Algebra 1 · Equations and Inequalities

Virginia SOL A.EI.3

Virginia SOL A.EI.3 is part of the Equations and Inequalities strand in Algebra 1 (Math). Under this Standards of Learning objective, students represent, solve, and interpret solutions to quadratic equations in one variable. Below is what A.EI.3 covers in plain language, the specific skills it is assessed on, the key concepts to review, and how to practice A.EI.3 for the Virginia SOL test.

Practice A.EI.3 All Algebra 1 standards

What SOL A.EI.3 means

Represent, solve, and interpret solutions to quadratic equations in one variable.

Practice Algebra 1 SOL questions

Free Algebra 1 questions from official Virginia Department of Education released SOL tests — good practice while you work on A.EI.3 and the rest of the course. Pick an answer to check it instantly, or open “Show answer” to review.

1. Which is a simplified form of ((4xy^3)(xy^4))?
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Answer: C — (x^5y^7)
2. Which is equivalent to (2.3 10^4-6.5 10^3)?
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Answer: J — 16,500
3. What is the value of ( (mn)/(r^2) ) if (m=7), (n=18), and (r=6)?
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Answer: A — 3.5
4. When factored completely, (x^2-9) equals
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Answer: J — ((x+3)(x-3))

→ Take the full free Algebra 1 SOL practice test

Skills you’ll practice for A.EI.3

Solve a quadratic equation in one variable over the set of real numbers with rational or irrational solutions, including contextual problems.
Determine and justify if a quadratic equation in one variable has no real solutions, one real solution, or two real solutions.
Verify possible solutions to a quadratic equation in one variable algebraically, graphically, and with technology.

Key concepts covered by A.EI.3

solve quadratic equations
real solutions
rational solutions
irrational solutions
contextual problems
quadratic solutions
no real solutions
one real solution
two real solutions
justify solutions
verify quadratic solutions
algebraic verification
graphical verification
technology verification

How to study and practice SOL A.EI.3

Start with a quick diagnostic to see whether A.EI.3 is already solid, then work each skill above with guided notes, flashcards, and SOL-style practice questions. For official released items, see our Virginia SOL practice tests guide and how to study for the SOL test.

→ Take the free Algebra 1 SOL practice test

A.EI.1 — Represent, solve, explain, and interpret solutions to multistep linear equations, inequalities, and literal equations.
A.EI.2 — Represent, solve, explain, and interpret solutions to systems of linear equations, inequalities, and linear inequalities in two variables.

Frequently asked questions about SOL A.EI.3

What is Virginia SOL A.EI.3?

SOL A.EI.3 is a Algebra 1 Standard of Learning in the Equations and Inequalities strand. It expects students to represent, solve, and interpret solutions to quadratic equations in one variable.

What skills does SOL A.EI.3 cover?

SOL A.EI.3 is assessed on 3 skills: solve a quadratic equation in one variable over the set of real numbers with rational or irrational solutions, including contextual problems; determine and justify if a quadratic equation in one variable has no real solutions, one real solution, or two real solutions; verify possible solutions to a quadratic equation in one variable algebraically, graphically, and with technology.

What strand of Algebra 1 is SOL A.EI.3 in?

SOL A.EI.3 belongs to the Equations and Inequalities reporting strand of the Algebra 1 Virginia Standards of Learning.

How do I study and practice for SOL A.EI.3?

Start with a diagnostic to see whether A.EI.3 is already solid, then work the 3 skills above with guided notes, flashcards, and SOL-style practice questions. For official released items, see the Virginia SOL practice tests guide.