MathsQ&A by dot point

Calculate and interpret measures of center (mean, median) and spread (range, interquartile range, standard deviation), and choose appropriate measures based on the shape of the distribution and the presence of outliers (MA.912.DP.1.2, MA.912.DP.1.3).

Interpret the correlation coefficient as a measure of the strength and direction of a linear association, distinguish correlation from causation, and use residuals to assess the fit of a linear model (MA.912.DP.2.6, MA.912.DP.2.8, MA.912.DP.2.9).

Represent and interpret univariate numerical data using dot plots, histograms, and box plots, and describe the shape (symmetric, skewed left, skewed right) of a distribution (MA.912.DP.1.1, MA.912.DP.1.2).

Fit a linear function to bivariate numerical data on a scatter plot, interpret the slope and intercept in context, and use the model to make predictions (MA.912.DP.2.4, MA.912.DP.2.5).

Construct and interpret two-way frequency tables of categorical data, and calculate joint, marginal, and conditional relative frequencies (MA.912.DP.2.4, MA.912.DP.3.1).

Distinguish among linear, quadratic, and exponential functions using their rates of change from tables, equations, and graphs, and recognize that a quantity growing exponentially eventually exceeds one growing linearly or quadratically (MA.912.F.1.6, MA.912.AR.5.6).

Write, evaluate, and interpret exponential functions that model growth and decay, identifying the initial value and the growth or decay factor and rate (MA.912.AR.5.4, MA.912.F.1.6).

Graph exponential functions and identify key features including the y-intercept, the horizontal asymptote, domain, range, and whether the function is increasing or decreasing (MA.912.F.1.3, MA.912.AR.5.6).

Graph and interpret key features of square-root, cube-root, absolute-value, and piecewise-defined functions, including domain restrictions and points of interest (MA.912.F.1.1, MA.912.AR.4.3).

Calculate and interpret the average rate of change of a function over a specified interval from a graph, a table, or an equation (MA.912.F.1.4).

Compare key features (intercepts, rate of change, maximums, and minimums) of two functions each represented differently, such as one as an equation and one as a table or graph (MA.912.F.1.5).

Evaluate and interpret function notation, determine whether a relation is a function, and identify the domain and range of a function from multiple representations (MA.912.F.1.1, MA.912.F.1.2).

Identify and interpret key features of a graph, including x- and y-intercepts, intervals where the function is increasing or decreasing, relative maximums and minimums, and end behavior, in terms of a context (MA.912.F.1.3).

Identify the effect on the graph of a function of replacing f(x) with f(x) + k, f(x - h), and a times f(x), including vertical and horizontal translations, stretches, compressions, and reflections (MA.912.F.2.1, MA.912.F.2.2).

Solve absolute-value equations and inequalities in one variable and graph the solution set, recognizing the two-case structure and no-solution cases (MA.912.AR.4.1, MA.912.AR.4.2).

Solve multi-step linear equations in one variable, including equations with the variable on both sides and with rational-number coefficients, and identify when an equation has one solution, no solution, or infinitely many solutions (MA.912.AR.2.1, MA.912.AR.2.2).

Solve multi-step linear inequalities in one variable, graph the solution set on a number line, and interpret it in a real-world context (MA.912.AR.2.4, MA.912.AR.2.5).

Solve systems of two linear equations in two variables by graphing, substitution, and elimination, and interpret the solution, including consistent, inconsistent, and dependent systems (MA.912.AR.9.1, MA.912.AR.9.4).

Graph linear inequalities in two variables and systems of linear inequalities, identifying the solution region and testing whether a point is a solution, including in real-world constraint contexts (MA.912.AR.9.6).

Determine the slope and intercepts of a linear function, write its equation in slope-intercept, point-slope, and standard form, and graph it, including parallel and perpendicular lines (MA.912.AR.2.3, MA.912.AR.3.1).

Write and evaluate explicit and recursive formulas for arithmetic and geometric sequences, and relate arithmetic sequences to linear functions and geometric sequences to exponential functions (MA.912.AR.5 and MA.912.F).

Rewrite algebraic expressions in equivalent forms using properties of operations, and interpret parts of an expression (coefficients, factors, terms) in terms of a real-world context (MA.912.AR.1.2).

Apply the laws of exponents to numerical and algebraic expressions with integer and rational exponents, and rewrite radical expressions using rational exponents (MA.912.NSO.1).

Factor polynomial expressions using common factors, the difference of two squares, perfect-square trinomials, and grouping (MA.912.AR.1.3).

Add, subtract, and multiply polynomial expressions with rational number coefficients, recognizing that polynomials are closed under these operations (MA.912.AR.1.1).

Recognize and use the standard, vertex, and factored forms of a quadratic function, identifying which key features each form reveals and converting between them (MA.912.AR.3.8, MA.912.AR.1.2).

Graph a quadratic function and identify and interpret its key features: vertex, axis of symmetry, x- and y-intercepts, direction of opening, and maximum or minimum value (MA.912.AR.3.7, MA.912.F.1.3).

Model real-world situations with quadratic functions and solve, interpreting the vertex as a maximum or minimum and the zeros as start or end points, and rejecting solutions that do not fit the context (MA.912.AR.3.6, MA.912.AR.3.9).

Solve quadratic equations using the quadratic formula from the reference sheet, and use the discriminant to determine the number and nature of the real solutions (MA.912.AR.3.4, MA.912.AR.3.5).

Solve quadratic equations in one variable by factoring and applying the zero-product property, and interpret the solutions as the zeros of the related function (MA.912.AR.3.4).

Solve quadratic equations by taking square roots and by completing the square, including writing the equation in vertex form (MA.912.AR.3.4, MA.912.AR.3.8).