Ohio State Tests Grade 8 Functions Practice

What the test measures

Functions skills

Define, evaluate, and compare functions, and use functions to model relationships between quantities

Standards basis

Ohio's Learning Standards (mathematics) — Common Core-derived (CCSS-M) — Ohio

How the Ohio State Tests reports it

Ohio's State Tests are Ohio-specific assessments built around Ohio's Learning Standards for Mathematics, which are CCSS-derived and retain the Common Core grade-level domains and (at high school) conceptual categories nearly verbatim. Math is tested in grades 3-8 and via end-of-course exams; the high-school graduation pathway uses Algebra I and Geometry, but students in an integrated sequence take Integrated Mathematics I and II in their place (these integrated courses are not given their own bands here — Integrated Math I draws on the same Algebra/Functions/Number & Quantity/Geometry/Statistics content as Algebra I plus early Geometry, and Integrated Math II adds the remaining Geometry/Functions/Probability content). The reporting categories below are the official math subscore categories Ohio publishes per test; because no public item-percentage blueprint was retrievable, the cluster-level Common Core domains those subscores cover are used (the standards' grade-level domains, which the reporting categories mirror).

Blueprint & weighting

Ohio publishes per-test math subscore (reporting) categories in its Subscore Definitions chart and raw-score subscale ranges, but no public per-category item-percentage blueprint was retrievable; the statistical summaries report the number of items per subscore by administration rather than a fixed blueprint weighting.

Official sources

Ohio Department of Education and Workforce — Ohio's State Tests Subscore Definitions (OSTSubscoreChart.pdf)
Ohio Department of Education and Workforce — Ohio's State Tests Spring 2025 Statistical Summary
Ohio Department of Education and Workforce — Ohio's State Tests in ELA, Mathematics, Science and Social Studies

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

What is the $y$ -intercept of the line $y = \dfrac{3}{4}x - 5$ ?

In $y = mx + b$ , the $y$ -intercept is $b = -5$ .

Practice playmedium

The linear function $h$ is defined by $h(x) = mx + 45$ , where $m$ is a constant. Given that $h(9) = 0$ , evaluate $h(4)$ .

Substitute $x = 9$ : $9m + 45 = 0$ , so $9m = -45$ and $m = -5$ . The rule is $h(x) = -5x + 45$ , so $h(4) = -5(4) + 45 = -20 + 45 = 25$ .

Practice playeasy

A school club starts a fundraiser with $\text{\char36}50$ already collected and earns $\text{\char36}8$ for each cake sold. Let $x$ be the number of cakes sold and $y$ be the total money raised in dollars. Which equation models the situation?

The club begins at $\text{\char36}50$ and gains $\text{\char36}8$ per cake, so $y = 8x + 50\textsf{.}$

Practice playeasy

What is the slope of the line through $(-4, 3)$ and $(2, 3)$ ?

The $y$ -values are equal, so the line is horizontal: slope $= \dfrac{3 - 3}{2 - (-4)} = \dfrac{0}{6} = 0\textsf{.}$

Practice playeasy

What is the slope of the line $y = \dfrac{1}{2}x - 2$ ?

In $y = mx + b$ , the slope is $m = \dfrac{1}{2}$ .

Practice playhard

The rule $r(x) = -4x + d$ describes a linear function, and $d$ is a constant. If $r(3) = 5$ , what is $r(-2)\textsf{?}$

Substitute $x = 3$ : $-4(3) + d = 5$ , so $-12 + d = 5$ and $d = 17$ . The rule is $r(x) = -4x + 17$ , so $r(-2) = -4(-2) + 17 = 8 + 17 = 25$ .

Practice playeasy

A kayak rental shop charges $\text{\char36}18$ per hour with no upfront fee. Let $x$ be the number of hours rented and $y$ be the total cost in dollars. Which equation models the situation?