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MassachusettsMaths

Number and Quantity

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

How do the laws of exponents let you simplify expressions, and how are zero and negative exponents handled on the MCAS?

Apply the product, quotient, and power rules for exponents, interpret zero and negative integer exponents, and simplify expressions with integer exponents without a calculator.
A Grade 10 Math MCAS answer on the laws of exponents: the product, quotient, and power rules, the meaning of zero and negative exponents, and how to simplify exponential expressions, including in the no-calculator session.
9 min answer →

How do you simplify radicals and rewrite them as rational exponents on the MCAS?

Simplify square and cube roots, perform operations with radicals, and convert between radical form and rational-exponent form using the relationship a^(1/n) equals the nth root of a.
A Grade 10 Math MCAS answer on simplifying square and cube roots, adding and multiplying radicals, and converting between radical form and rational-exponent form, with the no-calculator skills the test rewards.
9 min answer →

How do you set up and solve proportions, and how do percent change and unit rates appear on the MCAS?

Set up and solve proportions, compute and compare unit rates, and apply percent increase, decrease, and percent change to real-world quantities.
A Grade 10 Math MCAS answer on proportional reasoning: setting up and solving proportions, comparing unit rates, and computing percent increase, decrease, and percent change in context.
9 min answer →

What makes a number rational or irrational, and how do operations on them behave on the Grade 10 MCAS?

Classify real numbers as rational or irrational, explain why sums and products of rational and irrational numbers behave as they do, and place numbers on the real number line.
A Grade 10 Math MCAS answer on classifying real numbers as rational or irrational, why a rational plus an irrational is irrational, why a nonzero rational times an irrational is irrational, and ordering numbers on the real number line.
9 min answer →

How do you convert units, use rates, and report answers with appropriate precision on the MCAS?

Use unit analysis to convert measurements and rates, choose appropriate units for a quantity, and report answers with a level of accuracy suited to the context.
A Grade 10 Math MCAS answer on unit conversion by dimensional analysis, working with rates and compound units, choosing appropriate units, and reporting answers with sensible precision and rounding.
9 min answer →