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United StatesMaths

Algebra

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you solve linear equations in one variable and interpret what their solutions mean?

Linear equations in one variable: solve equations that reduce to ax + b = c, handle equations with no solution or infinitely many solutions, and interpret solutions in context.
A focused answer to the Digital SAT Algebra skill of solving linear equations in one variable, including clearing fractions and parentheses, recognising no-solution and infinite-solution cases, and interpreting solutions in word problems.
10 min answer →

How do you work with linear equations in two variables, moving between slope-intercept, standard and point-slope forms?

Linear equations in two variables: graph and interpret lines, find slope and intercepts, convert between slope-intercept and standard form, and find the equation of a line from given information.
A focused answer to the Digital SAT Algebra skill of linear equations in two variables: slope-intercept, standard and point-slope forms, finding slope and intercepts, parallel and perpendicular slopes, and building a line's equation.
11 min answer →

How do you interpret and use linear functions, including slope as a rate of change and the meaning of the intercepts?

Linear functions: interpret slope as a rate of change and the y-intercept as an initial value, use function notation, and build linear models from a rate and a starting amount.
A focused answer to the Digital SAT Algebra skill of linear functions: slope as rate of change, the y-intercept as a starting value, function notation, and interpreting the parameters of a linear model in context.
10 min answer →

How do you solve linear inequalities in one or two variables, and what do their solution sets look like?

Linear inequalities in one or two variables: solve and graph inequalities, remember to flip the sign when multiplying or dividing by a negative, and interpret feasible regions in context.
A focused answer to the Digital SAT Algebra skill of linear inequalities in one or two variables: solving, the sign-flip rule for negatives, graphing half-plane solution regions, and interpreting constraints in word problems.
10 min answer →

How do you solve a system of two linear equations, and when does a system have no solution or infinitely many?

Systems of two linear equations in two variables: solve by substitution and elimination, solve graphically, and determine when a system has one solution, no solution, or infinitely many.
A focused answer to the Digital SAT Algebra skill of systems of two linear equations: solving by substitution, elimination and graphing, and using slope and intercept to tell one solution from no solution or infinitely many.
11 min answer →