Free Practice Questions for KSA Math Grade 8

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Sample KSA Math Grade 8 Practice Questions

Try these sample questions to review concepts for the KSA Math Grade 8 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.\(\sqrt{11}\)

B.\(3.5\)

C.\(\frac{2}{3}\)

D.\(\sqrt{16}\)

Explanation: \(\sqrt{11}\) is irrational because 11 is not a perfect square, so its decimal expansion is non-repeating and non-terminating.

2What is the repeating decimal \(0.\bar{7}\) expressed as a fraction in simplest form?

A.\(\frac{7}{9}\)

B.\(\frac{7}{10}\)

C.\(\frac{7}{99}\)

D.\(\frac{3}{4}\)

Explanation: Let \(x = 0.\bar{7}\). Multiplying both sides by 10 gives \(10x = 7.\bar{7}\). Subtracting \(x\) yields \(9x = 7\), so \(x = \frac{7}{9}\).

3Which statement correctly classifies √18?

A.It is irrational because √18 = 3√2 and √2 is irrational

B.It is rational because 18 is an integer

C.It is rational because √18 = 9

D.It is irrational because every square root is irrational

Explanation: Since 18 = 9 × 2, √18 = 3√2. Multiplying the irrational number √2 by the nonzero rational number 3 produces an irrational number.

4Which decimal is the best approximation for \(\sqrt{50}\) to the nearest tenth?

A.\(7.1\)

B.\(6.9\)

C.\(7.5\)

D.\(25.0\)

Explanation: Since \(7^2 = 49\) and \(8^2 = 64\), \(\sqrt{50}\) is slightly greater than 7. Squaring \(7.1\) gives \(50.41\), which is extremely close to 50.

5Which list correctly orders the numbers \(3.1\), \(\pi\), \(\sqrt{10}\), and \(\frac{13}{4}\) from least to greatest?

A.\(3.1 < \pi < \sqrt{10} < \frac{13}{4}\)

B.\(3.1 < \sqrt{10} < \pi < \frac{13}{4}\)

C.\(\pi < 3.1 < \sqrt{10} < \frac{13}{4}\)

D.\(\frac{13}{4} < \sqrt{10} < \pi < 3.1\)

Explanation: Converting each to approximate decimal values: \(3.1 = 3.100\), \(\pi \approx 3.14159\), \(\sqrt{10} \approx 3.162\), and \(\frac{13}{4} = 3.250\). Comparing these gives \(3.1 < 3.14159 < 3.162 < 3.250\).

6Which statement is true regarding the expression \(\sqrt{2} + 5\)?

A.It is an irrational number because the sum of an irrational number and a rational number is always irrational.

B.It is a rational number because adding 5 makes the value terminating.

C.It is an integer because 5 is an integer.

D.It is a repeating decimal because \(\sqrt{2}\) has a repeating pattern.

Explanation: The sum of a rational number (5) and an irrational number (\(\sqrt{2}\)) is always irrational.

7What is the repeating decimal \(0.1\bar{6}\) converted into a simplified fraction?

A.\(\frac{1}{6}\)

B.\(\frac{16}{99}\)

C.\(\frac{16}{100}\)

D.\(\frac{1}{5}\)

Explanation: Let \(x = 0.1666...\). Then \(10x = 1.666...\) and \(100x = 16.666...\). Subtracting gives \(90x = 15\), so \(x = \frac{15}{90} = \frac{1}{6}\).

8What is the value of \(\pi^2 + \sqrt{20}\) estimated to the nearest integer?

A.\(14\)

B.\(11\)

C.\(17\)

D.\(24\)

Explanation: Using approximations: \(\pi \approx 3.1416 \Rightarrow \pi^2 \approx 9.87\). Since \(4^2 = 16\) and \(5^2 = 25\), \(\sqrt{20} \approx 4.47\). Adding them gives \(9.87 + 4.47 = 14.34\), which rounds to 14.

9Which number is irrational?

A.√2

B.0.75

C.−4

D.7/9

Explanation: √2 cannot be written as a ratio of integers and has a nonterminating, nonrepeating decimal expansion, so it is irrational.

10Between which two consecutive integers does √50 lie?

A.5 and 6

B.6 and 7

C.7 and 8

D.8 and 9

Explanation: Since 7² = 49 and 8² = 64, and 50 lies between 49 and 64, √50 lies between 7 and 8.

About the KSA Math Grade 8 Exam

Kentucky Summative Assessment Mathematics — Grade 8 measures the Kentucky Academic Standards for Mathematics. This local 100-question bank is an English-language MCQ study adaptation. It does not replace worked solutions, modeling, technology-enhanced tasks, or constructed responses. It is not an official translation, format simulation, or substitute for the KSA.

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

Assessment

The official assessment is administered online at school and uses selected-response, technology-enhanced, and extended-response items, including quantitative reasoning and modeling. No separate assignment, oral examination, practical examination, or case study is required; extended-response and technology-enhanced items remain part of the official assessment.

Time Limit

120 KDE-recommended minutes across 2 parts; this is recommended testing time rather than a candidate-selected appointment limit.

Passing Score

KSA is not a certification exam and has no single pass mark. Results use four performance levels: Novice, Apprentice, Proficient, and Distinguished.

Exam / Certification Fees

No separate student fee; Kentucky's public-school accountability assessment is state funded.

Exam sponsor website

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

Official sources

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.

25–30%

Expressions & Equations