STATE STANDARDS
Precalculus |
| NUMBER AND QUANTITY |
| The Complex Number System |
| A. Perform arithmetic
operations with complex numbers |
|
N.CN.A.3+ |
Find the conjugate of a complex number; use
conjugates to find moduli and quotients of complex numbers. |
|
B. Represent complex numbers and
their operations on the complex plane |
|
N.CN.B.4+ |
a. Represent complex numbers on the complex plane in
rectangular and polar form (including real and imaginary numbers), and
convert between rectangular and polar forms of a given complex number.
b. Determine whether rectangular or polar form is more efficient given
the context. |
|
N.CN.B.5+ |
Represent addition, subtraction, multiplication, and
conjugation of complex numbers geometrically on the complex plane; use
properties of this representation for computation. |
|
N.CN.B.6+ |
a. Calculate the distance between two points in the
complex plane.
b. Find the midpoint of the segment whose endpoints are in the complex
plane. |
| C. Use complex numbers in polynomial
identities and equations |
|
N.CN.C.8+ |
Extend polynomial identities to the complex numbers. |
|
N.CN.C.9+ |
State the Fundamental Theorem of Algebra and use it
to find roots of polynomials. |
|
Vector and Matrix Quantities |
|
A. Represent and model with
vector quantities |
|
N.VM.A.1+ |
Represent a vector analytically and geometrically |
|
N.VM.A.2+ |
Find the magnitude and direction of a given vector |
|
N.VM.A.3+ |
Solve problems using vectors analytically and
geometrically |
|
B. Perform operations on vectors |
|
N.VM.B.4+ |
Add and subtract vectors analytically and
geometrically |
|
N.VM.B.5+ |
Multiply a vector by a scalar analytically and
geometrically |
|
C. Perform operations on matrices and use matrices in
applications |
|
N.VM.C.6+ |
Use matrices to represent and model real world
situations |
|
N.VM.C.7+ |
Multiply matrices by scalars |
|
N.VM.C.8+ |
Add, subtract, and multiply matrices |
|
N.VM.C.9+ |
Understand that, unlike multiplication of numbers,
matrix multiplication for square matrices is not a commutative
operation, but still satisfies the associative and distributive
properties |
|
N.VM.C.11+ |
Use matrices to perform linear transformations in
the plane |
|
N.VM.C.12+ |
Calculate and interpret the determinant of a matrix |
| ALGEBRA |
| Arithmetic with Polynomials & Rational
Expressions |
| C. Use polynomial identities to solve
problems |
|
A.APR.C.4+ |
Prove polynomial identities and use them to describe
numerical relationships |
|
A.APR.C.5+ |
Use the Binomial Theorem for the expansion of (x +
y)n for a positive integer n |
| D. Rewrite rational expressions
|
|
A.APR.D.7+ |
Understand that rational expressions form a system
analogous to the rational numbers, closed under addition, subtraction,
multiplication, and division by a nonzero rational expression; add,
subtract, multiply, and divide rational expressions |
| Reasoning with Equations & Inequalities |
| C. Solve systems of equations |
|
A.REI.C.6+ |
b. Solve systems of linear equations in three
variables |
|
A.REI.C.8+ |
Solve a simple system consisting of a linear
equation and a quadratic equation in two variables algebraically and
graphically. For example, find the points of intersection
between the line y = –3x and the circle x2 + y2 =
3. |
|
A.REI.C.9+ |
Find the inverse of a matrix if it exists and use it
to solve systems of linear equations (using technology for matrices of
dimension 3 × 3 or greater) |
| FUNCTIONS |
| Interpreting Functions |
| C. Analyze functions using different
representations |
|
F.IF.C.7+ |
d. Graph rational functions, identifying zeros and
asymptotes when suitable factorizations are available |
| Building Functions |
| A. Build a function that models a
relationship between two quantities |
|
F.BF.A.1+ |
c. Compose functions and state resulting domain |
| B. Build new functions from existing
functions |
|
F.BF.B.3+ |
c. Determine algebraically whether or not a function
is even or odd |
|
F.BF.B.4+ |
