# High School Pre-Calculus Course

**Time4Learning offers an online, interactive high school math curriculum that correlates to state standards. **It can be used as a primary homeschool curriculum, a supplement to your current curriculum and as an afterschool or summer skill building program. At the high school level, Time4Learning is organized by courses rather than grade levels, so parents have the option of choosing any four as part of membership.

**The pre-calculus curriculum is one of five math courses offered at the high school level. **Pre-calculus is taught using practical, real-life math problems delivered by a combination of multimedia lessons, instructional videos, printable worksheets, quizzes, tests and both online and offline projects.

**This page includes information about the material covered in the high school pre-calculus course.**

### Chapter 1 – Functions and Graphs

**The materials in this chapter introduce and cover Functions and Graphs. **It is organized into sections that teach, reinforce and test students on the properties of functions, limits and continuity, inverse functions, and piecewise functions.

**In this chapter, students will learn how to:**

- Transform parent functions by using vertical and horizontal translations, stretches, and compressions.
- Identify the domain and range of a function from a graph, equation, or a table and use line and point symmetry to determine whether a function is even or odd.
- Use graphs and function rules to find limits of functions and determine whether they are continuous.
- Analyze and graph inverse functions using the composition and the difference quotient. They will also be asked to find the inverse of a function from a table, graph, or equation, and explore the relationship between functions and their inverses by using composition.
- Analyze and graph piecewise functions, including greatest integer functions.

### Chapter 2 – Lines and Rates of Change

**The materials in this chapter introduce and cover the Lines and Rates of Change. **It is organized into sections that teach, reinforce and test students on how to analyze and graph linear functions, and understand rates of change.

**In this chapter, students will learn how to:**

- Find the slope of a line from two points, a graph, an equation, or a table. They will identify the y-intercept and find the equation of and graph linear functions.
- Find the slope as a rate of change, estimate the slope of a curve using secant and tangent lines, and the difference quotient.

### Chapter 3 – Sequences and Series

**The materials in this chapter introduce and cover Sequences and Series. **It is organized into sections that teach, reinforce and test students on the concepts of sequences, series, and proofs by induction.

**In this chapter, students will learn how to:**

- Define, notate, analyze, apply, and prove the formulas for both an arithmetic and geometric sequence and series. They will also be asked to apply those sequences and series to situations, including Riemann sums.
- Determine whether sequences are divergent or convergent, find the limit of convergent sequences and convergent infinite geometric series.
- Use mathematical induction to prove theorems and make proofs.

### Chapter 4 – Polynomial & Rational Functions

**The materials in this chapter introduce and cover Polynomial & Rational Functions. **It is organized into sections that teach, reinforce and test students on analyzing and graphing polynomial and rational functions.

**In this chapter, students will learn how to:**

- Find the x – and y – intercepts of polynomial functions. They will also learn to evaluate, find the roots, and describe the behavior of polynomial functions using synthetic division and theorems such as the Remainder Theorem.
- Estimate and compute maxima and minima by using graphical and algebraic methods. They will also learn to use roots, maxima and minima, and end behavior to graph polynomial functions.
- Students will use the Binomial Theorem to expand powers of binomials.
- Find vertical, horizontal, and slant asymptotes of rational functions. They will also use roots, asymptotes, maxima and minima, and end behavior to graph rational functions.

### Chapter 5 – Exponential & Logarithmic Functions

**The materials in this chapter introduce and cover Exponential & Logarithmic Functions. **It is organized into sections that teach, reinforce and test students on graphing exponential and logarithmic functions, including functions with base e.

**In this chapter, students will learn how to:**

- Analyze and graph exponential functions, including models of growth and decay, logarithmic functions, and exponential and logarithmic functions. They will also apply and use the properties of logarithms to solve exponential equations, logarithmic equations, and inequalities.
- Students will analyze, graph, and apply exponential functions and equations with base e and natural logarithmic functions..

### Chapter 6 – Analytic Geometry

**The materials in this chapter introduce and cover Analytic Geometry. **It is organized into sections that teach, reinforce and test students on how to analyze, graph, and apply conic sections and functions in polar and parametric forms.

**In this chapter, students will learn how to:**

- Graph parabolas, circles, ellipses, and hyperbolas as conic sections, identify features of the graphs, and write the equations given a graph. They will also derive the equation of a hyperbola and an ellipse given the foci and a vertex, or the center, a focus, and a vertex.
- Graph functions in polar coordinates, translate between rectangular and polar coordinates, and use De Moivre’s Theorem.
- Graph functions in parametric form, translate between rectangular and parametric equations, and solve application problems by using parametric equations.

### Chapter 7 – Linear Algebra and Matrices

**The materials in this chapter introduce and cover Linear Algebra and Matrices. **It is organized into sections that teach, reinforce and test students on how to perform matrix operations, find inverse matrices and determinants, and solve systems of equations by using matrix methods such as the Gauss- Jordan Method, inverse matrices, and Cramer’s Rule.

**In this chapter, students will learn how to:**

- Perform the operations of addition, subtraction, and scalar multiplication on matrices. They will also define the inverse of a matrix and find inverses of 2 x 2 matrices.
- Use geometric and algebraic methods such as matrix methods, including the Gauss- Jordan Method, inverse matrices, and Cramer’s Rule to solve systems of equations. They will interpret 2 x 2 and 3 x 3 systems of equations geometrically, and represent them using matrices that include dependent, independent, and inconsistent systems.

### Chapter 8 – Probability and Statistics

**The materials in this chapter introduce and cover Probability and Statistics. **It is organized into sections that teach, reinforce and test students on how to determine probability distributions, find linear, polynomial, exponential, and logarithmic graphs of best fit using regression equations, and analyze frequency distributions.

**In this chapter, students will learn how to:**

- Define, determine probability, and find the expected values of random variables by using probability density functions.
- Create and use scatter plots to solve regression equations and find linear, polynomial, exponential, and logarithmic graphs of best fit.
- Students will create histograms and identify shapes of common frequency distributions to analyze normal and binomial distributions. They will also use the properties of normal curves, and z -scores to find areas under normal curves.