Free Practice Questions for North Carolina EOC NC Math 3

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North Carolina EOC NC Math 1

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Key Facts: North Carolina EOC NC Math 3 Exam

NCDPI

State Agency

NC Department of Public Instruction

NC Math 3 (High School)

Course

NCSCOS for Mathematics (2016)

100 Practice Questions

Question Count

OpenExamPrep Bank

NCSCOS NC Math 3 (Number/Quantity/Algebra, Functions, Geometry, Stats)

Standards

NCDPI EOC Math Test Specifications (April 2026)

Prepare for the North Carolina EOC NC Math 3 test with 100 practice questions spanning polynomial, rational and radical expressions, advanced and trigonometric functions, circle and triangle geometry, and probability and inference.

Sample North Carolina EOC NC Math 3 Practice Questions

Try these sample questions to review concepts for the North Carolina EOC NC Math 3 exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Simplify i^23, where i = sqrt(-1).

A.i

B.-1

C.-i

D.1

Explanation: Powers of i cycle every 4: i^1=i, i^2=-1, i^3=-i, i^4=1. Divide the exponent by 4: 23 = 4(5) + 3, so the remainder is 3. Therefore i^23 = i^3 = -i.

2Add the complex numbers: (3 + 2i) + (5 - 7i).

A.8 - 5i

B.8 + 5i

C.8 - 9i

D.-2 + 9i

Explanation: Add real parts and imaginary parts separately: (3 + 5) + (2i - 7i) = 8 - 5i.

3Multiply: (2 + 3i)(1 - 4i).

A.14 - 5i

B.14 + 5i

C.-10 - 5i

D.2 - 5i

Explanation: Use FOIL: 2(1) + 2(-4i) + 3i(1) + 3i(-4i) = 2 - 8i + 3i - 12i^2. Since i^2 = -1, -12i^2 = +12. Combine: (2 + 12) + (-8i + 3i) = 14 - 5i.

4Add the rational expressions: 3/x + 2/(x + 1).

A.(5x + 3)/(x(x + 1))

B.5/(2x + 1)

C.(3x + 2)/(x(x + 1))

D.5/(x(x + 1))

Explanation: The common denominator is x(x + 1). Rewrite each term: 3/x = 3(x + 1)/(x(x + 1)) = (3x + 3)/(x(x + 1)), and 2/(x + 1) = 2x/(x(x + 1)). Adding the numerators gives (3x + 3 + 2x)/(x(x + 1)) = (5x + 3)/(x(x + 1)).

5Rewrite sqrt(x^3) using a rational exponent.

A.x^(3/2)

B.x^(2/3)

C.3x^(1/2)

D.x^3 / 2

Explanation: The rule sqrt(x^n) = x^(n/2) converts a radical to a rational exponent. Here sqrt(x^3) = x^(3/2): the numerator is the power and the denominator is the index of the root.

6Evaluate 8^(2/3).

A.4

B.16

C.2

D.1

Explanation: 8^(2/3) = (cube root of 8)^2 = 2^2 = 4. Equivalently, take the cube root first (8^(1/3) = 2), then square.

7Use the Remainder Theorem to find the remainder when p(x) = x^3 - 4x + 6 is divided by (x - 2).

A.6

B.0

C.2

D.14

Explanation: The Remainder Theorem says the remainder of p(x) divided by (x - c) equals p(c). Here c = 2, so evaluate p(2) = 2^3 - 4(2) + 6 = 8 - 8 + 6 = 6. The remainder is 6, so (x - 2) is not a factor.

8What is the degree of the polynomial 3x^4 - 2x^3 + 5x - 7?

A.4

B.3

C.7

D.2

Explanation: The degree of a polynomial is the largest exponent on a variable. The leading term is 3x^4, so the degree is 4.

9Factor completely: x^2 + 5x + 6.

A.(x + 2)(x + 3)

B.(x + 1)(x + 6)

C.(x - 2)(x - 3)

D.(x + 5)(x + 1)

Explanation: Find two numbers whose product is 6 and whose sum is 5: those numbers are 2 and 3. So x^2 + 5x + 6 = (x + 2)(x + 3).

