PARCC Geometry Expressing Geometric Properties with Equations Practice

Expressing Geometric Properties with Equations skills

Translate between the geometric description and the equation for a conic section

Use coordinates to prove simple geometric theorems algebraically

Find geometric measurements and relate them to equations

Standards basis

Common Core State Standards for Mathematics (CCSS-M) / PARCC Model Content Frameworks — national

How the PARCC reports it

PARCC was a multistate assessment system built around the Common Core-era PARCC mathematics model content frameworks rather than a separate proprietary standards set. Its math structure is organized by grade/course and aligned to CCSS-M content categories and model content frameworks.

Blueprint & weighting

No single published PARCC weighting table was located in the accessible sources used here.

Official sources

PARCC Assessment
Common Core State Standards Initiative

8 free questions · 0/0 correct

Practice playeasy

Find the area of a sector with radius $6$ and central angle $120°$ . Use $\pi = 3$ .

Sector area $= \dfrac{120}{360} \times \pi r^2 = \dfrac{120}{360} \times 3 \times 36 = 36$ .

Practice playeasy

A circle in the coordinate plane has a diameter with endpoints $(8, 0)$ and $(8, 6)\textsf{.}$ What is the radius of the circle?

The endpoints share the same $x$ -coordinate, so the diameter is vertical with length $|6 - 0| = 6\textsf{.}$ The radius is half the diameter, so $r = \dfrac{6}{2} = 3\textsf{.}$

Practice playmedium

The equation $x^2 + (y + 2)^2 = 16$ represents Circle A. Circle B is obtained by shifting Circle A down $5$ units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center $(0, -2)$ and radius $4$ . Shifting down $5$ moves the center to $(0, -7)$ , so Circle B is $x^2 + (y + 7)^2 = 16$ .

Practice playmedium

The graph of the equation $(x + 6)^2 + (y - 4)^2 = 100$ is a circle in the coordinate plane. The point $(a, b)$ lies on the circle. Which of the following is a possible value for $a\textsf{?}$

The center is $(-6, 4)$ and the radius is $10\textsf{.}$ A point on the circle must satisfy $-6 - 10 \le a \le -6 + 10\textsf{,}$ so $-16 \le a \le 4\textsf{.}$ The value $-11$ is in this interval.

Practice playeasy

The ellipse $\dfrac{x^{2}}{25} + \dfrac{y^{2}}{9} = 1$ crosses the positive x-axis at one point. What is the x-coordinate of that point?

Set $y = 0$ : then $x^{2} = 25$ , and the positive solution is $x = 5$ .

Practice playeasy

A circle in the coordinate plane has equation $(x - 1)^{2} + (y - 4)^{2} = 81\textsf{.}$ What is the value of $r^{2}\textsf{?}$

In standard form the right side equals $r^{2}\textsf{,}$ so $r^{2} = 81\textsf{.}$

Practice playeasy

$M(4, 7)$ is the midpoint of segment $AB$ , and $A = (1, 5)$ . What is the $x$ -coordinate of $B$ ?

Since $\dfrac{1 + B_x}{2} = 4$ , we get $B_x = 8 - 1 = 7$ .

Practice playmedium

The equation of a line is $y = \dfrac{1}{2}x - 4$ . Which equation represents the line that is parallel to this line and passes through the point $(6, 1)$ ?

Parallel lines have the same slope, so $m = \dfrac{1}{2}$ . Substitute $(6, 1)$ into $y = \dfrac{1}{2}x + b$ : $1 = \dfrac{1}{2}(6) + b = 3 + b$ , so $b = -2$ . The equation is $y = \dfrac{1}{2}x - 2\textsf{.}$

PARCC Geometry Expressing Geometric Properties with Equations. Practice it free.

Expressing Geometric Properties with Equations skills

Translate between the geometric description and the equation for a conic section

Use coordinates to prove simple geometric theorems algebraically

Find geometric measurements and relate them to equations

Topics mapped to this domain

Advanced area formulas

Circle diameter endpoints to radius (SAT)

Circle equation translations (ACT/SAT/PSAT 8/9/10)

Possible coordinates on a circle (SAT)

Conic sections

Equation of a circle

Midpoint formula

Parallel and perpendicular lines through a point (SAT)

Parallel and perpendicular slopes from slope-intercept form

Perimeter and arc length

8 free questions · 0/0 correct

Turn expressing geometric properties with equations into game time.

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