ADVANCED MATH
“I Can…” Statements
Complex Numbers
I can identify and simplify complex numbers.
I can graph complex numbers in rectangular form.
I can convert a complex number to a polar coordinate.
I can perform mathematical operations using complex numbers.
Inverse Functions
I can identify and define a function.
I can write an equation for the inverse of a function.
I can graph a function and its inverse.
I can prove a function’s inverse using composite functions.
I can compose two functions to create a new one.
I can solve real-world problems involving inverses and compositions of functions.
Rational Functions
I can multiply and divide rational functions.
I can add and subtract rational functions.
I can graph rational functions, identifying zeros, asymptotes, discontinuities and end behavior.
I can solve rational equations, identifying extraneous solutions.
I can solve real-world variation and inverse variation problems.
Conic Sections
I can identify a conic section from the quadratic relation.
I can graph a conic section from the quadratic relation.
Sequences
I can generate missing terms in a sequence.
I can calculate the arithmetic or geometric mean of a sequence.
I can calculate the value of a specific term in a sequence.
I can calculate the term number of a given value in a sequence.
I can calculate the partial sum of sequence.
I can expand a binomial using Pascal’s Triangle.
I can solve real-world problems involving sequences.
Unit Circle/Trig
I can find a reference angle and use it to find all six trig ratios.
I can convert between radians and degrees.
I can convert between decimal degrees and degrees, minutes, seconds.
I can find the angle for given ratios using special triangles.
I can sketch graphs all six trig functions.
I can perform transformations on sine and cosine graphs.
I can generate an equation from a transformed sine or cosine graph.
I can solve real-world problems involving trig functions.
Trig Identities
I can prove trig identities.
I can identify even and odd trig functions.
I can calculate half and double angles.
I can solve trig equations using the trig identities.
Triangles and Vectors
I can solve real-world, right triangle problems using trig and inverse trig functions.
I can solve oblique triangle problems using Law of Cosines and Law of Sines.
I can derive the formula for the area of a triangle and evaluate area problems.
I can solve area problems using Hero’s formula.
I can calculate all possible values for the missing side and angles of a SAS triangle.
I can represent vector qualities using directed line segments.
I can add and subtract vectors geometrically.
I can add and subtract vectors in component form.
I can multiply vectors geometrically.
I can multiply vectors in component form.
I can real-world problems involving bearing and velocity using vectors.
Probability
I can calculate the number of outcomes for an event.
I can calculate probabilities using permutations and combinations.
I can determine if an event is mutually exclusive or not and calculate the probability for these events.
I can determine if an event is dependent or independent and calculate the probability for these events.
I can calculate probabilities for “at least” problems.
I can calculate conditional probabilities from a two way table.
I can calculate and graph the probability of a binomial event.
I can solve real-world problems involving probability.
Data Analysis
I can display data in a variety of forms.
I can calculate the measures of central tendency.
I can describe the properties of a normal curve.
I can summarize and interpret data from a two way table.
I can data in a scatterplot and find the line of best fit.
I can generate the equation for the line of best fit.
I can explain the difference between correlation and causation.
I can estimate a population mean from a survey.
I can analyze, evaluate, and compare data from multiple surveys.
Matrices
I can add and subtract matrices.
I can multiply a matrix by a scalar.
I can multiply a matrix by another matrix.
I can solve problems involving matrix multiplication.
I can represent directed networks with matrices.
I can calculate the determinant of a matrix.
I can create the inverse of a matrix.
I can solve systems of equations using inverse matrices.