Tennessee · TDOESyllabus
Maths syllabus, dot point by dot point
Every dot point in the Tennessee Mathssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Equations and Inequalities
Module overview →- How do you create an equation or inequality from a real-world description, and how do you interpret its solution in context?Create equations and inequalities in one or more variables from a context and use them to solve problems, interpreting solutions as viable or nonviable (TN A1.A.CED.A.1, A.2, A.3).10 min answer →
- How do you rearrange a formula to isolate a chosen variable, treating the other letters as constants?Rearrange formulas and literal equations to isolate a quantity of interest, using the same reasoning as solving a numerical equation (TN A1.A.CED.A.4).9 min answer →
- How do you solve simple rational and radical equations, and why can these produce extraneous solutions?Solve simple rational and radical equations in one variable and explain how extraneous solutions can arise, checking every solution (TN A1.A.REI.A.2).10 min answer →
- How do you solve a linear equation in one variable, and how does each step follow from the properties of equality?Solve linear equations in one variable, including those with variables on both sides and with coefficients represented by letters, justifying each step (TN A1.A.REI.A.1, A1.A.REI.B.3).10 min answer →
- How do you solve a linear inequality in one variable, and why does multiplying or dividing by a negative flip the inequality?Solve linear inequalities in one variable and represent the solution on a number line and in interval form, reversing the inequality when multiplying or dividing by a negative (TN A1.A.REI.B.3).10 min answer →
Functions
Module overview →- How do you calculate and interpret the average rate of change of a function over an interval?Calculate and interpret the average rate of change of a function over a specified interval from a graph or table (TN A1.F.IF.C.6).9 min answer →
- How do you compare linear, quadratic, and exponential functions across tables, graphs, and equations, and recognize which models a situation?Compare properties of linear, quadratic, and exponential functions represented in different ways, and identify the family that models a situation (TN A1.F.IF.D.9, A1.F.LE.A.3).10 min answer →
- How do you model and graph exponential growth and decay, and how do you tell an exponential situation from a linear one?Construct and graph exponential functions, distinguish exponential from linear growth, and interpret growth and decay models (TN A1.F.IF.D.7e, A1.F.LE.A.1, A1.F.LE.A.2).11 min answer →
- What makes a relation a function, and how do you use function notation, domain, and range?Understand that a function assigns each input exactly one output, use function notation to evaluate functions, and identify domain and range (TN A1.F.IF.A.1, A1.F.IF.A.2, A1.F.IF.C.5).10 min answer →
- How do you read and interpret the key features of a function's graph, such as intercepts, intervals of increase or decrease, and maximums or minimums?Interpret key features of graphs and tables (intercepts, intervals of increase and decrease, maxima and minima, end behavior) in terms of the quantities they model (TN A1.F.IF.C.4).10 min answer →
- How do you write arithmetic and geometric sequences explicitly and recursively, and how are they related to linear and exponential functions?Write arithmetic and geometric sequences both recursively and explicitly, and recognize sequences as functions on the integers (TN A1.F.BF.A.2, A1.F.IF.B.3).10 min answer →
- How do you write the equation of a line from a slope and a point, two points, a graph, or a context?Write linear functions and equations of lines using slope-intercept and point-slope form, from a graph, two points, or a real-world description (TN A1.F.LE.A.2, A1.A.CED.A.2).11 min answer →
Quadratic Equations
Module overview →- How do you graph a quadratic function and identify its vertex, axis of symmetry, intercepts, and direction of opening?Graph quadratic functions and show key features including the vertex, axis of symmetry, intercepts, maximum or minimum, and direction of opening (TN A1.F.IF.D.7a).11 min answer →
- How do you use a quadratic model to answer real-world questions about maximum height, landing time, or area?Model real-world situations with quadratic equations and interpret the solutions, including projectile motion and area problems (TN A1.A.REI.B.4, A1.A.CED.A.1).11 min answer →
- How do you use the quadratic formula to solve any quadratic, and what does the discriminant tell you about the number of real solutions?Solve quadratic equations by applying the quadratic formula, and use the discriminant to determine the number of real solutions (TN A1.A.REI.B.4).11 min answer →
- How do you solve a quadratic equation by factoring, and why must one side be zero first?Solve quadratic equations in one variable by factoring, using the zero-product property after writing the equation equal to zero (TN A1.A.REI.B.4).10 min answer →
