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100+ Free VTCAP Math Grade 8 Practice Questions

Prepare for the Vermont Comprehensive Assessment Program Mathematics Grade 8 exam with instant access — no signup required.

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Not published as a pass rate. Statewide mathematics proficiency ranged from 33% to 48% across Grades 3-9 in 2024-2025 (Vermont AOE). Pass Rate
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2026 Statistics

Key Facts: VTCAP Math Grade 8 Exam

41 (adaptive)

Operational items on the real test

VTCAP Test Specifications, Spring 2026

55 points

Operational points on the Grade 8 mathematics form

VTCAP Test Specifications, Spring 2026

1750

Scale score marking Level 3 proficiency

VTCAP Score Interpretation Guide, Spring 2026

Untimed

Test sessions are not timed

VTCAP Test Administrator's Manual, Spring 2026

100

Practice questions in this free bank

OpenExamPrep Bank

The VTCAP Grade 8 Math exam is untimed and computer-adaptive, worth 55 operational points weighted to Expressions & Equations (20-31%), Functions (18-29%), Geometry (18-29%), Statistics & Probability (18-22%) and The Number System (7%), with 1750 marking Level 3 proficiency. This practice bank features 100 English-language four-option questions with step-by-step worked solutions and distractor rationale; it does not reproduce the adaptive engine or the human-scored constructed responses.

Sample VTCAP Math Grade 8 Practice Questions

Try these sample questions to test your VTCAP 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.√7
B.3/4
C.0.25
D.√16
Explanation: An irrational number cannot be expressed as a simple fraction a/b where a and b are integers. √7 is non-terminating and non-repeating because 7 is not a perfect square. In contrast, 3/4 is a fraction, 0.25 = 1/4, and √16 = 4, all of which are rational.
2What is the principal square root of 81?
A.9
B.8.1
C.18
D.40.5
Explanation: The principal square root of a number is its non-negative square root. Since 9 × 9 = 81, √81 = 9.
3Simplify the expression: 5³ × 5⁴
A.5¹²
B.5⁷
C.25⁷
D.25¹²
Explanation: According to the product rule of exponents (aᵐ × aⁿ = aᵐ⁺ⁿ), when multiplying powers with the same base, add the exponents: 5³⁺⁴ = 5⁷.
4What is the value of 8⁰ + 2³?
A.9
B.8
C.11
D.0
Explanation: Any non-zero number raised to the power of 0 equals 1, so 8⁰ = 1. Also, 2³ = 2 × 2 × 2 = 8. Adding them gives 1 + 8 = 9.
5Write the number 45,000 in scientific notation.
A.4.5 × 10⁴
B.45 × 10³
C.0.45 × 10⁵
D.4.5 × 10⁻⁴
Explanation: Scientific notation has the form a × 10ⁿ where 1 ≤ a < 10. Moving the decimal point 4 places to the left gives 4.5, so 45,000 = 4.5 × 10⁴.
6Simplify the expression: x⁹ / x³
A.
B.x⁶
C.x¹²
D.x²⁷
Explanation: Using the quotient rule of exponents (xᵐ / xⁿ = xᵐ⁻ⁿ), subtract the denominator exponent from the numerator exponent: x⁹⁻³ = x⁶.
7What is the slope of the line given by the equation y = -3x + 7?
A.7
B.-3
C.3
D.-3/7
Explanation: In slope-intercept form y = mx + b, m represents the slope. Here m = -3 and b = 7.
8If 4 notebooks cost $12.00, what is the unit price per notebook?
A.$3.00
B.$4.00
C.$0.33
D.$8.00
Explanation: To find the unit price, divide total cost by the number of units: $12.00 / 4 = $3.00 per notebook.
9Solve for x: 2x + 5 = 15
A.x = 10
B.x = 5
C.x = 7.5
D.x = 20
Explanation: Subtract 5 from both sides: 2x = 10. Divide by 2: x = 5.
10What is the standard decimal form of 3.2 × 10⁻³?
A.0.0032
B.0.032
C.0.00032
D.-3200
Explanation: A negative exponent of -3 moves the decimal point 3 places to the left: 3.2 → 0.32 → 0.032 → 0.0032.

