IndianaIndiana Pre-Calculus: Algebra Curriculum
Video lessons and practice for every Pre-Calculus Algebra topic. Aligned to Indiana Academic Standards for Math for high school students.
Indiana Pre-Calculus: Algebra Curriculum | StudyPugHelp
ID | Standard | StudyPug Topic |
|---|---|---|
CC.HSN.RN.B.3 | Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. |
CC.HSN.Q.A.1 | Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. |
CC.HSN.Q.A.2 | Define appropriate quantities for the purpose of descriptive modeling. |
CC.HSA.SSE.A.1 | Interpret expressions that represent a quantity in terms of its context. |
CC.HSA.SSE.A.2 | Use the structure of an expression to identify ways to rewrite it. |
CC.HSA.SSE.B.3 | Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. |
CC.HSA.CED.A.1 | Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. |
CC.HSA.CED.A.2 | Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. |
CC.HSA.CED.A.3 | Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. |
CC.HSA.CED.A.4 | Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. |
CC.HSA.REI.A.1 | Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. |
CC.HSA.REI.B.3 | Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. |
CC.HSA.REI.C.5 | Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. |
CC.HSA.REI.C.6 | Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. |
CC.HSA.REI.D.10 | Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). |
CC.HSA.REI.D.11 | Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. |
CC.HSA.REI.D.12 | Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. |
CC.HSF.IF.A.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). |
CC.HSF.IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. |
CC.HSF.IF.A.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. |
CC.HSF.IF.B.4 | 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. |
CC.HSF.IF.B.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. |
CC.HSF.IF.B.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. |
CC.HSF.IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. |
CC.HSF.IF.C.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. |
CC.HSF.IF.C.9 | Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). |
CC.HSF.BF.A.1 | Write a function that describes a relationship between two quantities. |
CC.HSF.BF.A.2 | Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. |
CC.HSF.BF.B.3 | Identify 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 graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. |
CC.HSF.LE.A.1 | Distinguish between situations that can be modeled with linear functions and with exponential functions. |
CC.HSF.LE.A.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). |
CC.HSG.GPE.B.7 | Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. |
CC.HSS.ID.A.1 | Represent data with plots on the real number line (dot plots, histograms, and box plots). |
CC.HSS.ID.A.2 | Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. |
CC.HSS.ID.A.3 | Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). |
CC.HSS.ID.B.5 | Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. |
CC.HSS.ID.B.6 | Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. |
Indiana Pre-Calculus: Algebra — What Students Learn
Indiana high school students in Pre-Calculus Algebra build the mathematical foundation needed for advanced coursework. The course begins with the number system, asking students to explain why the sum or product of two rational numbers is rational, and why adding a rational number to an irrational number always produces an irrational result. These foundational ideas support every algebraic skill that follows.
Expressions, Equations, and Inequalities
A large portion of Indiana Pre-Calculus Algebra focuses on working fluently with expressions and equations. Students learn to:
- Interpret expressions that represent a quantity in context
- Use the structure of an expression to rewrite it in useful ways
- Create and solve equations and inequalities in one variable, including those from linear, quadratic, rational, and exponential functions
- Rearrange formulas to highlight a quantity of interest
- Solve systems of linear equations exactly and approximately, using graphs and algebraic methods
- Graph linear inequalities and systems of linear inequalities in two variables
These skills align directly to Indiana Academic Standards for Math and prepare students for the reasoning demands of Pre-Calculus and Calculus.
Functions and Their Graphs
Understanding functions is central to Pre-Calculus Algebra. Indiana students learn the formal definition of a function, use function notation, and evaluate functions for inputs in their domain. Key topics include:
- Interpreting key features of graphs and tables — intercepts, intervals of increase or decrease, maximum and minimum values
- Calculating and interpreting the average rate of change over a specified interval
- Graphing linear, quadratic, absolute value, exponential, and logarithmic functions
- Identifying the effect of transformations such as f(x) + k, k·f(x), f(kx), and f(x + k) on a graph
- Comparing properties of two functions represented in different ways
- Recognizing sequences as functions and writing arithmetic and geometric sequences recursively and explicitly
StudyPug has video lessons for every one of these function topics, with practice problems that mirror what Indiana students see in class and on assessments.
Modeling with Mathematics
Indiana Academic Standards for Math emphasize using mathematics to model real-world situations. In Pre-Calculus Algebra, students practice choosing appropriate units, defining quantities for descriptive modeling, and creating equations in two or more variables to represent relationships. They also learn to distinguish between situations best modeled by linear functions versus exponential functions, and construct both types given a graph, table, or verbal description.
Data Analysis and Statistics
The course closes with data analysis skills that connect algebra to real-world data. Students learn to:
- Represent data with dot plots, histograms, and box plots
- Compare center and spread of data sets using mean, median, interquartile range, and standard deviation
- Interpret differences in shape, center, and spread, including the effect of outliers
- Summarize categorical data in two-way frequency tables and interpret joint, marginal, and conditional relative frequencies
- Create scatter plots for two quantitative variables and describe how the variables are related
How StudyPug Helps Indiana Pre-Calculus Algebra Students
StudyPug provides video lessons and practice problems for every topic in Indiana's Pre-Calculus Algebra course. Each lesson is broken into short, focused segments students can pause and replay. After watching, students practice with problems that build confidence step by step. Whether your child needs help with tonight's homework or wants to get ahead before an exam, StudyPug is available on any device, anytime.
All content is aligned to Indiana Academic Standards for Math, so students and parents can trust they're studying exactly what Indiana schools teach.