NC EOG/EOC NC Math 3 Geometry. Practice it free.

EOC NC Math 3 domain (20-24% of the test, Table 1). Understand and apply theorems about circles, including arc length and sectors (G-C); prove geometric theorems (G-CO); explain volume formulas and use them (G-GMD); translate between the geometric description and the equation for a conic section / derive the equation of a circle (G-GPE); and apply geometric concepts in modeling (G-MG). This NC Math 3 reporting domain maps to 7 practice skills and 8 representative questions from the playable bank.

NC Math 3G7 mapped skills
What the test measures

Geometry skills

  1. Understand and apply theorems about circles, including inscribed angles, and find arc lengths and areas of sectors (NC.M3.G-C.2, NC.M3.G-C.5)

  2. Prove geometric theorems about lines, angles, triangles, and parallelograms (NC.M3.G-CO.10, NC.M3.G-CO.11, NC.M3.G-CO.14)

  3. Explain volume formulas and use them to solve problems and visualize cross-sections of solids (NC.M3.G-GMD.3, NC.M3.G-GMD.4)

  4. Translate between the geometric description and the equation for a conic section and derive the equation of a circle (NC.M3.G-GPE.1)

  5. Apply geometric concepts and density in modeling situations (NC.M3.G-MG.1)

Standards basis

North Carolina Standard Course of Study (NCSCOS) — North Carolina

How the NC EOG/EOC reports it

North Carolina’s math assessments are state-developed EOG/EOC tests aligned to the North Carolina Standard Course of Study (NCSCOS) for Mathematics, adopted June 2016, rather than a shared multistate framework. The EOG Grades 3-8 Mathematics Test Specifications and the EOC NC Math 1 and NC Math 3 Test Specifications publish, in Table 1/Table 2, the range of total items by domain (the official domain weight distributions). The NCSCOS K-8 domains carry CCSS domain codes (NC.3.OA, NC.8.F, …) and are CCSS-derived; NC Math 1 and NC Math 3 are integrated high-school EOC courses whose standards carry NC.M1/NC.M3 conceptual-category codes (Number and Quantity, Algebra, Functions, Geometry, Statistics and Probability).

Blueprint & weighting

Published per-domain weight ranges come from the NC DPI EOG/EOC Mathematics Test Specifications (April 2026), Table 1/Table 2 (range of total items by domain). EOG grades 3-5 (Table 1): Operations and Algebraic Thinking 32-36% (g3) / 14-18% (g4) / 9-13% (g5); Number and Operations in Base Ten 9-13% / 25-29% / 25-29%; Number and Operations – Fractions 28-32% / 30-34% / 39-43%; Measurement and Data, Geometry 23-27% / 23-27% / 19-23%. EOG grades 6-8 (Table 2): Ratios and Proportional Relationships 24-28% (g6) / 24-28% (g7) / — (g8); The Number System 20-24% / 8-12% / —; Expressions and Equations 22-26% / 20-24% / —; The Number System, Expressions and Equations (combined) — / — / 24-28%; Functions — / — / 28-32%; Geometry 12-16% / 16-20% / 24-28%; Statistics and Probability 12-16% / 22-26% / 16-20%. EOC (Table 1): NC Math 1 — Number and Quantity and Algebra 36-40%, Functions 32-36%, Geometry 8-12%, Statistics and Probability 18-20%; NC Math 3 — Number and Quantity and Algebra 32-36%, Functions 32-36%, Geometry 20-24%, Statistics and Probability 8-12%.

Practice by skill

Topics mapped to this domain

Surface area and volume

Grade 1015 questions

Circle diameter endpoints to radius (SAT)

Grade 1010 questions

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

Grade 1010 questions

Equation of a circle

Grade 1020 questions

Volume word problems (ACT)

Grade 910 questions

Advanced area formulas

Grade 1015 questions

Perimeter and arc length

Grade 1015 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

Find the volume of a cone with radius 33 and height 55. Use π=3\pi = 3.

V=13πr2h=13×3×9×5=45V = \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 3 \times 9 \times 5 = 45.

Practice playeasy

A circle in the coordinate plane has a diameter with endpoints (2,−4)(2, -4) and (18,−4).(18, -4)\textsf{.} What is the radius of the circle?

The endpoints share the same yy-coordinate, so the diameter is horizontal with length ∣18−2∣=16.|18 - 2| = 16\textsf{.} The radius is half the diameter, so r=162=8.r = \dfrac{16}{2} = 8\textsf{.}

Practice playmedium

The equation (x−4)2+(y−2)2=36(x - 4)^2 + (y - 2)^2 = 36 represents Circle A. Circle B is obtained by shifting Circle A left 55 units in the coordinate plane. Which of the following equations represents Circle B?

Circle A has center (4,2)(4, 2) and radius 66. Shifting left 55 moves the center to (−1,2)(-1, 2), so Circle B is (x+1)2+(y−2)2=36(x + 1)^2 + (y - 2)^2 = 36.

Practice playeasy

A circle in the coordinate plane has equation (x−2)2+(y−7)2=36.(x - 2)^{2} + (y - 7)^{2} = 36\textsf{.} What is the measure of the diameter of the circle?

The radius measures 66 units, so the diameter measures 1212 units.

Practice playmedium

A cylindrical rain barrel has an inside radius of 33 feet. After a storm, the water level rises 44 inches. What is the volume of the added water, in cubic feet?

Convert 44 inches to 13\dfrac{1}{3} foot. V=πr2h=π(3)2(13)=3πV = \pi r^{2} h = \pi (3)^{2}\left(\dfrac{1}{3}\right) = 3\pi cubic feet.

Practice playeasy

A triangle has sides 33, 44, and 55. What is its area?

This is a right triangle (33-44-55). Area =12×3×4=6= \dfrac{1}{2} \times 3 \times 4 = 6.

Practice playeasy

A triangle has sides 77, 1010, and 1212. What is its perimeter?

P=7+10+12=29P = 7 + 10 + 12 = 29.

Practice playeasy

Find the volume of a cylinder with radius 33 and height 22. Use π=3\pi = 3.

V=πr2h=3×9×2=54V = \pi r^{2} h = 3 \times 9 \times 2 = 54.

Keep practicing

Turn geometry into game time.

The NC EOG/EOC placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Related Common Core standards
7.G.B.6HSG.GMD.A.3HSG.GPE.A.1HSG.C.B.5
Geometry in other NC EOG/EOC grades
Grade 6Grade 7Grade 8NC Math 1
Source and test overview
All NC EOG/EOC prepOfficial test source
Reporting categories

More NC Math 3 domains

Number and Quantity and AlgebraEOC NC Math 3 domain (32-36% of the test, Table 1). Use the Fundamental Theorem of Algebra (N-CN.9); interpret and rewrite polynomial, rational, and exponential expressions (A-SSE); perform arithmetic on polynomials and rational expressions including the Remainder Theorem and zeros (A-APR); and create and solve equations, including logarithmic and rational equations (A-CED, A-REI).8 QsPractice →FunctionsEOC NC Math 3 domain (32-36% of the test, Table 1). Interpret and analyze functions including polynomial, rational, exponential, logarithmic, and trigonometric functions (F-IF); build new functions and find inverses (F-BF); use logarithms to solve exponential models (F-LE); and extend trigonometry to radian measure and the unit circle (F-TF).8 QsPractice →Statistics and ProbabilityEOC NC Math 3 domain (8-12% of the test, Table 1). Understand and evaluate random processes underlying statistical experiments, and make inferences and justify conclusions from sample surveys, experiments, and observational studies (S-IC).8 QsPractice →