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Free Practice Questions for MCAP Grade 8 Math

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Sample MCAP Grade 8 Math Practice Questions

Try these sample questions to review concepts for the MCAP Grade 8 Math exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Which of the following numbers is an irrational number?
A.\(\sqrt{18}\)
B.\(\frac{7}{8}\)
C.\(\sqrt{49}\)
D.\(0.45\)
Explanation: \(\sqrt{18} = 3\sqrt{2}\). Since 18 is not a perfect square, its square root is an irrational number with a non-terminating, non-repeating decimal expansion.
2Express the repeating decimal \(0.\bar{6}\) as a fraction in simplest form.
A.\(\frac{2}{3}\)
B.\(\frac{3}{5}\)
C.\(\frac{6}{10}\)
D.\(\frac{6}{99}\)
Explanation: Let \(x = 0.666...\). Then \(10x = 6.666...\). Subtracting yields \(9x = 6\), so \(x = \frac{6}{9} = \frac{2}{3}\).
3Simplify the numerical expression \(4^3 \times 4^{-5}\).
A.\(\frac{1}{16}\)
B.\(\frac{1}{64}\)
C.\(-16\)
D.\(16\)
Explanation: Using the product rule for exponents with the same base, \(4^3 \times 4^{-5} = 4^{3 + (-5)} = 4^{-2} = \frac{1}{4^2} = \frac{1}{16}\).
4What is the value of \(\sqrt[3]{125} + \sqrt{64}\)?
A.\(13\)
B.\(11\)
C.\(15\)
D.\(21\)
Explanation: \(\sqrt[3]{125} = 5\) because \(5^3 = 125\), and \(\sqrt{64} = 8\) because \(8^2 = 64\). Adding them together gives \(5 + 8 = 13\).
5Write \(0.00045\) in standard scientific notation.
A.\(4.5 \times 10^{-4}\)
B.\(4.5 \times 10^{-5}\)
C.\(45 \times 10^{-5}\)
D.\(4.5 \times 10^4\)
Explanation: Move the decimal point 4 places to the right to obtain a coefficient between 1 and 10 (\(4.5\)). Moving right indicates a negative exponent: \(4.5 \times 10^{-4}\).
6Between which two consecutive integers does \(\sqrt{70}\) lie on a number line?
A.\(8\) and \(9\)
B.\(7\) and \(8\)
C.\(9\) and \(10\)
D.\(6\) and \(7\)
Explanation: Identify the bounding perfect squares: \(64 < 70 < 81\). Taking square roots gives \(\sqrt{64} < \sqrt{70} < \sqrt{81}\), which simplifies to \(8 < \sqrt{70} < 9\).
7What is the repeating decimal \(0.\bar{27}\) expressed as a fraction in lowest terms?
A.\(\frac{3}{11}\)
B.\(\frac{27}{100}\)
C.\(\frac{9}{33}\)
D.\(\frac{27}{90}\)
Explanation: Let \(x = 0.\bar{27}\). Then \(100x = 27.\bar{27}\). Subtracting \(x\) gives \(99x = 27\), so \(x = \frac{27}{99}\). Dividing numerator and denominator by 9 simplifies to \(\frac{3}{11}\).
8Evaluate the expression \(\frac{(2^3)^{-2} \cdot 2^8}{2^4}\).
A.\(\frac{1}{4}\)
B.\(\frac{1}{2}\)
C.\(1\)
D.\(4\)
Explanation: Simplify numerator first: \((2^3)^{-2} = 2^{-6}\), so numerator is \(2^{-6} \cdot 2^8 = 2^2\). Divide by denominator: \(\frac{2^2}{2^4} = 2^{2-4} = 2^{-2} = \frac{1}{4}\).
9Evaluate \((3.2 \times 10^5) + (4.8 \times 10^4)\) and write the result in scientific notation.
A.\(3.68 \times 10^5\)
B.\(8.0 \times 10^9\)
C.\(3.68 \times 10^4\)
D.\(8.0 \times 10^5\)
Explanation: Convert to the same power of 10: \(4.8 \times 10^4 = 0.48 \times 10^5\). Add coefficients: \((3.2 + 0.48) \times 10^5 = 3.68 \times 10^5\).
10Find the quotient of \(\frac{7.2 \times 10^8}{1.8 \times 10^{-3}}\), expressed in scientific notation.
A.\(4.0 \times 10^{11}\)
B.\(4.0 \times 10^5\)
C.\(4.0 \times 10^{-24}\)
D.\(5.4 \times 10^{11}\)
Explanation: Divide coefficients: \(\frac{7.2}{1.8} = 4.0\). Subtract exponents: \(8 - (-3) = 8 + 3 = 11\). Thus, the answer is \(4.0 \times 10^{11}\).

About the MCAP Grade 8 Math Exam

The Grade 8 assessment is available in English and Spanish. This is an English-language MCQ adaptation, not an official translation or format simulation; it does not replace equation entry, modeling, or constructed reasoning.

Exam sponsor: Maryland State Department of Education (MSDE). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Four sections using selected-response, equation-entry, constructed-response, and technology-enhanced tasks.

Time Limit

Four 40-minute sections (160 minutes total)

Passing Score

Not a pass/fail exam; results are reported in performance levels.

Exam / Certification Fees

No individual candidate fee; administered through eligible Maryland schools.

Exam sponsor website

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

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.

2 operational items

The Number System

Irrational numbers and decimal expansions.

10 operational items

Expressions and Equations

Exponents, equations, systems, and linear relationships.

5 operational items

Functions

Function concepts, comparison, and modeling.

4 operational items

Geometry

Transformations, similarity, Pythagorean theorem, and volume.

2 operational items

Statistics and Probability

Bivariate data and association.

6 items each

Mathematical Reasoning and Modeling

Reasoning and application/modeling across content domains.

Preparing for the MCAP Grade 8 Math Exam

What You Need to Know

  • Passing score: Not a pass/fail exam; results are reported in performance levels.
  • Assessment: Four sections using selected-response, equation-entry, constructed-response, and technology-enhanced tasks.
  • Time limit: Four 40-minute sections (160 minutes total)
  • Exam / certification fees: No individual candidate fee; administered through eligible Maryland schools. Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

MCAP Grade 8 Math: Suggested Study Strategy

1Show reasoning for multi-step problems.
2Practice equation-entry and modeling tasks.
3Review the official blueprint.

Frequently Asked Questions

How long is it?

Four 40-minute sections in the Spring 2026 manual.

Is there one fixed question count?

No; computer-adaptive forms vary and field-test items may be included.

What languages are official?

English and Spanish versions are available; this site keeps one English-language MCQ bank.