NAEP Grade 12 Measurement and Geometry Practice

Measurement and Geometry skills

measurement processes

area and volume

geometric properties

trigonometry-related geometry

conic sections reference

interest rates in applied settings

combinations and permutations reference

mathematical 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

8 free questions · 0/0 correct

Practice playeasy

Find the volume of a cylinder with radius $2$ and height $4$ . Use $\pi = 3$ .

$V = \pi r^2 h = 3 \times 4 \times 4 = 48$ .

Practice playeasy

A culvert pipe is a right circular cylinder with an inside diameter of $12$ inches and a length of $20$ inches. What is the volume of the pipe's interior, in cubic inches?

The radius is $6$ inches. $V = \pi r^{2} h = \pi (6)^{2}(20) = 720\pi$ cubic inches.

Practice playeasy

The function $h$ is defined by $h(t) = 125(1.18)^t$ . The function $h$ models the number of members in a club, where $t$ is the number of years after the club was founded. According to the model, what is the estimated number of members when the club was founded?

When the club was founded, $t = 0$ . So $h(0) = 125(1.18)^0 = 125$ members.

Practice playeasy

A substance has a half-life of $4$ years. What fraction remains after $12$ years?

$12 \div 4 = 3$ half-lives. Remaining: $\left(\dfrac{1}{2}\right)^{3} = \dfrac{1}{8}$ .

Practice playeasy

Taxi cost, in dollars, after $x$ miles:
$\begin{array}{c|c} x & f(x) \\ \hline 1 & 6 \\ 2 & 10 \\ 3 & 14 \\ 4 & 18 \end{array}$
The cost is $f(x)=mx+2\textsf{.}$ What is $m\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ The cost increases by $\text{\char36}4$ per mile, so $m = 4\textsf{.}$

Practice playmedium

The table shows values of a linear function $n\textsf{.}$
$\begin{array}{c|cccc} x & 2 & 4 & 6 & 8 \\ \hline n(x) & 11 & 15 & 19 & 23 \end{array}$
Which of the following is $n(x)\textsf{?}$

From $x = 2$ to $x = 4\textsf{,}$ $n(x)$ increases by $4\textsf{,}$ so the constant rate is $\dfrac{4}{2} = 2\textsf{.}$ Using the point $(2, 11)$ gives $2(2) + b = 11\textsf{,}$ so $b = 7\textsf{.}$ Therefore $n(x) = 2x + 7\textsf{.}$

Practice playmedium

A line has slope $\dfrac{3}{2}$ and passes through the point $(4, 1)$ . Which equation represents this line in slope-intercept form?

Slope-intercept form is $y = mx + b$ . Substituting $(4, 1)$ with $m = \dfrac{3}{2}$ gives $1 = \dfrac{3}{2}(4) + b = 6 + b$ , so $b = -5$ . The equation is $y = \dfrac{3}{2}x - 5\textsf{.}$

Practice playeasy

Two parallel lines are cut by a transversal. A pair of corresponding angles measure $(3x+16)°$ and $(2x+34)°$ . What is the measure of each of these angles?

Corresponding angles are congruent: $3x+16=2x+34$ , so $x=18$ . Each angle measures $3(18)+16=70°$ .

NAEP Grade 12 Measurement and Geometry. Practice it free.

Measurement and Geometry skills

measurement processes

area and volume

geometric properties

trigonometry-related geometry

conic sections reference

interest rates in applied settings

combinations and permutations reference

mathematical reasoning

Topics mapped to this domain

Surface area and volume

Volume word problems (ACT)

Exponential functions in context (SAT)

Exponential and log formulas

Linear functions from tables (ACT/SAT)

Linear rule from a function table (ACT)

Slope-point line equations (ACT/SAT/PSAT 8/9/10)

Algebra and polygon angle measures (ACT)

Geometric reasoning

Law of sines and cosines

Similar triangle shadows (ACT/SAT/PSAT 8/9/10)

Special right triangles

8 free questions · 0/0 correct

Turn measurement and geometry into game time.

More Grade 12 domains