Florida · FLDOESyllabus
Maths syllabus, dot point by dot point
Every dot point in the Florida 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.
Data Analysis and Probability
Module overview →- How do you calculate and compare measures of center (mean, median) and spread (range, IQR, standard deviation), and choose the right one for a distribution?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).10 min answer →
- What does the correlation coefficient tell you, why does correlation not imply causation, and how do residuals show whether a linear model fits?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).11 min answer →
- How do you read and interpret dot plots, histograms, and box plots, and describe the shape of a distribution?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).10 min answer →
- How do you fit a line to bivariate data, interpret its slope and intercept, and use it to predict?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).11 min answer →
- How do you read a two-way frequency table and compute joint, marginal, and conditional relative frequencies?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).10 min answer →
Exponential and Nonlinear Functions
Module overview →- How do you tell linear, quadratic, and exponential functions apart from a table, an equation, or a graph, and why does exponential growth eventually overtake the others?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).10 min answer →
- How do you write and use exponential growth and decay models, and interpret the initial value and the growth or decay rate?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).11 min answer →
- How do you graph an exponential function and identify its y-intercept, horizontal asymptote, domain, range, and growth or decay behavior?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).10 min answer →
- How do you graph and read key features of square-root, cube-root, absolute-value, and piecewise functions?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).10 min answer →
Functions
Module overview →- How do you calculate the average rate of change of a function over an interval, and what does it mean in a real-world context?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).9 min answer →
- How do you compare properties of two functions when they are given in different forms: equation, table, graph, or verbal description?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).9 min answer →
- How do you use function notation, decide whether a relation is a function, and state the domain and range from a graph, table, or context?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).10 min answer →
- How do you identify and interpret the key features of a graph: intercepts, increasing and decreasing intervals, maximums and minimums, and end behavior?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).10 min answer →
- How do the constants in f(x) + k, f(x + h), and a times f(x) shift, stretch, and reflect the graph of a function?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).10 min answer →
Linear and Absolute-Value Equations, Inequalities, and Systems
Module overview →- How do you solve absolute-value equations and inequalities, and why do they split into two cases?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).10 min answer →
- How do you solve multi-step linear equations in one variable, including those with variables on both sides, and recognize no-solution and infinitely-many-solution cases?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).9 min answer →
- How do you solve and graph linear inequalities in one variable, and why does the inequality sign flip when you multiply or divide by a negative?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).9 min answer →
- How do you solve a system of two linear equations by graphing, substitution, and elimination, and what do one, none, or infinitely many solutions mean?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).11 min answer →
- How do you graph a linear inequality in two variables and the solution region of a system of inequalities, and how do you test a point?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).10 min answer →
- How do you find the slope and intercepts of a line, write its equation in slope-intercept and point-slope form, and graph it?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).11 min answer →
Number Sense and Expressions
Module overview →- How do you write and use explicit and recursive formulas for arithmetic and geometric sequences, and connect them to linear and exponential functions?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).10 min answer →
- How do you rewrite an algebraic expression in equivalent forms to reveal its structure, and how do you interpret the parts of an expression in context?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).9 min answer →
- How do you simplify expressions using the properties of integer and rational exponents, and rewrite radicals as rational exponents?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).10 min answer →
- How do you factor polynomials using the greatest common factor, trinomial patterns, difference of squares, and grouping?Factor polynomial expressions using common factors, the difference of two squares, perfect-square trinomials, and grouping (MA.912.AR.1.3).11 min answer →
- How do you add, subtract, and multiply polynomials, and why is the set of polynomials closed under these operations?Add, subtract, and multiply polynomial expressions with rational number coefficients, recognizing that polynomials are closed under these operations (MA.912.AR.1.1).9 min answer →
Quadratic Functions and Equations
Module overview →- How do the standard, vertex, and factored forms of a quadratic each reveal different key features, and how do you convert between them?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).11 min answer →
- How do you graph a quadratic function and identify its vertex, axis of symmetry, intercepts, and direction of opening?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).11 min answer →
- How do you model and solve real-world problems with quadratics, deciding when to use the vertex versus the zeros and which solutions to reject?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).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 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).11 min answer →
- How do you solve a quadratic equation by factoring and applying the zero-product property?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).10 min answer →
- How do you solve a quadratic by taking square roots, and how does completing the square solve any quadratic and produce vertex form?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).11 min answer →