RISE Grade 8 Geometry Practice — Sports Academy Games

What the test measures

Geometry skills

Understand congruence and similarity using physical models, transparencies, or geometry software
Understand and apply the Pythagorean theorem
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres

Standards basis

Utah Core Standards for Mathematics (CCSS-aligned Utah math standards) — Utah

How the RISE reports it

Utah’s RISE mathematics assessment is a state assessment aligned to Utah Core Standards rather than a separately branded national framework. The official Utah pages point to Utah Core standards resources and the RISE administration guidance, with no separate public math blueprint published on the assessment page itself.

Blueprint & weighting

RISE mathematics weighting by domain was not located on the official Utah assessment page; the official page only points to the RISE assessment overview/administration resources and the Utah Core Standards resources. Grade 6 administration guidance notes a two-segment math test with Segment 1 no calculator and Segment 2 calculator allowed, and the proctor guide states Mathematics has an expected testing time of 90 minutes for most students and 135 minutes for all students.

Official sources

Utah State Board of Education Assessments
Utah State Board of Education Learning Resources for Families
Utah State Board of Education Assessment Contacts PDF

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

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

$V = \pi r^2 h = 3 \times 4 \times 3 = 36$ .

Practice playeasy

The distance between $(0, 0)$ and $(6, 8)$ is $d$ . What is $d^{2}$ ?

$d^{2} = 6^2 + 8^2 = 36 + 64 = 100$ .

Practice playmedium

In $\triangle JKL$ , $\angle J$ and $\angle L$ are congruent. The measure of each of these angles is $61.7^{\circ}$ . What is the measure of $\angle K$ ?

The two congruent angles total $2 \times 61.7^{\circ} = 123.4^{\circ}$ , so $\angle K = 180^{\circ} - 123.4^{\circ} = 56.6^{\circ}$ .

Practice playeasy

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

A decagon has $10$ sides: $(10-2) \times 180 = 1440°$ .

Practice playmedium

In a right triangle, one leg is $9$ feet and the hypotenuse is $41$ feet. How long is the other leg?

Let the missing leg be $x$ . Then $x^{2} + 9^{2} = 41^{2}$ , so $x^{2} = 41^{2} - 9^{2} = 1{,}681 - 81 = 1{,}600$ and $x = \sqrt{1{,}600} = 40$ .

Practice playeasy

One leg of a right triangle is $10$ and the hypotenuse is $26$ . What is the missing leg?

$26^{2} - 10^{2} = 676 - 100 = 576$ , so the missing leg is $\sqrt{576} = 24\textsf{.}$

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 $15$ : $\sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17\text{ cm}\textsf{.}$