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MassachusettsMaths

Algebra and Expressions

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you translate a real-world situation into an equation or inequality and interpret the answer?

Create linear, quadratic, and exponential equations and inequalities from a verbal context, solve them, and interpret the solution back in the situation with units.
A Grade 10 Math MCAS answer on modeling: translating words into linear, quadratic, and exponential equations and inequalities, solving them, and interpreting the solution in context with correct units and reasoning.
9 min answer →

How do you read the structure of an algebraic expression and rewrite it to reveal what it means?

Interpret the parts of an expression (terms, factors, coefficients) in context, and rewrite expressions in equivalent forms to reveal a quantity such as a y-intercept, a zero, a maximum, or a rate.
A Grade 10 Math MCAS answer on reading the structure of expressions (terms, factors, coefficients), interpreting parts in context, and rewriting expressions in equivalent forms that reveal an intercept, a zero, a vertex, or a rate of change.
9 min answer →

How do you solve linear equations and inequalities, and when does the inequality sign flip?

Solve multi-step linear equations and inequalities in one variable, rearrange literal equations for a chosen variable, and represent inequality solutions on a number line.
A Grade 10 Math MCAS answer on solving multi-step linear equations and inequalities, the sign-flip rule when multiplying or dividing by a negative, rearranging literal equations, and graphing inequality solutions on a number line.
9 min answer →

How do you add, subtract, and multiply polynomials, and how do you factor them completely?

Add, subtract, and multiply polynomials, and factor completely using the greatest common factor, the difference of two squares, and trinomial factoring.
A Grade 10 Math MCAS answer on polynomial arithmetic (adding, subtracting, multiplying) and factoring completely using the greatest common factor, the difference of two squares, and trinomial methods, with the order of factoring the test rewards.
9 min answer →

How do you solve a quadratic equation, and how do you choose between factoring, square roots, and the formula?

Solve quadratic equations by factoring with the zero-product property, by taking square roots, and by the quadratic formula, use the discriminant to count real roots, and interpret solutions in context.
A Grade 10 Math MCAS answer on solving quadratics by factoring (zero-product property), taking square roots, and the quadratic formula, using the discriminant to count real roots, and discarding solutions that make no sense in context.
10 min answer →

How do you solve a system of equations, and how many solutions can a system have?

Solve systems of linear equations by substitution and elimination, recognize systems with one, no, or infinitely many solutions, and find the solution region of a system of inequalities.
A Grade 10 Math MCAS answer on solving systems of linear equations by substitution and elimination, classifying systems as one, none, or infinitely many solutions, and finding the overlap region for a system of inequalities.
9 min answer →