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.

Dividing Polynomials Using Synthetic Division

Polynomials and Linear Factors

Roots of a Quadratic

PCT.P.2: Demonstrate an understanding of the trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent). Relate the functions to their geometric definitions.

Cosine Function

Simplifying Trigonometric Expressions

Sine Function

Sine, Cosine, and Tangent Ratios

Sum and Difference Identities for Sine and Cosine

Tangent Function

PCT.P.3: Use matrices to solve systems of linear equations. Apply to the solution of everyday problems.

Solving Linear Systems (Matrices and Special Solutions)

PCT.P.4: Given algebraic, numeric, and/or graphical representations, recognize functions as polynomial, rational, logarithmic, or exponential.

Compound Interest

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Quadratics in Factored Form

Rational Functions

PCT.P.5: Combine functions by composition, as well as by addition, subtraction, multiplication, and division.

Addition and Subtraction of Functions

Function Machines 1 (Functions and Tables)

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.

Function Machines 3 (Functions and Problem Solving)

Logarithmic Functions

PCT.P.7: Identify maximum and minimum values of functions. Apply to the solution of problems.

Absolute Value with Linear Functions

Quadratics in Factored Form

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.

Introduction to Exponential Functions

Rational Functions

Zap It! Game

PCT.P.9: Derive and apply basic trigonometric identities i.e., sin²theta + cos²theta = 1, tan²theta + 1 = sec²theta and the laws of sines and cosines.

Sine, Cosine, and Tangent Ratios

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.

Sum and Difference Identities for Sine and Cosine

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.

Translating and Scaling Sine and Cosine Functions

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.

Absolute Value with Linear Functions

Quadratics in Factored Form

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.

Chords and Arcs

Constructing Congruent Segments and Angles

Inscribed Angles

Parallel, Intersecting, and Skew Lines

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.

Cosine Function

Sine Function

Tangent Function

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.

Polling: City

Polling: Neighborhood

PCT.D.3: Compare the results of simulations (e.g., random number tables, random functions, and area models) with predicted probabilities.

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.