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100+ Free OSTP Math Grade 8 Practice Questions

Prepare for the Oklahoma School Testing Program — Mathematics, Grade 8 exam with instant access — no signup required.

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Key Facts: OSTP Math Grade 8 Exam

OSDE

Administering agency

Oklahoma State Department of Education

Cognia

Testing vendor

OSDE Assessment Materials

50 (+10 field test)

Operational items

Grade 8 Mathematics Test and Item Specifications

Algebraic Reasoning, 44-48%

Largest reporting category

Grade 8 Mathematics Test Blueprint

OPI 200-399; 300 = Proficient

Score scale

OSDE Understanding OSTP Results

Practise for the OSTP Grade 8 Math test with 100 free questions weighted to the official OSDE blueprint, where Algebraic Reasoning and Algebra carries 44-48% of items. This English-language MCQ bank is a study aid, not an official form.

Sample OSTP Math Grade 8 Practice Questions

Try these sample questions to test your OSTP 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.\(\sqrt{45}\)
B.\(\sqrt{49}\)
C.\(\frac{7}{11}\)
D.\(0.85\)
Explanation: \(\sqrt{45} = 3\sqrt{5}\). Since 45 is not a perfect square, its square root cannot be expressed as a ratio of two integers, making it an irrational number with a non-repeating, non-terminating decimal expansion.
2Between which two consecutive integers does \(\sqrt{80}\) lie on a number line?
A.7 and 8
B.8 and 9
C.9 and 10
D.10 and 11
Explanation: Identify perfect squares surrounding 80: \(64 < 80 < 81\). Taking square roots yields \(\sqrt{64} < \sqrt{80} < \sqrt{81}\), which simplifies to \(8 < \sqrt{80} < 9\). Therefore, \(\sqrt{80}\) lies between 8 and 9.
3What is the value of \(\sqrt{120}\) rounded to the nearest tenth?
A.10.5
B.11.0
C.11.5
D.12.0
Explanation: Since \(11^2 = 121\) and 120 is extremely close to 121, \(\sqrt{120} \approx 10.9544\). Rounding 10.9544 to the nearest tenth yields 11.0.
4A square carpet has an area of 135 square feet. Which measurement best estimates the length of one side of the carpet?
A.11.2 ft
B.11.6 ft
C.12.1 ft
D.12.5 ft
Explanation: The side length of a square carpet is \(s = \sqrt{135}\). Since \(11^2 = 121\) and \(12^2 = 144\), \(\sqrt{135}\) is between 11 and 12. Testing \(11.6^2 = 134.56\), 11.6 ft is the closest estimate to \(\sqrt{135}\).
5Which set of numbers is ordered correctly from least to greatest?
A.\(\sqrt{15}, 3.8, \frac{17}{4}, \sqrt{20}\)
B.\(3.8, \sqrt{15}, \frac{17}{4}, \sqrt{20}\)
C.\(\sqrt{15}, 3.8, \sqrt{20}, \frac{17}{4}\)
D.\(3.8, \sqrt{15}, \sqrt{20}, \frac{17}{4}\)
Explanation: Convert each number to decimal form for comparison: \(3.8 = 3.800\), \(\sqrt{15} \approx 3.873\), \(\frac{17}{4} = 4.250\), and \(\sqrt{20} \approx 4.472\). Comparing these decimals shows \(3.800 < 3.873 < 4.250 < 4.472\), so the correct order is \(3.8, \sqrt{15}, \frac{17}{4}, \sqrt{20}\).
6Which interval on the number line contains the value of \(\sqrt{32}\)?
A.Between 4 and 5
B.Between 5 and 6
C.Between 6 and 7
D.Between 7 and 8
Explanation: Check perfect squares around 32: \(5^2 = 25\) and \(6^2 = 36\). Since \(25 < 32 < 36\), taking square roots gives \(5 < \sqrt{32} < 6\). Thus, \(\sqrt{32}\) lies between 5 and 6.
7Converting the repeating decimal \(0.\overline{54}\) into a fraction in simplest form yields which result?
A.\(\frac{6}{11}\)
B.\(\frac{27}{50}\)
C.\(\frac{54}{100}\)
D.\(\frac{5}{9}\)
Explanation: Let \(x = 0.\overline{54}\). Then \(100x = 54.\overline{54}\). Subtracting \(x\) from \(100x\) gives \(99x = 54\), so \(x = \frac{54}{99}\). Dividing numerator and denominator by their greatest common factor, 9, gives \(\frac{6}{11}\).
8A right triangle has legs measuring 7 cm and 11 cm. What is the exact length of the hypotenuse, and is this length rational or irrational?
A.\(\sqrt{170}\) cm, irrational
B.\(\sqrt{170}\) cm, rational
C.13 cm, rational
D.\(\sqrt{18}\) cm, irrational
Explanation: By the Pythagorean theorem, \(c = \sqrt{7^2 + 11^2} = \sqrt{49 + 121} = \sqrt{170}\) cm. Since 170 is not a perfect square, its square root cannot be written as a fraction of integers, making it an irrational number.
9Which of the following numerical expressions simplifies to a rational number?
A.\(\sqrt{18} + \sqrt{2}\)
B.\(\sqrt{12} \cdot \sqrt{3}\)
C.\(\sqrt{20} \div \sqrt{2}\)
D.\(\sqrt{5} + 5\)
Explanation: Multiply radicals: \(\sqrt{12} \cdot \sqrt{3} = \sqrt{12 \times 3} = \sqrt{36} = 6\). Since 6 is an integer, it is a rational number.
10What is the value of \(3.4 \times 10^5\) written in standard decimal notation?
A.34,000
B.340,000
C.3,400,000
D.0.000034
Explanation: Multiplying by \(10^5\) requires moving the decimal point 5 places to the right: \(3.4 \to 340,000\).

