SAT · SAT Math domains
Heart of Algebra
Signed-number arithmetic inside linear equations and inequalities.
A note on this mapping: Negative numbers are never the question on the SAT; they are the arithmetic every algebra question is written in.
Creating, interpreting and rewriting linear expressions.
Solving linear equations in one variable.
Solving linear equations in one variable, including with literal coefficients.
Linear equations with rational coefficients.
Solving and interpreting linear inequalities and their solution sets.
Absolute value equations and compound inequalities in one variable.
Slope, intercepts, and the equation and graph of a line.
Moving between the equation, table and graph of a linear relationship.
Systems of two linear equations and the meaning of their solution.
Writing the equation of a line in any form, and parallel and perpendicular lines.
Systems of linear inequalities in two variables and their solution regions.
The 12 skills that cover it
- Negative NumbersExtend the number line to the left of zero and compute with signed numbers. Negatives measure debt, cold, and depth below sea level.Read the lesson →
- Variables & ExpressionsUse letters to stand for unknown or changing quantities, evaluate expressions, and combine like terms.Read the lesson →
- Two-Step EquationsSolve equations of the form ax + b = c by undoing operations in reverse order.Read the lesson →
- Multi-Step EquationsSolve equations that need distributing, combining like terms, or moving variables to one side.Read the lesson →
- Equations with FractionsClear fractions from an equation by multiplying through by the least common denominator, then solve as usual.Read the lesson →
- Linear InequalitiesSolve inequalities the way you solve equations, with one extra rule: multiplying or dividing by a negative flips the sign.Read the lesson →
- Absolute Value & Compound InequalitiesSolve equations with an absolute value by splitting them into two cases, and solve compound inequalities joined by "and" or "or", writing each solution as an interval on the number line.Read the lesson →
- Linear FunctionsWork with straight lines: slope as a rate of change, intercepts, and the equation y = mx + b.Read the lesson →
- Graphs, Tables & EquationsMove fluently between the four faces of a function: equation, table, graph and words.Read the lesson →
- Systems of EquationsSolve two equations at once by graphing, substitution or elimination, and interpret the intersection point.Read the lesson →
- Forms of a LineWrite the equation of a line in point-slope, slope-intercept and standard form, convert between the three, read intercepts off standard form, and build parallel and perpendicular lines through a point.Read the lesson →
- Systems of InequalitiesGraph a linear inequality in two variables as a half-plane with a solid or dashed boundary, test whether a point satisfies a system of inequalities, and write a system from the constraints of a situation.Read the lesson →
What a student should be able to do
- Compare and order integers on a number line.
- Add and subtract integers, including subtracting a negative.
- Multiply and divide integers and predict the sign of the result.
- Model temperature, elevation and debt problems with integers.
- Translate a phrase in words into an algebraic expression.
- Evaluate an expression for given values of its variables.
- Combine like terms and apply the distributive property.
- Tell the difference between an expression and an equation.
- Undo addition or subtraction before undoing multiplication or division.
- Solve two-step equations with negative and fractional coefficients.
- Check solutions by substitution.
- Model two-step word problems with an equation.
- Distribute and combine like terms before solving.
- Solve equations with the variable on both sides.
- Recognise equations with no solution or infinitely many solutions.
- Translate multi-step word problems into equations.
- Multiply both sides by the least common denominator to clear fractions.
- Solve equations with fractional coefficients and constants.
- Solve simple proportions as rational equations.
- Check solutions and exclude values that make a denominator zero.
- Solve one- and two-step inequalities.
- Flip the inequality sign when multiplying or dividing by a negative.
- Graph a solution set on a number line.
- Write and solve inequalities from constraint word problems.
- Solve |x - a| = b and |ax + b| = c, giving both solutions.
- Solve an "and" compound inequality such as -3 < 2x + 1 <= 7.
- Solve an "or" compound inequality and describe its solution set.
- Solve an absolute value inequality and write the solution as a compound inequality.
- Compute the slope between two points.
- Write the equation of a line from a slope and a point.
- Interpret slope and intercept in a real-world context.
- Identify parallel and perpendicular slopes.
- Build a table of values from an equation.
- Read a slope and intercept off a graph or a table.
- Match a graph to its equation.
- Describe a function in words from any representation.
- Solve a system by substitution.
- Solve a system by elimination.
- Interpret a system with no solution or infinitely many solutions.
- Model two-quantity word problems with a system.
- Write the equation of a line from a point and a slope in point-slope form, and from two points.
- Convert between slope-intercept form y = mx + b and standard form Ax + By = C.
- Find both intercepts of a line given in standard form.
- Write the equation of the line through a point that is parallel or perpendicular to a given line.
- Decide whether a point is a solution of a linear inequality in two variables, or of a system.
- Match a shaded graph to its inequality, choosing the boundary style and the side to shade.
- Describe the solution region of a system of two linear inequalities.
- Write a system of inequalities from the constraints of a word problem.