100+ Free New Hampshire NH SAS Mathematics Grade 8 Practice Questions

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Key Facts: New Hampshire NH SAS Mathematics Grade 8 Exam

NHDOE

State Agency

New Hampshire Department of Education, Office of Assessment

34 operational items (38-42 total)

Official Test Length

NH SAS 2022-23 Technical Report Vol. 2 Part 1

2 hr 15 min

Estimated Testing Time

NH SAS Test Administration Manual, Table 2

English and Spanish

Delivery Languages

NH SAS Test Administration Manual

100 practice questions

Practice Bank Size

OpenExamPrep

Prepare for the NH SAS Math Grade 8 test with 100 practice questions weighted to the official blueprint — Expressions, Equations and the Number System 29-38%, Functions 24-29%, and Geometry with Statistics 38-47% — with worked explanations for every answer.

Sample New Hampshire NH SAS Mathematics Grade 8 Practice Questions

Try these sample questions to test your New Hampshire NH SAS Mathematics 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 irrational?

A.0.\overline{3}

B.\sqrt{16}

C.\sqrt{2}

D.\frac{5}{8}

Explanation: An irrational number cannot be written as a ratio of two integers and has a decimal expansion that never terminates or repeats. The square root of 2 is not a perfect square, so \sqrt{2} cannot be expressed as a fraction and is irrational. The other choices are rational: 0.\overline{3}=\frac{1}{3}, \sqrt{16}=4, and \frac{5}{8}=0.625.

2Which decimal is a repeating decimal?

A.0.25

B.0.375

C.0.\overline{6}

D.0.625

Explanation: A repeating decimal has one or more digits that repeat forever. The bar over the 6 in 0.\overline{6} means 6 repeats without end, so it equals \frac{6}{9}=\frac{2}{3}. The other decimals terminate after a fixed number of digits.

3Which value is the best approximation of \sqrt{2}?

A.1.14

B.1.41

C.1.73

D.2.00

Explanation: Since 1.4^2=1.96 and 1.5^2=2.25, \sqrt{2} lies between 1.4 and 1.5. A more accurate value is 1.414..., so 1.41 is the best approximation. The value 1.73 approximates \sqrt{3}, not \sqrt{2}.

4What fraction is equal to 0.\overline{7}?

A.\frac{7}{10}

B.\frac{7}{9}

C.\frac{7}{100}

D.\frac{70}{99}

Explanation: For a one-digit repeating decimal 0.\overline{7}, let x = 0.7777...; then 10x = 7.7777..., so 10x - x = 7, giving 9x = 7 and x = \frac{7}{9}. The denominator is 9 (one 9 per repeating digit).

5What fraction is equal to 0.\overline{45}?

A.\frac{45}{100}

B.\frac{5}{11}

C.\frac{45}{990}

D.\frac{5}{99}

Explanation: For the two-digit repeating decimal 0.\overline{45}, let x = 0.454545...; then 100x = 45.4545..., so 99x = 45 and x = \frac{45}{99} = \frac{5}{11}. The denominator uses one 9 for each repeating digit, then simplify.

6Between which two consecutive integers does \sqrt{10} lie?

A.2 and 3

B.3 and 4

C.4 and 5

D.5 and 6

Explanation: Since 3^2 = 9 and 4^2 = 16, \sqrt{10} falls between 3 and 4 because 10 is between 9 and 16. A closer estimate is \sqrt{10}\approx 3.16, which confirms this interval.

7Which statement about \sqrt{7} and 2.6 is true?

A.\sqrt{7} < 2.6

B.\sqrt{7} > 2.6

C.\sqrt{7} = 2.6

D.\sqrt{7} < 2.5

Explanation: Square 2.6 to compare: 2.6^2 = 6.76, which is less than 7, so \sqrt{7} > 2.6. A decimal estimate is \sqrt{7}\approx 2.646, confirming it is just above 2.6.

8What is the value of \sqrt{3} to the nearest hundredth?

A.1.41

B.1.73

C.2.44

D.2.73

Explanation: Since 1.7^2 = 2.89 and 1.8^2 = 3.24, \sqrt{3} is between 1.7 and 1.8. Refining gives \sqrt{3}\approx 1.732, which rounds to 1.73 to the nearest hundredth.

9What fraction is equal to 0.\overline{27}?

A.\frac{27}{100}

B.\frac{3}{11}

C.\frac{27}{999}

D.\frac{3}{37}

Explanation: Let x = 0.272727..., so 100x = 27.272727... and 99x = 27, giving x = \frac{27}{99} = \frac{3}{11}. Two repeating digits means a denominator of 99, then simplify by dividing by 9.

