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North CarolinaMaths

Expressions and Operations

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 factor a quadratic expression, and how does the factored form reveal the zeros?

Factor quadratic expressions including common factor, trinomials, and difference of squares, and use the factored form to reveal zeros (NC.M1.A-SSE.3).
An NC Math 1 EOC answer on factoring quadratics (NC.M1.A-SSE.3): pulling out a GCF, factoring trinomials with leading coefficient 1 and greater, the difference of squares, and reading zeros from the factored form.
11 min answer →

How do you read the parts of an algebraic expression and explain what each part means in a real context?

Interpret the parts of a linear, exponential, or quadratic expression (terms, factors, coefficients, exponents) and interpret a multi-part expression as a combination of entities (NC.M1.A-SSE.1a, A-SSE.1b).
An NC Math 1 EOC answer on interpreting expressions (NC.M1.A-SSE.1): naming terms, factors, coefficients, and exponents, and reading what each part means in a real context for linear, quadratic, and exponential models.
10 min answer →

How do you add, subtract, and multiply polynomials, and why do they behave like the integers?

Understand that polynomials are closed under addition, subtraction, and multiplication, and perform these operations (NC.M1.A-APR.1).
An NC Math 1 EOC answer on polynomial operations (NC.M1.A-APR.1): combining like terms to add and subtract, distributing the minus sign, multiplying with the distributive property and FOIL, and why polynomials form a closed system like the integers.
10 min answer →

How does a rational exponent relate to a radical, and how do you rewrite expressions using the properties of exponents?

Explain how rational exponents extend the integer-exponent properties and rewrite expressions with radicals and rational exponents (NC.M1.N-RN.1, N-RN.2).
An NC Math 1 EOC answer on radicals and rational exponents (NC.M1.N-RN.1, N-RN.2): converting between radical and exponent form, the exponent properties, and simplifying numerical and algebraic expressions.
11 min answer →

When is a sum or product of numbers rational, and when is it irrational?

Explain why sums and products of rational and irrational numbers are rational or irrational (NC.M1.N-RN.3).
An NC Math 1 EOC answer on rational and irrational numbers (NC.M1.N-RN.3): the closure of rationals, why rational plus irrational is irrational, and why a nonzero rational times an irrational is irrational.
9 min answer →

How can you use the structure of an expression to rewrite it in an equivalent, more useful form?

Use the structure of an expression to identify ways to rewrite it, and write an equivalent factored form of a quadratic to reveal zeros (NC.M1.A-SSE.2, A-SSE.3).
An NC Math 1 EOC answer on rewriting expressions using structure (NC.M1.A-SSE.2, A-SSE.3): spotting common factors, difference of squares, and perfect-square trinomials, and writing factored form to reveal the zeros of a quadratic.
10 min answer →