NAEP Grade 8 Geometry Practice — Sports Academy Games

What the test measures

Geometry skills

spatial reasoning
geometric properties
Pythagorean theorem problems
geometry reasoning

Standards basis

NAEP Mathematics Framework (National Assessment Governing Board framework; not a CCSS-M/state standards test blueprint) — national

How the NAEP reports it

NAEP mathematics is organized by the National Assessment Governing Board’s framework, not by state standards. The current framework assesses Grades 4, 8, and 12 and uses five content areas, with item distributions and complexity levels specified in the official framework; it is a national assessment and not aligned to Common Core as a governing blueprint, though it reflects broadly modern school math expectations.

Blueprint & weighting

Published item distribution by grade and content area: Grade 4 — Number Properties and Operations 40%, Measurement 20%, Geometry 15%, Data Analysis/Statistics/Probability 10%, Algebra 15%; Grade 8 — Number Properties and Operations 20%, Measurement 15%, Geometry 20%, Data Analysis/Statistics/Probability 15%, Algebra 30%; Grade 12 — Number Properties and Operations 10%, Measurement and Geometry 30%, Data Analysis/Statistics/Probability 25%, Algebra 35%.

Official sources

National Center for Education Statistics
National Center for Education Statistics
National Center for Education Statistics

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playmedium

In $\triangle MNO$ , $\angle M$ and $\angle O$ are congruent. The measure of $\angle N$ is $105.2^{\circ}$ . What is the measure of $\angle M$ ?

Each congruent angle is $\dfrac{180^{\circ} - 105.2^{\circ}}{2} = 37.4^{\circ}$ .

Practice playeasy

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

A heptagon has $7$ sides: $(7-2) \times 180 = 900°$ .

Practice playeasy

If $m\angle A = 50^{\circ}$ and $m\angle B = 78^{\circ}$ in a triangle, what is $m\angle C\textsf{?}$

The sum of the interior angles of a triangle is $180^{\circ}\textsf{.}$ So $m\angle C = 180^{\circ} - 50^{\circ} - 78^{\circ} = 52^{\circ}\textsf{.}$

Practice playeasy

What is the distance from $(0, 0)$ to $(5, 12)$ ?

$\sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13$ .

Practice playeasy

The hypotenuse of a right triangle measures $26$ meters, and one leg measures $24$ meters. What is the length of the second leg?

Let the missing leg be $x$ . Then $x^{2} + 24^{2} = 26^{2}$ , so $x^{2} = 26^{2} - 24^{2} = 676 - 576 = 100$ and $x = \sqrt{100} = 10$ .

Practice playeasy

A right triangle has legs $3$ and $4$ . What is the hypotenuse?

$3^{2} + 4^{2} = 9 + 16 = 25$ , so the hypotenuse is $\sqrt{25} = 5\textsf{.}$

Practice playeasy

A wheelchair ramp rises $5$ feet over a horizontal distance of $12$ feet. What is the length of the ramp?

The ramp is the hypotenuse of a right triangle with legs $5$ and $12$ : $\sqrt{5^{2} + 12^{2}} = \sqrt{25 + 144} = \sqrt{169} = 13$ feet.

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