Virginia · VDOESyllabus
Maths syllabus, dot point by dot point
Every dot point in the Virginia 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 solve absolute-value equations and inequalities, and why do they split into two cases?Solve absolute-value equations and inequalities in one variable, splitting into two cases and representing solution sets symbolically and on a number line (A.EI.3).9 min answer →
- How do you rearrange a literal equation or formula to solve for a specified variable?Rearrange formulas and literal equations to solve for a specified variable, treating the other letters as constants and using inverse operations (A.EI.1).9 min answer →
- How do you solve multi-step linear equations in one variable, including those with variables on both sides, and identify equations with one, no, or infinitely many solutions?Solve multi-step linear equations in one variable, including equations with the variable on both sides and with rational-number coefficients, and classify an equation as having one solution, no solution, or infinitely many solutions (A.EI.1).9 min answer →
- How do you solve linear inequalities in one variable and represent the solution set on a number line?Solve multi-step linear inequalities in one variable, represent the solution set on a number line and in interval notation, and interpret solutions in context, flipping the inequality when multiplying or dividing by a negative (A.EI.2).9 min answer →
- How do you solve a system of two linear equations by graphing, substitution, and elimination, and what does the number of solutions mean?Solve systems of two linear equations in two variables by graphing, substitution, and elimination, and interpret one solution, no solution, or infinitely many solutions in context (A.EI.4).9 min answer →
- How do you graph a system of linear inequalities and identify the solution region?Graph systems of linear inequalities in two variables, identify the overlapping solution region, and determine whether a given point is a solution (A.EI.5).9 min answer →
Exponential and Comparing Functions
Module overview →- How do you compare linear, quadratic, and exponential functions across tables, graphs, and contexts to decide which model fits?Compare and contrast linear, quadratic, and exponential functions using tables, graphs, and equations, and determine which family best models a situation (A.F.2).9 min answer →
- What is an exponential function, how do you recognize it from a table or graph, and how do you interpret its initial value and growth factor?Identify and interpret exponential functions of the form f(x) = ab^x from tables, graphs, equations, and contexts, including the initial value and the constant growth or decay factor (A.F.2).9 min answer →
- How do you model and solve exponential growth and decay problems using the percent-change form?Model and interpret exponential growth and decay using the form y = a(1 + r)^t for growth and y = a(1 - r)^t for decay, and evaluate to solve real-world problems (A.F.2).9 min answer →
- How do you identify and find terms of arithmetic and geometric sequences using the explicit formulas?Distinguish arithmetic from geometric sequences and use the explicit nth-term formulas to find terms and relate sequences to linear and exponential functions (A.F.2).9 min answer →
Expressions and Operations
Module overview →- How do you determine whether two algebraic expressions are equivalent, and how do you rewrite an expression in a more useful form?Determine whether two algebraic expressions are equivalent, and use equivalent forms (expanded, factored, or simplified) to reveal structure and interpret meaning (A.EO.6).9 min answer →
- How do you use the properties of exponents to simplify expressions with integer exponents, and how do you convert between standard form and scientific notation?Simplify expressions involving integer exponents using the laws of exponents, and represent and operate with very large or very small numbers in scientific notation (A.EO.2).9 min answer →
- How do you factor polynomial expressions in one variable, including greatest common factors, trinomials, and special products?Factor polynomial expressions in one variable: a greatest common monomial factor, trinomials of the form ax^2 + bx + c, perfect-square trinomials, and the difference of two squares (A.EO.5).9 min answer →
- How do you add, subtract, and multiply polynomial expressions in one variable?Add, subtract, and multiply polynomial expressions in one variable, including multiplying binomials and applying special products (A.EO.4).9 min answer →
- How do you simplify numerical and algebraic expressions in one variable using the order of operations and the properties of real numbers?Apply the order of operations and the properties of real numbers (commutative, associative, distributive, identity, and inverse) to simplify and evaluate numerical and algebraic expressions in one variable (A.EO.1).9 min answer →
- How do you simplify radical expressions and rewrite between radical form and rational-exponent form?Simplify square-root and cube-root radical expressions involving numerical and monomial radicands, and convert between radical notation and rational-exponent notation (A.EO.3).9 min answer →
Functions
Module overview →- How do you determine the domain and range of a function from its graph, table, or context, including discrete versus continuous?Determine and represent the domain and range of a function from a graph, table, set of ordered pairs, or context, distinguishing discrete from continuous and reasonable domains in real situations (A.F.2).9 min answer →
- What is a function, how do you recognize one, and how do you use and evaluate function notation?Determine whether a relation is a function from a table, graph, mapping, or equation, and use and evaluate function notation f(x) (A.F.1).9 min answer →
- How do you find and interpret the slope of a linear function as a rate of change, and read it from a graph, table, or equation?Calculate and interpret the slope of a linear function as a rate of change from a graph, table, equation, or two points, and identify the meaning of slope and intercepts in context (A.F.3).9 min answer →
- How do you graph and analyze a quadratic function, including its vertex, axis of symmetry, and the forms of its equation?Graph and analyze quadratic functions, identifying the vertex, axis of symmetry, intercepts, and direction of opening, and connecting standard, vertex, and factored forms (A.F.5).9 min answer →
- How do you write the equation of a linear function from a graph, a slope and a point, or two points, and what are the relationships for parallel and perpendicular lines?Write equations of linear functions in slope-intercept and point-slope form given a graph, a slope and a point, or two points, and apply the slope relationships for parallel and perpendicular lines (A.F.4).9 min answer →
- How do you identify the key features of a function's graph: intercepts, zeros, maximum or minimum, and intervals of increase and decrease?Identify and interpret key features of a function graph, including x- and y-intercepts, zeros, maximum or minimum values, and intervals where the function increases or decreases (A.F.1).9 min answer →
Quadratic Equations
Module overview →- How do you solve a quadratic equation by completing the square, and how does it produce vertex form?Solve quadratic equations by completing the square, and use completing the square to rewrite a quadratic in vertex form (A.EI.6).8 min answer →
- How do you use the quadratic formula to solve any quadratic, and what does the discriminant tell you about the solutions?Solve quadratic equations using the quadratic formula, and use the discriminant to determine the number and nature of the real solutions (A.EI.6).9 min answer →
- How do you solve a quadratic equation by factoring, using 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 (A.EI.6).9 min answer →
- How do you solve a quadratic equation by taking square roots, and when is that method the right choice?Solve quadratic equations of the form x^2 = k or a(x - h)^2 = k by taking square roots, including the plus-or-minus sign, and recognize when there is no real solution (A.EI.6).8 min answer →