100+ Free KSA Math Grade 8 Practice Questions

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Sample KSA Math Grade 8 Practice Questions

Try these sample questions to test your KSA Math Grade 8 exam readiness. 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.

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 Fee

No separate student fee; Kentucky's public-school accountability assessment is state funded. (Kentucky Department of Education (KDE))