TCAP High School (EOC courses) Algebra Practice

TCAP High School (EOC courses) Algebra. Practice it free.

See structure in expressions, write expressions in equivalent forms to solve problems, and analyze, solve, and prove equations and inequalities. This High School (EOC courses) reporting domain maps to 44 practice skills and 8 representative questions from the playable bank.

High School (EOC courses)44 mapped skills

Algebra skills

HSA.SSE.1 Interpret expressions that represent a quantity in terms of its context

HSA.SSE.2 Use the structure of an expression to identify ways to rewrite it

HSA.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression

HSA.APR.1 Understand that polynomials form a system analogous to the integers

HSA.APR.2 Know and apply the Remainder Theorem

HSA.APR.3 Identify zeros of polynomials when suitable factorizations are available

HSA.APR.4 Prove polynomial identities

HSA.APR.5 Know and apply the Binomial Theorem

HSA.CED.1 Create equations and inequalities in one variable and use them to solve problems

HSA.CED.2 Create equations in two or more variables to represent relationships between quantities

HSA.CED.3 Represent constraints by equations or inequalities and interpret solutions

HSA.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step

HSA.REI.2 Solve simple rational and radical equations in one variable

HSA.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters

HSA.REI.4 Solve quadratic equations in one variable

HSA.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions

HSA.REI.6 Solve systems of linear equations exactly and approximately

HSA.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation

HSA.REI.8 Represent a system of linear equations as a single matrix equation

HSA.REI.9 Find the inverse of a matrix if it exists and use it to solve systems of equations

Standards basis

Tennessee Academic Standards for Mathematics — Tennessee

How the TCAP reports it

TCAP math is Tennessee’s state assessment program and its blueprints are aligned to Tennessee Academic Standards, which closely mirror the Common Core content structure in grades 3-8 and the CCSS-style high school conceptual categories. The blueprint page lists the current 2025-26 assessment overviews, including Math Grade 2, Grades 3-5, Grades 6-8, and Math EOC. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Blueprint & weighting

Published TCAP math blueprints assign content emphasis by grade/course, but the exact percentage table was not recoverable from the accessible blueprint page in this session. The state blueprint landing page confirms the math overviews but did not expose the PDF links in the fetched page content. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Official sources

Tennessee Department of Education TCAP Blueprints
Tennessee Education Glossary (academic standards entry)

8 free questions · 0/0 correct

Practice playeasy

$|x - 25| = 40$

Which of the following gives both solutions to the given equation?

The equation means $x - 25 = 40$ or $x - 25 = -40$ . So $x = 65$ or $x = -15$ . Both solutions are $-15$ and $65\textsf{.}$

Practice playeasy

If $|3x - 9| = 24$ , what is the negative value of $x - 3$ ?

Factor: $|3x - 9| = |3(x - 3)| = |3|\,|x - 3| = 3|x - 3|$ . Since $3|x - 3| = 24$ , divide by $3$ to get $|x - 3| = 8$ . The values of $x - 3$ are $8$ and $-8$ ; the negative value is $-8\textsf{.}$

Practice playeasy

What is $4!$ ?

$4! = 4 \times 3 \times 2 \times 1 = 24$ .

Practice playeasy

Which is the completely factored form of $9x^{2} - 6x$ ?

The greatest common factor of $9x^{2}$ and $6x$ is $3x\textsf{.}$ Factoring gives $3x(3x - 2)$ .

Practice playeasy

A shipping label allows a package weight $w$ , in pounds, that is more than $2$ pounds but at most $10$ pounds. Which inequality represents the possible values of $w$ ?

More than $2$ means $w > 2$ . At most $10$ means $w \le 10$ , so $2 < w \le 10$ .

Practice playeasy

Which expression is equivalent to $4x^{2} - 81$ ?

$4x^{2} - 81 = (2x)^{2} - 9^{2} = (2x - 9)(2x + 9)$ .

Practice playeasy

How many distinct real roots does $x^{2} - 6x + 9 = 0$ have?

Here $a = 1$ , $b = -6$ , and $c = 9$ . Substituting into $b^{2} - 4ac$ gives $(-6)^{2} - 4(1)(9) = 0\textsf{,}$ so there is exactly $1$ distinct real root.

Practice playeasy

Solve using the quadratic formula: $x^{2} + 4x + 1 = 0$ .

Here $a = 1$ , $b = 4$ , and $c = 1$ . Substituting into the quadratic formula gives $x = \dfrac{-4 \pm \sqrt{4^{2} - 4(1)(1)}}{2(1)} = \dfrac{-4 \pm \sqrt{12}}{2} = -2 \pm \sqrt{3}$ .

TCAP High School (EOC courses) Algebra. Practice it free.

Algebra skills

HSA.SSE.1 Interpret expressions that represent a quantity in terms of its context

HSA.SSE.2 Use the structure of an expression to identify ways to rewrite it

HSA.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression

HSA.APR.1 Understand that polynomials form a system analogous to the integers

HSA.APR.2 Know and apply the Remainder Theorem

HSA.APR.3 Identify zeros of polynomials when suitable factorizations are available

HSA.APR.4 Prove polynomial identities

HSA.APR.5 Know and apply the Binomial Theorem

HSA.CED.1 Create equations and inequalities in one variable and use them to solve problems

HSA.CED.2 Create equations in two or more variables to represent relationships between quantities

HSA.CED.3 Represent constraints by equations or inequalities and interpret solutions

HSA.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step

HSA.REI.2 Solve simple rational and radical equations in one variable

HSA.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters

HSA.REI.4 Solve quadratic equations in one variable

HSA.REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions

HSA.REI.6 Solve systems of linear equations exactly and approximately

HSA.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation

HSA.REI.8 Represent a system of linear equations as a single matrix equation

HSA.REI.9 Find the inverse of a matrix if it exists and use it to solve systems of equations

Topics mapped to this domain

Absolute value equation solutions

Absolute value equations (ACT/SAT)

Binomial theorem and factorials

Common factor factoring (SAT)

Compound inequality situations

Difference of squares factoring

Discriminant analysis

The discriminant and quadratic formula

Equivalent rational expressions (SAT)

Factoring quadratic expressions (ACT)

Factorable polynomial zeros (ACT)

Factoring patterns

8 free questions · 0/0 correct

Turn algebra into game time.

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