10Which list shows the numbers in order from least to greatest?

A.\sqrt{2},\ \sqrt{3},\ \sqrt{5},\ 2.5

B.\sqrt{5},\ \sqrt{3},\ \sqrt{2},\ 2.5

C.2.5,\ \sqrt{5},\ \sqrt{3},\ \sqrt{2}

D.\sqrt{2},\ 2.5,\ \sqrt{3},\ \sqrt{5}

Explanation: Approximate each root: \sqrt{2}\approx 1.41, \sqrt{3}\approx 1.73, \sqrt{5}\approx 2.24, and 2.5. Ordering these gives \sqrt{2} < \sqrt{3} < \sqrt{5} < 2.5, which matches the first list.

About the New Hampshire NH SAS Mathematics Grade 8 Exam

The New Hampshire Statewide Assessment System (NH SAS) Mathematics assessment at Grade 8 measures proficiency on the New Hampshire College and Career Ready Standards. It is a computer-adaptive test administered online through the NH SAS Portal (Cambium Assessment) each spring, and NHDOE offers a Spanish presentation of the Mathematics session in addition to English. This 100-question practice bank is an English-language four-option MCQ study adaptation weighted to the official reporting categories.

Assessment

One online computer-adaptive Mathematics session delivered through the NH SAS Portal (Cambium Assessment), drawing 34 operational items from a grade-level pool plus 6-8 embedded field-test items. This local bank contains 100 English four-option practice MCQs across the three official reporting categories.

Time Limit

Not timed; NHDOE estimates 2 hours 15 minutes

Passing Score

No pass mark. Four achievement levels are reported (Level 1 through Level 4); Levels 3 and 4 count as proficient and above. Scale score ranges differ by grade and subject.

Exam Fee

No fee to students (New Hampshire Department of Education (NHDOE))

New Hampshire NH SAS Mathematics Grade 8 Exam Content Outline

29-38%

Expressions and Equations, and the Number System

Rational and irrational numbers, repeating decimals, integer exponents, roots, scientific notation, proportional graphs and slope, and linear equations and systems.

24-29%

Functions

Definition of a function, comparing representations, linear versus nonlinear, rate of change and initial value, modelling linear relationships, and qualitative graph description.

38-47%

Geometry, and Statistics and Probability

Transformations and congruence, dilations and similarity, angle relationships, the Pythagorean Theorem, coordinate distance, volume of cones, cylinders and spheres, scatter plots, lines of best fit, and two-way tables.

How to Pass the New Hampshire NH SAS Mathematics Grade 8 Exam

What You Need to Know

Passing score: No pass mark. Four achievement levels are reported (Level 1 through Level 4); Levels 3 and 4 count as proficient and above. Scale score ranges differ by grade and subject.
Assessment: One online computer-adaptive Mathematics session delivered through the NH SAS Portal (Cambium Assessment), drawing 34 operational items from a grade-level pool plus 6-8 embedded field-test items. This local bank contains 100 English four-option practice MCQs across the three official reporting categories.
Time limit: Not timed; NHDOE estimates 2 hours 15 minutes
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

New Hampshire NH SAS Mathematics Grade 8 Study Tips from Top Performers

1Memorize the exponent rules as one system: same base means add, subtract, or multiply exponents.

2Convert to and from scientific notation by counting decimal places, then check the sign of the exponent.

3Test whether a relation is a function by asking whether any input appears twice with different outputs.

4Draw the right triangle before applying the Pythagorean Theorem to a coordinate or real-world problem.

5On a scatter plot, describe direction, form, and strength before you interpret the line of best fit.

Frequently Asked Questions

What is the NH SAS Math Grade 8 test?

It is the New Hampshire Statewide Assessment System Mathematics assessment for Grade 8, a computer-adaptive test administered online through the NH SAS Portal (Cambium Assessment) each spring.

How many questions are on the real NH SAS Math test?

The published blueprint sets 34 operational items plus 6-8 embedded field-test items, about 38-42 items in total. Because the test is computer-adaptive, the exact items differ from student to student.

Is the NH SAS Math test only multiple choice?

No. Alongside multiple-choice and multiple-select items, students construct equations, plot on grids, and complete tables. This practice bank uses four-option MCQs as a study aid, not as a format simulation.

Is the NH SAS Math test available in Spanish?

Yes. NHDOE offers a Spanish presentation for the Mathematics and Science sessions, with a toggle back to English. This practice bank is English-language only.

How are NH SAS results reported?

There is no pass mark. NHDOE reports four achievement levels (Level 1 through Level 4), with Levels 3 and 4 counted as proficient and above.

100+ Free New Hampshire NH SAS Mathematics Grade 8 Practice Questions

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