b. Verify by composition that one function is the
inverse of another
c. Given the graph or table of an invertible function, determine
coordinates of its inverse
d. Determine an invertible function from a non-invertible function by
restricting the domain |
|
F.BF.B.5+ |
b. Use inverse relationships to solve problems
involving logarithms and exponents
c. Apply the properties of logarithms to rewrite logarithmic expressions
in equivalent forms and solve logarithmic equations |
| Trigonometric Functions |
| A. Extend the domain of trigonometric
functions using the unit circle |
|
F.TF.A.3+ |
c. Use special triangles to determine geometrically
the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the
unit circle to express the values of sine, cosines, and tangent for x, π
+ x, and 2π – x in terms of their values for x, where x is any real
number |
|
B. Model periodic phenomena
with trigonometric functions |
|
F.TF.B.6+ |
Understand that restricting a trigonometric function
to a domain on which it is always increasing or always decreasing allows
its inverse to be constructed |
|
F.TF.B.7+ |
Solve trigonometric equations: analytically with
inverse functions and graphically with technology; and interpret
solutions in terms of the context |
|
C. Prove and apply
trigonometric identities |
|
F.TF.C.9+ |
Prove the sum and difference formulas for sine,
cosine, and tangent and use them to solve problems |
| GEOMETRY |
| Similarity, Right
Triangles and Trigonometry |
|
D. Apply trigonometry to
general triangles |
|
G.SRT.D.10+ |
Prove the Law of Sines and
the Law of Cosines and apply in all cases, including the ambiguous case |
|
G.SRT.D.11+ |
Understand and apply the Law
of Sines and the Law of Cosines to find unknown measurements in right
and non-right triangles |
| Circles |
|
A. Understand and apply theorems
about circles |
|
G.C.A.3+ |
Construct the inscribed and circumscribed circles of a
triangle, and prove properties of angles for a quadrilateral inscribed
in a circle. |
| G.C.A.4+ |
Construct a tangent line from
a point outside a given circle to the circle |
| Expressing Geometric Properties with
Equations |
|
A. Translate between the
geometric description and the equation for a conic section |
|
G.GPE.A.2+ |
Explore the relationship among the parabola, focus,
and directrix and use the equation to model a real-life situation, using
technology as appropriate |
|
G.GPE.A.3+ |
a. Derive the equations of ellipses and hyperbolas
given the foci
b. Use these equations to model real life situations |
|
Geometric Measurement and Dimension |
|
A. Explain volume formulas and
use them to solve problems |
|
G.GMD.A.2+ |
Give an informal argument using Cavalieri’s
principle for the formulas for the volume of a sphere and other solid
figures |
| Statistics & Probability |
| Interpreting Categorical & Quantitative
Data |
| B. Summarize, represent, and interpret data
on two categorical and quantitative variables |
|
S.ID.B.6+ |
b. Informally assess the fit of a function by
plotting and analyzing residuals |
| Conditional Probability & the Rules of
Probability |
| B. Use the rules of probability to compute
probabilities of compound events in a uniform probability model |
|
S.CP.B.9+ |
Solve problems using permutations and combinations
to compute probabilities of compound events |
|
Using Probability to Make Decisions |
|
A. Calculate expected values and
use them to solve problems |
|
S.MD.A.1+ |
a. Define a random variable for a quantity of
interest
b. Graph a probability distribution for a discrete random variable based
on either empirical or theoretical probabilities |
|
S.MD.A.2+ |
Calculate and interpret the expected value of a
random variable |
|
B. Use probability to evaluate
outcomes of decisions |
|
S.MD.B.5+ |
Use expected values from probability distributions
to evaluate and compare the outcomes of decisions |
|
S.MD.B.6+ |
Use probabilities to make fair decisions |
|
S.MD.B.7+ |
Using probability concepts, evaluate decisions and
strategies |