limited)/Range

← Graphing

← Using right triangles to find exact values

← 6.8

← Applications of trig functions

← Harmonic motion

Unit 7:

← 7.1

← Fundamental trig identities

← Simplifying trig expressions

← Factoring trig expressions

← 7.2

← Verifying trig identities

← Manipulating equations

← Things to look for:

o Identities already in the problem

o Things to factor

o Get common denominator

o If all else fails, change everything to sines and cosines

← 7.3

← Solving trig equations

← Recognizing quadratics

← Never divide by a trig function to solve!

← Determining the number of possible solutions

← Finding all solutions

← Factoring

← Extraneous solutions

← 7.4 and 7.5

← Sum and difference identities

← Proving the identities

← Double angle identities

← Half-angle identities

← Derivatives of trig functions

Unit 8:

← 8.1

← Area of triangles using trig

← Solving triangles

← Law of Sines

← When there are 0, 1, or 2 solutions

← Proof

← 8.2

← Law of Cosines

← Solving triangles

← Proof

← 8.3

← Vectors

← Initial and terminal points

← Component form

← Vector operations

← Direction

← Magnitude

← Standard position

← Scalar

← Direction angle

← Parallel and orthogonal vectors

← 8.4 and 8.5

← Trig form of complex numbers

← Absolute value of a complex number (Magnitude)

← Products and quotients of complex numbers

← DeMoivre’s theorem

← Roots and powers of complex numbers

← Unit circle

Unit 9 and P8:

← Writing equations of circles

← Ellipses

← Major and minor axes

← Focus/foci

← Hyperbolas

o Asymptotes

o Foci

o Vertices

Unit 11:

← 11.1 and 11.2

← Finite and infinite sequences

← Arithmetic sequences

← Geometric sequences

← Recursive form

← Closed form

← Series

← Partial sum

← Infinite sum

← Common difference

← Common ratio

← Nth term

← Summation notation

← 11.3

← Mathematical Induction

← 11.5

← Fundamental counting principle

← Combinations

← Permutations

← 11.6

← Probability

← Event

← Mutually exclusive

← Complement of an event

← Independent events

Unit 10:

← Solving systems of equations algebraically

← Solving systems using matrices

Additional topics:

← Applications of derivatives

← Anti-derivatives

← Finding areas under curves using [pic]

Italic = Time permitting Bold = Not in book

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