MathsQ&A by dot point

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

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).

Solve quadratic equations by taking square roots and by completing the square, recognizing when each method applies (TN A1.A.REI.B.4).

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).

Interpret the correlation coefficient of a linear fit and distinguish correlation from causation (TN A1.S.ID.C.8, A1.S.ID.C.9).

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).

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).

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).

Apply the properties of integer and rational exponents to simplify expressions, and rewrite radicals using rational exponents (TN A1.N.Q.A, exponent properties).

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).

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).

Add, subtract, and multiply polynomials, understanding that polynomials form a system closed under these operations (TN A1.A.APR.A.1).

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).

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).

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).

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).

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).

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).