MathsQ&A by dot point

Compute and interpret measures of center (mean, median) and spread (range, IQR, standard deviation), and compare two distributions using center, spread, and shape (A.DSR, Data and Statistical Reasoning).

Interpret the correlation coefficient, distinguish correlation from causation, and use residuals and a residual plot to judge how well a linear model fits (A.DSR, Data and Statistical Reasoning).

Represent one-variable quantitative data with dot plots, histograms, and box plots, and describe the shape of a distribution (A.DSR, Data and Statistical Reasoning).

Fit a line of best fit (linear regression) to two-variable data, interpret the slope and y-intercept in context, and use the line to make predictions (A.DSR, Data and Statistical Reasoning).

Represent two-variable quantitative data with scatterplots and describe the association by its form, direction, strength, and any outliers (A.DSR, Data and Statistical Reasoning).

Find the distance between two points using the distance formula (from the Pythagorean theorem) and the midpoint of a segment using the midpoint formula (A.GSR, Geometric and Spatial Reasoning).

Apply the mathematical modeling process: define variables, build a model, solve, interpret, and check the reasonableness of the result in context (A.MM, Mathematical Modeling).

Find the perimeter and area of polygons in the coordinate plane using the distance formula and area formulas, and apply these to modeling problems (A.GSR and A.MM, Geometric and Spatial Reasoning and Modeling).

Interpret slope as a rate of change and as a geometric measure of steepness, and use the slope relationships for parallel (equal slopes) and perpendicular (negative reciprocal slopes) lines (A.GSR, Geometric and Spatial Reasoning).

Construct and interpret arithmetic sequences with explicit and recursive rules, and connect them to linear functions whose domain is the integers (A.FGR, Functional and Graphical Reasoning).

Distinguish linear from exponential functions using constant difference versus constant ratio, and recognize that a quantity growing by equal factors over equal intervals is exponential (A.FGR, Functional and Graphical Reasoning).

Construct and interpret exponential functions, including growth and decay models, and identify the initial value and the growth or decay factor from an equation or context (A.FGR, Functional and Graphical Reasoning).

Determine whether a relation is a function, use function notation to evaluate and interpret functions, and identify domain and range from graphs and tables (A.FGR, Functional and Graphical Reasoning).

Construct and interpret geometric sequences with explicit and recursive rules, and connect them to exponential functions whose domain is the integers (A.FGR, Functional and Graphical Reasoning).

Identify linear functions by their constant rate of change, compute average rate of change from tables and graphs, and interpret slope and intercept in context (A.FGR, Functional and Graphical Reasoning).

Graph linear equations in two variables and identify key features (slope, x-intercept, y-intercept) from slope-intercept, point-slope, and standard form (A.PAR, Patterning and Algebraic Reasoning).

Graph linear inequalities in two variables using a boundary line and shading, and find the solution region of a system of linear inequalities (A.PAR, Patterning and Algebraic Reasoning).

Solve linear equations in one variable, including equations with variables on both sides and rational coefficients, and identify equations with one, none, or infinitely many solutions (A.PAR, Patterning and Algebraic Reasoning).

Solve linear inequalities in one variable, graph the solution on a number line, and interpret the solution set in context (A.PAR, Patterning and Algebraic Reasoning).

Solve systems of two linear equations by graphing, substitution, and elimination, and interpret the solution as the point where the lines meet (A.PAR, Patterning and Algebraic Reasoning).

Write linear equations in two variables from a slope and a point, from two points, and from a real-world context, and interpret slope and intercept in the model (A.PAR, Patterning and Algebraic Reasoning).

Interpret the parts of an expression (terms, factors, coefficients) in context, and use the structure of an expression to rewrite it in an equivalent form (A.PAR, Patterning and Algebraic Reasoning).

Add, subtract, and multiply polynomials, and factor quadratic expressions including GCF, trinomials, and the difference of squares (A.PAR, Patterning and Algebraic Reasoning).

Rewrite expressions involving radicals and rational exponents using the properties of exponents, and simplify square roots and cube roots (A.NR, Numerical Reasoning).

Classify real numbers as rational or irrational, and reason about the rationality of sums and products of rational and irrational numbers (A.NR, Numerical Reasoning).

Use units as a guide to setting up and solving modeling problems, convert units with conversion factors, and choose an appropriate level of accuracy (A.MM and A.NR, Modeling and Numerical Reasoning).

Solve quadratic equations by the square-root property and by completing the square, and use completing the square to rewrite a quadratic in vertex form (A.PAR, Patterning and Algebraic Reasoning).

Graph quadratic functions and identify key features: the vertex, the axis of symmetry, the y-intercept, the x-intercepts (zeros), and the direction of opening (A.FGR, Functional and Graphical Reasoning).

Build and use quadratic models for situations such as projectile motion and area, using the vertex for maximum or minimum values and the zeros for boundary values, and interpreting solutions in context (A.FGR and A.MM, Functional and Graphical Reasoning and Modeling).

Solve quadratic equations with the quadratic formula, and use the discriminant to determine the number and type of real solutions (A.PAR, Patterning and Algebraic Reasoning).

Solve quadratic equations by factoring using the zero-product property, after writing the equation in standard form (A.PAR, Patterning and Algebraic Reasoning).

Use vertex form to describe transformations of the parent function and to read the vertex, direction, and stretch of a quadratic (A.FGR, Functional and Graphical Reasoning).