Posted: Tue, 07/03/2018 - 2:11pm Updated: Thu, 01/31/2019 - 8:32am

This Teacher Resource Guide has been developed to provide supporting materials to help educators successfully implement the Indiana Academic Standards for Pre-Calculus. These resources are provided to help you in your work to ensure all students meet the rigorous learning expectations set by the Indiana Academic Standards. Use of these resources are optional; teachers should decide which resources will work best in their classroom for their students.

The resources on this webpage are for illustrative purposes only, to promote a base of clarity and common understanding. Each item illustrates a standard but please note that the resources are not intended to limit interpretation or classroom applications of the standards.

The links compiled and posted on this webpage have been provided by classroom teachers, the Department of Education, and other sources. The IDOE has not attempted to evaluate any posted materials. They are offered as samples for your reference only and are not intended to represent the best or only approach to any particular issue. The IDOE does not control or guarantee the accuracy, relevance, timeliness, or completeness of information contained on a linked website; does not endorse the views expressed or services offered by the sponsor of a linked website; and cannot authorize the use of copyrighted materials contained in linked websites. Users must request such authorization from the sponsor of the linked website.

POLAR COORDINATES AND COMPLEX NUMBERS

Activities, Examples, or Resources

PC.PCN.1: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

Complex Distance

PC.PCN.2: Understand and use complex numbers, including real and imaginary numbers, on the complex plane in rectangular and polar form, and explain why the rectangular and polar forms of a given complex number represent the same number.

PC.PCN.3: Understand and use addition, subtraction, multiplication, and conjugation of complex numbers, including real and imaginary numbers, on the complex plane in rectangular and polar form.

PC.PCN.4: State, prove, and use DeMoivre’s Theorem.

FUNCTIONS

Activities, Examples, or Resources

PC.F.1: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

PC.F.2: Find linear models by using median fit and least squares regression methods.  Decide which among several linear models gives a better fit.  Interpret the slope and intercept in terms of the original context.

PC.F.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

PC.F.4: Determine if a graph or table has an inverse, and justify if the inverse is a function, relation, or neither.  Identify the values of an inverse function/relation from a graph or a table, given that the function has an inverse.   Derive the inverse equation from the values of the inverse.

PC.F.5: Produce an invertible function from a non-invertible function by restricting the domain.

PC.F.6: Describe the effect on the graph of replacing f(x) by f(x) + k, k f(x),f(kx), and f(x + k) for specific values of k (both positive and negative).  Find the value of k given the graph f(x) and the graph of f(x) + k, k f(x), f(kx), or f(x + k).  Experiment with cases and illustrate an explanation of the effects on the graph using technology.  Recognize even and odd functions from their graphs and algebraic expressions.

PC.F.7: Decide if a function is continuous at a point.  Find the types of discontinuities of a function and relate them to finding limits of a function.  Use the concept of limits to describe discontinuity and end-behavior of the function.

PC.F.8: Define arithmetic and geometric sequences recursively.  Use a variety of recursion equations to describe a function. Model and solve word problems involving applications of sequences and series, interpret the solutions and determine whether the solutions are reasonable.

PC.F.9: Use iteration and recursion as tools to represent, analyze, and solve problems involving sequential change.

PC.F.10: Describe the concept of the limit of a sequence and a limit of a function. Decide whether simple sequences converge or diverge. Recognize an infinite series as the limit of a sequence of partial sums.

QUADRATIC, POLYNOMIAL, AND RATIONAL EQUATIONS AND FUNCTIONS

Activities, Examples, or Resources

PC.QPR.1: Use the method of completing the square to transform any quadratic equation into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form.

PC.QPR.2: Graph rational functions with and without technology.  Identify and describe features such as intercepts, domain and range, and asymptotic and end behavior.

PC.QPR.3: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

PC.QPR.4: Understand the Fundamental Theorem of Algebra.  Find a polynomial function of lowest degree with real coefficients when given its roots.

EXPONENTIAL AND LOGARITHMIC FUNCTIONS AND EQUATIONS

Activities, Examples, or Resources

PC.EL.1: Use the definition of logarithms to convert logarithms from one base to another and prove simple laws of logarithms.

PC.EL.2: Use the laws of logarithms to simplify logarithmic expressions and find their approximate values.

PC.EL.3: Graph and solve real-world and other mathematical problems that can be modeled using exponential and logarithmic equations and inequalities; interpret the solution and determine whether it is reasonable.

PC.EL.4: Use technology to find a quadratic, exponential, logarithmic, or power function that models a relationship for a bivariate data set to make predictions; compute (using technology) and interpret the correlation coefficient.

Regressions

PARAMETRIC EQUATIONS