Ohio State Tests Grade 7 Geometry Practice

What the test measures

Geometry skills

Draw, construct, and describe geometrical figures and solve problems involving angle measure, area, surface area, and volume

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

Find the volume of a cone with radius $3$ and height $5$ . Use $\pi = 3$ .

$V = \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 3 \times 9 \times 5 = 45$ .

Practice playeasy

A rectangular prism has length $2$ , width $4$ , and height $9$ . What is its volume?

$V = 2 \times 4 \times 9 = 72$ .

Practice playeasy

Two lines cross. One angle formed is $20°$ . What is the vertical angle?

Vertical angles are equal: $20°$ .

Practice playeasy

A circle has a radius of $7$ meters. What is the area, in square meters, of the circle?

The area of a circle is $A = \pi r^{2}$ . Substitute $r = 7$ : $A = \pi(7)^{2} = 49\pi\textsf{.}$

Practice playeasy

A circle has radius $2$ . Using $\pi = 3$ , what is its area?

$A = \pi r^2 = 3 \times 4 = 12$ .

Practice playeasy

Rectangles $JKLM$ and $NPQR$ are similar. The perimeter of rectangle $JKLM$ is $18\textsf{,}$ and the perimeter of rectangle $NPQR$ is $45\textsf{.}$ Side $JK$ corresponds to side $NP\textsf{,}$ and $JK = 6\textsf{.}$ What is the length of $NP\textsf{?}$

The scale factor from rectangle $JKLM$ to rectangle $NPQR$ equals the perimeter ratio $\dfrac{45}{18} = \dfrac{5}{2}\textsf{.}$ So $NP = 6 \cdot \dfrac{5}{2} = 15\textsf{.}$

Practice playhard

A rectangular prism has volume $160$ cubic inches and height $5$ inches. The length is twice the width. What is the length, in inches?

$V = \ell w h$ and $\ell = 2w$ , so $160 = (2w)(w)(5) = 10w^2$ . Then $w^2 = 16$ , so $w = 4$ and $\ell = 8\text{ in}\textsf{.}$

Practice playmedium

A paint store sells open-top metal cans with radius $2$ inches and height $6$ inches. The cans have a bottom but no lid. What is the exterior surface area, in square inches, of one open can?

An open can has one circular base and a lateral surface: $SA = \pi r^2 + 2\pi rh$ . With $r = 2$ and $h = 6$ , $SA = \pi(4) + 2\pi(2)(6) = 4\pi + 24\pi = 28\pi$ square inches.