10Simplify sqrt(72).

A.6sqrt(2)

B.8sqrt(3)

C.36sqrt(2)

D.2sqrt(36)

Explanation: Find the largest perfect square factor of 72: 72 = 36 * 2, so sqrt(72) = sqrt(36)*sqrt(2) = 6sqrt(2).

About the North Carolina EOC NC Math 3 Exam

The North Carolina EOC NC Math 3 Test measures proficiency on the NCSCOS for Mathematics across Number & Quantity and Algebra, Functions, Geometry, and Statistics & Probability. It is administered online through NCTest at course completion with all items calculator active. This 100-question practice bank is an English-language MCQ study adaptation with worked calculation items.

Exam sponsor: North Carolina Department of Public Instruction (NCDPI). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Online mathematics assessment delivered through NCTest with four-response-option multiple-choice, gridded response/numeric entry, and technology-enhanced items; all items calculator active. This local bank contains 100 English four-option practice MCQs across 4 standards domains.

Time Limit

Estimated 180 minutes; maximum 240 minutes

Passing Score

Four achievement levels: Not Proficient, Level 3, Level 4, Level 5. Level 3 and above denotes proficiency. EOC results count as at least 20% of the final course grade.

Exam / Certification Fees

No fee to students

Exam sponsor website

Reported exam pass rate: Not applicable (achievement levels are reported). Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

NCDPI EOC NC Math 1 and NC Math 3 Test Specifications
NCSCOS for Mathematics (2016)
NCTest released forms and Desmos graphing calculator

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

32-36%

Number & Quantity and Algebra

Reason with rational and polynomial expressions, perform arithmetic with complex numbers and vectors, build and interpret polynomial/rational/radical expressions and equations, and solve systems.

32-36%

Functions

Analyze and build polynomial, rational, square/cube root, trigonometric, and piecewise functions, interpret graph features, and model periodic phenomena.

20-24%

Geometry

Prove and apply theorems about lines, angles, triangles, and circles, use coordinates for geometric results, and apply right-triangle trigonometry and the Law of Sines/Cosines.

8-12%

Statistics & Probability

Understand independence and conditional probability, use probability rules for compound events, and make inferences about population parameters.

Preparing for the North Carolina EOC NC Math 3 Exam

What You Need to Know

Passing score: Four achievement levels: Not Proficient, Level 3, Level 4, Level 5. Level 3 and above denotes proficiency. EOC results count as at least 20% of the final course grade.
Assessment: Online mathematics assessment delivered through NCTest with four-response-option multiple-choice, gridded response/numeric entry, and technology-enhanced items; all items calculator active. This local bank contains 100 English four-option practice MCQs across 4 standards domains.
Time limit: Estimated 180 minutes; maximum 240 minutes
Exam / certification fees: No fee to students Official sources

Using Our Practice Resources

Work through all 100 available questions
Review every answer and explanation
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North Carolina EOC NC Math 3: Suggested Study Strategy

1Factor polynomials fully before solving or graphing; watch for common factors first.

2Identify function families (polynomial, rational, trigonometric) from their graph features.

3Connect circle theorems and inscribed angles to coordinate proofs where possible.

4Use tree diagrams or two-way tables to organize conditional probability problems.

Frequently Asked Questions

What is the NC EOC NC Math 3 test?

It measures proficiency on the NCSCOS for Mathematics via an online assessment delivered through NCTest with multiple-choice, gridded response, and technology-enhanced items; all 50 operational items are calculator active. Results count as at least 20% of the final course grade.

Are calculators allowed?

Yes — the NC Math 3 EOC is calculator active throughout; a graphing calculator (or the online Desmos graphing calculator) is available for all items.

Is this practice bank affiliated with NCDPI?

No. It is an independent study resource covering topics from the public NCSCOS for Mathematics NC Math 3; it is not an official NCTest product.