Pre-Calculus (Khan v.11.26.2016)
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Pre-Calculus Unit 1: Trigonometric Equations and Identities
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Pre-Calculus Unit 2: Conic Sections
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Pre-Calculus Unit 3: Vectors
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Pre-Calculus Unit 4: Matrices
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Pre-Calculus Unit 5: Imaginary and Complex Numbers
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Pre-Calculus Unit 6: Parametric Equations and Polar Coordinates
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Pre-Calculus Unit 7: Probability and Combinatorics
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Pre-Calculus Unit 8: Sequences, Series, and Induction
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Pre-Calculus Unit 9: Partial Fraction Expansion
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Pre-Calculus Unit 10: Limits
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Pre-Calculus (Khan v.11.26.2016)
Evaluate inverse
trigonometric functions
Use angle addition formulas
to find trig values
Student__________________________________________
Unit 1: Trigonometric equations and identities
Solve basic sinusoidal
equations
Solve advanced sinusoidal
equations
Solve sinusoidal modeling
functions
Practice using the trig angle
addition identities
Graph a circle from its
standard equations
Find the center and radii of
an ellipse from its equation
Write the equation of an
ellipse from its foci and other
features
Write the equation of a circle
Understanding scalar
multiplication
Direction angles
Unit 2: Conic Sections
Graph a circle according to its
features
Find the features of a circle
from its expanded equation
Find the foci of an ellipse
from its graph
Find the features of a circle
from its graph
Graph a circle form its
expanded equation
Find the foci of an ellipse
form its radii
Find the features of a circle
form its standard equation
Center and radii of an ellipse
and its graph
Find the foci of an ellipse
from its equation
Vertices and direction of a
hyperbola
Find the foci of a hyperbola
from its equation
Write the equation of a
hyperbola form its features
Write the equation of an
ellipse from its graph
Write the equation of a
parabola from its focus and
directrix
Unit 3: Vectors
Equivalent vectors
Components of vectors
Magnitude of vectors
Scalar multiplication
Vector addition and
subtraction
Converting from magnitude
and direction form to
component form
Graphically adding and
subtracting vectors
Adding vectors in magnitude
and direction (answer in
component form)
Combined vector operations
Unit vectors
Adding vectors in magnitude
and direction form
Vector word problems
Unit 4: Matrices
Understand Matrix
dimensions
Understand matrix
coordinates
Solve matrix equations with
addition and subtraction
Transform polygons with
matrices
Find the inverse of a 2x2
matrix
Multiply matrices by scalars
Analyze matrices as
transformations of the plane
Represent systems of
equations with matrix
equations
Represent systems of
equations with augmented
matrices
Solve matrix equations with
multiplication by a scalar
Find the determinant of a 2x2
matrix
Perform elementary matrix
row operations
Add and subtract matrices
Multiply matrices by matrices
Transform vectors using
matrices
Determine invertibility of 2x2
matrices
Determine whether matrices
are inverses
Pre-Calculus (Khan v.11.26.2016)
Simplify powers of the
imaginary unit
Add and subtract complex
numbers
Divide complex numbers
Find the midpoint of two
complex numbers
Student__________________________________________
Unit 5: Imaginary and Complex Numbers
Simplify square roots of
negative numbers
Represent addition and
subtraction of complex
numbers graphically
Find the absolute value of
complex numbers
Real and imaginary parts of
complex numbers
Multiply complex numbers by
real or imaginary numbers
Classify complex numbers
Find the angle of complex
numbers
Complex number polar form
intuition
Convert between rectangular
and polar forms of complex
numbers
Find complex numbers
according to absolute value
and angle
Multiply and divide complex
numbers in polar form
Multiply complex numbers
Plot complex numbers on the
complex plane
Find conjugates of complex
numbers
Find the distance between
two complex numbers
Powers of complex numbers
Unit 6: Parametric Equations and Polar Coordinates
Unit 7: Probability and Combinatorics
Simple probability
Probabilities of compound
events
Independent probability
Dependent probability
Permutations
Combinations
Permutations and
combinations
Probability with
permutations and
combinations
Find recursive formulas for
arithmetic sequences
Find any term of an
arithmetic sequence, given
the formula of the sequence
Find the next term of an
arithmetic sequence, given
the first few terms
Find explicit formulas for
arithmetic sequences
Evaluating basic sigma
notation
Evaluating finite arithmetic
series
Find the next term of a
geometric sequence, given
the first few terms
Find any term of a geometric
sequence, given the formula
of the sequence
Find explicit formulas for
geometric sequences
Find recursive formulas for
geometric sequences
Model real-world situations
with arithmetic and
geometric sequences
Challenge: Sigma notation
properties
Evaluating finite geometric
series
Finite geometric series word
problems
Writing finite arithmetic
series in sigma notation
Writing finite geometric
series in sigma notation
Is this infinite geometric
series convergent or
divergent
Evaluating infinite geometric
series
Unit 8: Sequences, Series, and Induction
Pre-Calculus (Khan v.11.26.2016)
Student__________________________________________
Unit 9: Partial Fraction Expansion
Partial Fraction Expansion
Unit 10: Limits
One-sided limits from graphs
Two-sided limits from graphs
Finding limits numerically
Two-sided limits using
algebra
Two-sided limits using
advanced algebra