Ohio State Tests Geometry Circles Practice

What the test measures

Circles skills

Understand and apply theorems about circles, find arc lengths and areas of sectors, and translate between the geometric description and the equation of a circle

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

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8 free questions · 0/0 correct

Practice playeasy

Find the area of a sector with radius $6$ and central angle $120°$ . Use $\pi = 3$ .

Sector area $= \dfrac{120}{360} \times \pi r^2 = \dfrac{120}{360} \times 3 \times 36 = 36$ .

Practice playeasy

A circle in the coordinate plane has a diameter with endpoints $(8, 0)$ and $(8, 6)\textsf{.}$ What is the radius of the circle?

The endpoints share the same $x$ -coordinate, so the diameter is vertical with length $|6 - 0| = 6\textsf{.}$ The radius is half the diameter, so $r = \dfrac{6}{2} = 3\textsf{.}$

Practice playmedium

The equation $x^2 + (y + 2)^2 = 16$ represents Circle A. Circle B is obtained by shifting Circle A down $5$ units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center $(0, -2)$ and radius $4$ . Shifting down $5$ moves the center to $(0, -7)$ , so Circle B is $x^2 + (y + 7)^2 = 16$ .

Practice playeasy

The ellipse $\dfrac{x^{2}}{25} + \dfrac{y^{2}}{9} = 1$ crosses the positive x-axis at one point. What is the x-coordinate of that point?

Set $y = 0$ : then $x^{2} = 25$ , and the positive solution is $x = 5$ .

Practice playeasy

A circle in the coordinate plane has equation $(x - 1)^{2} + (y - 4)^{2} = 81\textsf{.}$ What is the value of $r^{2}\textsf{?}$

In standard form the right side equals $r^{2}\textsf{,}$ so $r^{2} = 81\textsf{.}$

Practice playeasy

Find the arc length of a $180°$ arc on a circle with radius $5$ . Use $\pi = 3$ .

$L = \dfrac{180}{360} \times 2 \pi r = \dfrac{1}{2} \times 2 \times 3 \times 5 = 15$ .

Practice playeasy

A triangle has sides $3$ , $4$ , and $5$ . What is its area?

This is a right triangle ( $3$ - $4$ - $5$ ). Area $= \dfrac{1}{2} \times 3 \times 4 = 6$ .

Practice playeasy

A circle in the coordinate plane has a diameter with endpoints $(-6, 1)$ and $(12, 1)\textsf{.}$ What is the radius of the circle?

The endpoints share the same $y$ -coordinate, so the diameter is horizontal with length $|12 - (-6)| = 18\textsf{.}$ The radius is half the diameter, so $r = \dfrac{18}{2} = 9\textsf{.}$