MCAP Grade 8 Expressions and Equations Practice

Expressions and Equations skills

8.EE.A Work with radicals and integer exponents.

8.EE.B Understand the connections between proportional relationships, lines, and linear equations.

8.EE.C Analyze and solve line equations and pairs of simultaneous linear equations.

Standards basis

Maryland College and Career Ready Standards for Mathematics (MCCRSM) — Maryland

How the MCAP reports it

MCAP is Maryland's statewide successor to PARCC, built on the Maryland College and Career Ready Standards for Mathematics (which mirror CCSS-M) — it is not a Smarter Balanced administration despite the claims-style family resemblance. Each grade/course High Level Blueprint (September 2022) organizes the assessment into three subclaims: Content (23-24 one-point machine-scored items, listed per domain/conceptual category as MCCRSM cluster headings), Reasoning (6 items), and Modeling (6 items), the latter two defined by per-grade evidence statements and including constructed-response items. Cluster headings are transcribed verbatim from the blueprints, including their minor typographical deviations from the parallel CCSS-M headings; two evident misprints are normalized (a duplicated sentence fragment on 4.OA.C, and the domain codes printed as G.P.E / T.TF for G.GPE / F.TF). Since March 2025, grade 6-7 students enrolled in a high-school mathematics course may take the corresponding MCAP course assessment instead of the grade-level test.

Blueprint & weighting

Each High Level Blueprint (September 2022) publishes per-domain operational item counts. Content Subclaim (1-point machine-scored items): Grade 3 — OA 7, NBT 2, NF 7, Measurement 5, Geometry 2 (23 items); Grade 4 — OA 4, NBT 5, NF 10, Measurement 3, Geometry 1 (23); Grade 5 — OA 2, NBT 6, NF 9, Measurement 4, Geometry 2 (23); Grade 6 — RP 3, NS 8, EE 8, Geometry 2, SP 2 (23); Grade 7 — RP 8, NS 4, EE 5, Geometry 3, SP 3 (23); Grade 8 — NS 2, EE 10, Functions 5, Geometry 4, SP 2 (23); Algebra I — Number and Quantity 1, Algebra 12, Functions 9, Statistics 2 (24); Geometry — G.CO 7, G.SRT 8, G.C 3, G.GPE 3, G.GMD 1, G.MG 1 (23); Algebra II — Number and Quantity 3, Algebra 8, Functions 11, Statistics 1 (23). Every assessment adds 6 Reasoning Subclaim and 6 Modeling Subclaim operational items — four 1-point machine-scored each, plus two constructed-response items (two 3-point in grades 3-4; one 3-point and one 4-point in grades 5-8; two 4-point in Algebra I, Geometry, and Algebra II) — so a form carries 35 operational items (36 for Algebra I).

Official sources

MSDE — MCAP Mathematics (current program page: grades 3-8, Algebra I, Geometry, Algebra II)
MSDE — MCAP Overview / High Level Blueprints summary
MSDE — MCAP Grade 3 Mathematics High Level Blueprint (September 2022)

8 free questions · 0/0 correct

Practice playeasy

What is the $y$ -intercept of the graph of $y = -11x + 6$ in the coordinate plane?

In $y = mx + b$ , the $y$ -intercept is the point $(0, b)$ . Here $b = 6$ , so the $y$ -intercept is $(0, 6)\textsf{.}$

Practice playeasy

$\dfrac{2^{7} \cdot 2^{4}}{2^{6}} = 2^{n}\textsf{.}$ What is $n\textsf{?}$

The Product of Powers Property says that powers with the same base are multiplied by adding the exponents, written $x^{m} \cdot x^{n} = x^{m+n}\textsf{.}$ The numerator is $2^{7} \cdot 2^{4} = 2^{7+4} = 2^{11}\textsf{.}$ The Quotient of Powers Property then subtracts the exponents of powers with the same base, written $\dfrac{x^{m}}{x^{n}} = x^{m-n}\textsf{.}$ So $\dfrac{2^{11}}{2^{6}} = 2^{11-6} = 2^{5}$ and $n = 5\textsf{.}$

Practice playmedium

Let $f(t) = 8e^{3t} + 50$ . Which of the following approximations, written as $a \times 10^n$ with one significant digit, is closest to the value of $f(2)$ ?

Substitute $t = 2$ : $f(2) = 8e^{6} + 50$ . Since $e^{6} \approx 403.4$ , $f(2) \approx 8(403.4) + 50 = 3{,}277 \approx 3 \times 10^{3}$ .

Practice playmedium

Which of these linear systems has no solution?

The first equation gives $y = -2x + 5\textsf{.}$ The second simplifies to $y = -2x + 6\textsf{,}$ so the slopes match but the intercepts differ and the system has no solution.

Practice playeasy

$\begin{cases} 3x + 4y = 10 \\ x - 2y = 1 \end{cases}$

How many solutions does the given system of equations have?

Rewrite in slope-intercept form: $y = -\dfrac{3}{4}x + \dfrac{5}{2}$ and $y = \dfrac{1}{2}x - \dfrac{1}{2}$ . The slopes $-\dfrac{3}{4}$ and $\dfrac{1}{2}$ are different, so the lines intersect at exactly one point.

Practice playmedium

What value of $x$ solves $\dfrac{1}{2}(4x + 6) + x = 15$ ?

Distribute $\dfrac{1}{2}$ : $2x + 3 + x = 15$ . Combine like terms: $3x + 3 = 15$ . Subtract $3$ from both sides: $3x = 12$ . Divide by $3$ : $x = 4\textsf{.}$

Practice playeasy

$0.0075 = c \times 10^{-3}$ . What is $c$ ?

Moving the decimal in $0.0075$ three places right gives $7.5$ , so $c = 7.5$ .

Practice playmedium

$(4 \times 10^{3})(5 \times 10^{4})$ equals

Multiply coefficients and add exponents: $4 \cdot 5 = 20$ and $3+4=7$ , giving $20 \times 10^{7}$ . Rewrite as $2 \times 10^{1} \times 10^{7}=2 \times 10^{8}\textsf{.}$

MCAP Grade 8 Expressions and Equations. Practice it free.

Expressions and Equations skills

8.EE.A Work with radicals and integer exponents.

8.EE.B Understand the connections between proportional relationships, lines, and linear equations.

8.EE.C Analyze and solve line equations and pairs of simultaneous linear equations.

Topics mapped to this domain

Y-intercept as a point

Exponent rules

Evaluating exponential functions

Inconsistent linear systems (ACT/SAT/PSAT 8/9/10)

Linear Algebra Basics: Systems

Multi-step linear equations

Scientific notation

Operations with scientific notation (ACT)

Solve linear equation for x (ACT)

Square roots and cube roots

8 free questions · 0/0 correct

Turn expressions and equations into game time.

More Grade 8 domains