Ohio State Tests Grade 8 Geometry Practice

What the test measures

Geometry skills

Understand congruence and similarity using transformations, apply the Pythagorean Theorem, and solve problems involving volume of cylinders, cones, and spheres

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

A cylinder has $r^2 = 9$ and height $3$ . Using $\pi = 3$ , what is its volume?

$V = \pi r^2 h = 3 \times 9 \times 3 = 81$ .

Practice playeasy

What is the distance from $(2, 3)$ to $(9, 3)$ ?

Both points have $y = 3$ , so the distance is $|9 - 2| = 7$ .

Practice playeasy

In $\triangle ABC$ , $\angle B$ and $\angle C$ are congruent. The measure of $\angle A$ is $124.8^{\circ}$ . What is the measure of $\angle C$ ?

Each congruent angle is $\dfrac{180^{\circ} - 124.8^{\circ}}{2} = 27.6^{\circ}$ .

Practice playeasy

What is the sum of the interior angles of a hexagon?

A hexagon has $6$ sides: $(6-2) \times 180 = 720°$ .

Practice playeasy

Find the hypotenuse of a right triangle whose legs are $21$ m and $28$ m.

The legs are $21$ and $28$ . By the Pythagorean theorem, $21^{2} + 28^{2} = 441 + 784 = 1{,}225$ , so the hypotenuse is $\sqrt{1{,}225} = 35$ .

Practice playeasy

A right triangle has one leg $5$ and hypotenuse $13$ . What is the other leg?

$13^{2} - 5^{2} = 169 - 25 = 144$ , so the other leg is $\sqrt{144} = 12\textsf{.}$

Practice playeasy

A $26$ -meter guy wire runs from the top of a pole to a stake $24$ meters from the pole's base. How tall is the pole?

The wire is the hypotenuse: $26^{2} - 24^{2} = 676 - 576 = 100$ , so the pole is $\sqrt{100} = 10$ meters tall.

Practice playhard

A rectangle has length $8$ centimeters and area $120$ square centimeters. What is the length of a diagonal of the rectangle, in centimeters?

Area $A = \ell w$ , so $120 = 8w$ and $w = 15$ . The diagonal is the hypotenuse of a right triangle with legs $8$ and $15$ : $\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17\text{ cm}\textsf{.}$