TCAP Grade 7 Geometry Practice — Sports Academy Games

What the test measures

Geometry skills

7.G.A.1 Solve problems involving scale drawings
7.G.A.2 Draw geometric shapes with given conditions
7.G.A.3 Describe the two-dimensional figures that result from slices of three-dimensional figures
7.G.B.4 Know the formulas for the area and circumference of a circle
7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles
7.G.B.6 Solve real-world and mathematical problems involving angle measure, area, surface area, and volume

Standards basis

Tennessee Academic Standards for Mathematics — Tennessee

How the TCAP reports it

TCAP math is Tennessee’s state assessment program and its blueprints are aligned to Tennessee Academic Standards, which closely mirror the Common Core content structure in grades 3-8 and the CCSS-style high school conceptual categories. The blueprint page lists the current 2025-26 assessment overviews, including Math Grade 2, Grades 3-5, Grades 6-8, and Math EOC. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Blueprint & weighting

Published TCAP math blueprints assign content emphasis by grade/course, but the exact percentage table was not recoverable from the accessible blueprint page in this session. The state blueprint landing page confirms the math overviews but did not expose the PDF links in the fetched page content. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Official sources

Tennessee Department of Education TCAP Blueprints
Tennessee Education Glossary (academic standards entry)

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

Find the volume of a sphere with radius $3$ . Use $\pi = 3$ .

$V = \dfrac{4}{3} \pi r^{3} = \dfrac{4}{3} \times 3 \times 27 = 108$ .

Practice playeasy

Two angles are complementary. One measures $60°$ . What is the other?

$90 - 60 = 30°$ .

Practice playeasy

A circle has a radius of $11$ centimeters. What is the circumference, in centimeters, of the circle?

The circumference of a circle is $C = 2\pi r$ . Substitute $r = 11$ : $C = 2\pi(11) = 22\pi\textsf{.}$

Practice playeasy

A circle has radius $1$ . Using $\pi = 3$ , what is its circumference?

$C = 2\pi r = 2 \times 3 \times 1 = 6$ .

Practice playeasy

Similar triangles $GHI$ and $JKL$ have perimeters $16$ and $48\textsf{.}$ Side $GH$ corresponds to side $JK\textsf{,}$ and $GH = 5\textsf{.}$ What is the length of $JK\textsf{?}$

The scale factor from $\triangle GHI$ to $\triangle JKL$ is $\dfrac{48}{16} = 3\textsf{.}$ Corresponding sides scale by $3\textsf{,}$ so $JK = 5 \cdot 3 = 15\textsf{.}$

Practice playhard

A rectangular prism has volume $72$ cubic centimeters and height $4$ centimeters. The length is twice the width. What is the width, in centimeters?

$V = \ell w h$ and $\ell = 2w$ , so $72 = (2w)(w)(4) = 8w^2$ . Then $w^2 = 9$ and $w = 3\text{ cm}\textsf{.}$

Practice playmedium

A factory seals soup in closed cylindrical cans with radius $3$ centimeters and height $5$ centimeters. What is the total exterior surface area, in square centimeters, of one closed can?

A closed cylinder has two circular bases and a lateral surface: $SA = 2\pi r^2 + 2\pi rh$ . With $r = 3$ and $h = 5$ , $SA = 2\pi(9) + 2\pi(3)(5) = 18\pi + 30\pi = 48\pi$ square centimeters.