- How do you solve a quadratic by taking square roots or by completing the square, and when is each the right method?Solve quadratic equations by taking square roots and by completing the square, recognizing when each method applies (TN A1.A.REI.B.4).11 min answer →
Statistics and Probability
Module overview →- How do you compare the center and spread of two data sets, and choose statistics appropriate to the shape?Use statistics appropriate to the shape of a distribution to compare center (mean, median) and spread (range, IQR, standard deviation), and interpret differences in context (TN A1.S.ID.A.2, A1.S.ID.A.3).10 min answer →
- What does the correlation coefficient tell you about a linear relationship, and why does correlation not imply causation?Interpret the correlation coefficient of a linear fit and distinguish correlation from causation (TN A1.S.ID.C.8, A1.S.ID.C.9).9 min answer →
- How do you represent a single-variable data set with dot plots, histograms, and box plots, and read each display?Represent data with plots on the real number line, including dot plots, histograms, and box plots, and read the five-number summary from a box plot (TN A1.S.ID.A.1).10 min answer →
- How do you fit a line to bivariate data on a scatter plot, and interpret its slope and intercept in context?Represent two quantitative variables on a scatter plot, describe the relationship, fit a linear model, and interpret its slope and intercept in context (TN A1.S.ID.C.6, A1.S.ID.C.7).10 min answer →
- How do you summarize two categorical variables in a two-way frequency table, and compute joint, marginal, and conditional relative frequencies?Summarize categorical data for two categories in two-way frequency tables, and interpret joint, marginal, and conditional relative frequencies (TN A1.S.ID.C.5).9 min answer →
Structure and Operations
Module overview →- How do you simplify expressions using the properties of exponents, including negative and rational exponents, and how do rational exponents relate to radicals?Apply the properties of integer and rational exponents to simplify expressions, and rewrite radicals using rational exponents (TN A1.N.Q.A, exponent properties).10 min answer →
- How do you factor a polynomial, and how do its factors reveal the zeros of the related function?Factor polynomials using common factors and standard patterns, and identify the zeros of a polynomial from its factored form (TN A1.A.SSE.A.2, A1.A.APR.A.3).11 min answer →
- How do you read an algebraic expression in terms of its context, identifying its terms, factors, and coefficients and what each part means?Interpret expressions that represent a quantity in terms of its context, identifying terms, factors, and coefficients, and view complicated expressions by treating parts as a single entity (TN A1.A.SSE.A.1).9 min answer →
- How do you add, subtract, and multiply polynomials, and why is the result always another polynomial?Add, subtract, and multiply polynomials, understanding that polynomials form a system closed under these operations (TN A1.A.APR.A.1).10 min answer →
- How do you use the structure of an expression to rewrite it in an equivalent, more useful form?Use the structure of an expression to identify ways to rewrite it, recognizing forms such as a difference of squares or a common factor (TN A1.A.SSE.A.2).9 min answer →
- How do you use units to guide and check the solution of a multistep problem, and choose an appropriate level of accuracy?Use units to understand problems and guide solutions, choose and interpret units and scales in graphs, define appropriate quantities for modeling, and choose a level of accuracy appropriate to the measurement (TN A1.N.Q.A.1-3).9 min answer →
Systems of Equations and Inequalities
Module overview →- How do you graph a linear inequality in two variables, and how do you find the solution region of a system of inequalities?Graph linear inequalities in two variables on the coordinate plane and find the solution set of a system of linear inequalities as the overlap of the half-planes (TN A1.A.REI.D.8, A1.A.REI.D.9).10 min answer →
- How do you solve a system made of a linear equation and a quadratic equation, both algebraically and graphically?Solve a simple system consisting of a linear equation and a quadratic equation in two variables, algebraically and graphically (TN A1.A.REI.C.7).10 min answer →
- How do you model a real-world situation with a system of equations or inequalities, and interpret the solution as viable constraints?Represent constraints by systems of equations and inequalities and interpret solutions as viable or nonviable options in a modeling context (TN A1.A.CED.A.3).10 min answer →
- How do you solve a system of two linear equations by graphing, substitution, and elimination, and what does the solution represent?Solve systems of two linear equations in two variables exactly and approximately by graphing, substitution, and elimination, and justify the elimination method (TN A1.A.REI.C.5, A1.A.REI.C.6).11 min answer →