Standards for Teaching and Learning
PCT.N.1: Define and conduct operations on complex numbers, in particular, addition, subtraction, multiplication, and division. Relate the system of complex numbers to the systems of real and rational numbers.
PCT.N.2: Plot complex numbers using both rectangular and polar coordinates systems. Represent complex numbers using polar coordinates, i.e., a + bi = r (cos theta + i sin theta).
PCT.P.1: Relate the number of roots of a polynomial to its degree. Solve quadratic equations with complex coefficients, including use of completing the square.
PCT.P.2: Demonstrate an understanding of the trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent). Relate the functions to their geometric definitions.
PCT.P.3: Use matrices to solve systems of linear equations. Apply to the solution of everyday problems.
PCT.P.4: Given algebraic, numeric, and/or graphical representations, recognize functions as polynomial, rational, logarithmic, or exponential.
PCT.P.5: Combine functions by composition, as well as by addition, subtraction, multiplication, and division.
PCT.P.6: Identify whether a function has an inverse and when functions are inverses of each other; explain why the graph of a function and its inverse are reflections of one another over the line y = x.
PCT.P.7: Identify maximum and minimum values of functions. Apply to the solution of problems.
PCT.P.8: Describe the translations and scale changes of a given function f(x) resulting from substitutions for the various parameters a, b, c, and d in y = a f(b (x + c/b)) + d. In particular, describe the effect of such changes on polynomial, rational, exponential, and logarithmic functions.
PCT.P.9: Derive and apply basic trigonometric identities i.e., sin²theta + cos²theta = 1, tan²theta + 1 = sec²theta and the laws of sines and cosines.
PCT.P.10: Demonstrate an understanding of the formulas for the sine and cosine of the sum or the difference of two angles. Relate the formulas to DeMoivre's theorem and use them to prove other trigonometric identities. Apply to the solution of problems.
PCT.P.11: Understand, predict, and interpret the effects of the parameters a, w, b, and c on the graph of y = asin (infinity (x - b)) + c; do the same for the cosine and tangent. Use to model periodic processes.
PCT.P.14: Approximate areas under a curve.
PCT.P.16: Identify maximum and minimum values of functions in simple situations. Apply to the solution of problems.
PCT.G.2: Use vectors to solve problems. Describe addition of vectors, multiplication of a vector by a scalar, and the dot product of two vectors, both symbolically and geometrically. Use vector methods to obtain geometric results.
PCT.G.3: Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve problems.
PCT.M.1: Describe the relationship between degree and radian measures, and use radian measure in the solution of problems, particularly problems involving angular velocity and acceleration.
PCT.M.2: Use dimensional analysis for unit conversion and to confirm that expressions and equations make sense.
PCT.D.1: Design surveys and apply random sampling techniques to avoid bias in the data collection.
PCT.D.3: Compare the results of simulations (e.g., random number tables, random functions, and area models) with predicted probabilities.
Correlation last revised: 1/20/2017