About the OSTP Math Grade 8 Exam

The OSTP Grade 8 Mathematics assessment measures proficiency against the Oklahoma Academic Standards Pre-Algebra strands. Nearly half the test is algebraic reasoning — linear functions, slope, systems and function notation — with real numbers and roots, the Pythagorean Theorem and 3-D volume, and bivariate data completing the blueprint.

Assessment

Online fixed-form test in two sections combining multiple-choice items (some linked to a common stimulus) and technology-enhanced items. Blueprint: Algebraic Reasoning and Algebra 44-48%, Geometry and Measurement 18-22%, Number and Operations 16-20%, Data and Probability 14-18%.

Time Limit

Approximately 100 minutes across two sections (suggested maximum 200 minutes); not strictly timed

Passing Score

No pass/fail mark. Reported on the Oklahoma Performance Index (OPI) 200–399 scale, where 300 is always Proficient, in four performance levels: Below Basic, Basic, Proficient, Advanced.

Exam Fee

No fee to students (Oklahoma State Department of Education (OSDE); delivered under contract by Cognia)

OSTP Math Grade 8 Exam Content Outline

44-48%

Algebraic Reasoning and Algebra

Linear and non-linear functions, linear function representations and problem solving, algebraic expressions, and equations and inequalities (PA.A.1-PA.A.4).

18-22%

Geometry and Measurement

The Pythagorean Theorem, and surface area and volume of cylinders, cones and spheres (PA.GM.1-PA.GM.2).

16-20%

Number and Operations

Real number operations, including rational and irrational numbers, square and cube roots, exponents and scientific notation (PA.N.1).

14-18%

Data and Probability

Data analysis and scatter plots, and probability (PA.D.1-PA.D.2).

How to Pass the OSTP Math Grade 8 Exam

What You Need to Know

  • Passing score: No pass/fail mark. Reported on the Oklahoma Performance Index (OPI) 200–399 scale, where 300 is always Proficient, in four performance levels: Below Basic, Basic, Proficient, Advanced.
  • Assessment: Online fixed-form test in two sections combining multiple-choice items (some linked to a common stimulus) and technology-enhanced items. Blueprint: Algebraic Reasoning and Algebra 44-48%, Geometry and Measurement 18-22%, Number and Operations 16-20%, Data and Probability 14-18%.
  • Time limit: Approximately 100 minutes across two sections (suggested maximum 200 minutes); not strictly timed
  • Exam fee: No fee to students

Keys to Passing

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

OSTP Math Grade 8 Study Tips from Top Performers

1Master linear functions: slope from two points, slope-intercept form, converting from standard form, and writing an equation from a table or context.
2Practise solving systems by substitution and elimination and interpreting the number of solutions from slopes and intercepts.
3Review the Pythagorean Theorem in both geometric and coordinate-distance settings, and volume of cylinders, cones and spheres.
4Work with rational and irrational numbers, square and cube roots, exponent rules and scientific notation arithmetic.
5Practise scatter plots, lines of best fit, residuals and two-way frequency tables including conditional relative frequency.

Frequently Asked Questions

How many questions are on the official OSTP Grade 8 Math test?

The official test contains 50 operational items plus 10 field-test items, for 60 items in total across two sections. Only the 50 operational items contribute to the scaled score.

Do Grade 8 students taking Algebra I still sit the Grade 8 Math test?

Yes. Eighth graders enrolled in Algebra I still take the OSTP Grade 8 Mathematics assessment.

Is a calculator allowed in Grade 8 mathematics?

Yes. For Grades 6-8 mathematics OSDE provides a formula sheet and an online calculator in the testing toolbox, and students may also use an approved handheld calculator. Scientific calculators are also permitted in Grade 8 science.

Is there a passing score?

No. Results are reported on the Oklahoma Performance Index scale of 200–399, where 300 is always Proficient, and in four performance levels: Below Basic, Basic, Proficient and Advanced.

How hard are the items?

The Grade 8 test and item specifications target roughly 10-20% Depth of Knowledge Level 1 (recall), 65-75% Level 2 (skills and concepts) and 15-25% Level 3 (strategic thinking).