About the VTCAP Math Grade 8 Exam

The Vermont Comprehensive Assessment Program (VTCAP) Mathematics Grade 8 assessment evaluates student mastery of Grade 8 standards, including real number systems, linear equations, functions, geometric transformations, the Pythagorean theorem, 3D geometry, and bivariate statistics.

Assessment

The official VTCAP Grade 8 mathematics test is computer-adaptive, delivered in two sessions, and reports two content indicators — Functions, and The Number System with Expressions and Equations — plus Geometry with Statistics and Probability and two Mathematical Practices indicators. Machine-scored items target 0-30% DOK 1, 50-80% DOK 2 and 5-30% DOK 3. Our practice bank provides 100 multiple-choice items at easy (30%), medium (50%) and hard (20%) difficulty; it does not reproduce the adaptive engine, equation-editor items, or the four constructed-response tasks.

Time Limit

Untimed; scheduling estimate is two sessions totalling about 120-130 minutes

Passing Score

Not pass/fail. Grade 8 mathematics scale score ranges are Level 1 (1500-1644), Level 2 (1645-1749), Level 3 (1750-1855) and Level 4 (1856-2000); 1750 and above (Level 3+) indicates grade-level proficiency.

Exam Fee

Free (Vermont Agency of Education in partnership with Cognia)

VTCAP Math Grade 8 Exam Content Outline

20-31%

Expressions & Equations

Target 11-17 of 55 operational points. Apply rules of integer exponents; work with scientific notation; graph proportional relationships and interpret unit rate as slope; solve multi-step linear equations; solve systems of two linear equations in two variables.

18-29%

Functions

Target 10-16 of 55 operational points. Define, evaluate, and compare functions presented algebraically, graphically, numerically, or verbally; model linear functions with y = mx + b; distinguish linear from non-linear functions.

18-29%

Geometry & Pythagorean Theorem

Target 10-16 of 55 operational points. Verify properties of translations, reflections, rotations, and dilations; apply congruence and similarity rules; use the Pythagorean Theorem to find missing side lengths and coordinate distances; compute volumes of cylinders, cones, and spheres.

18-22%

Bivariate Data & Statistics

Target 10-12 of 55 operational points. Construct and interpret scatter plots for bivariate measurement data; fit informal lines of best fit; evaluate linear association; construct and interpret two-way frequency tables.

11%

Constructed Response — Mathematical Practices

6 of 55 operational points scored on the Mathematical Practices rubric across the four human-scored constructed-response items.

7%

The Number System

Target 4 of 55 operational points. Distinguish rational from irrational numbers; approximate irrational numbers using rational numbers; convert repeating decimals to fractions; compute square and cube roots of perfect powers.

How to Pass the VTCAP Math Grade 8 Exam

What You Need to Know

  • Passing score: Not pass/fail. Grade 8 mathematics scale score ranges are Level 1 (1500-1644), Level 2 (1645-1749), Level 3 (1750-1855) and Level 4 (1856-2000); 1750 and above (Level 3+) indicates grade-level proficiency.
  • Assessment: The official VTCAP Grade 8 mathematics test is computer-adaptive, delivered in two sessions, and reports two content indicators — Functions, and The Number System with Expressions and Equations — plus Geometry with Statistics and Probability and two Mathematical Practices indicators. Machine-scored items target 0-30% DOK 1, 50-80% DOK 2 and 5-30% DOK 3. Our practice bank provides 100 multiple-choice items at easy (30%), medium (50%) and hard (20%) difficulty; it does not reproduce the adaptive engine, equation-editor items, or the four constructed-response tasks.
  • Time limit: Untimed; scheduling estimate is two sessions totalling about 120-130 minutes
  • Exam fee: Free

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

VTCAP Math Grade 8 Study Tips from Top Performers

1Practice multi-step linear equations with distributive property and fractions on both sides.
2Master slope-intercept form (y = mx + b), computing slope m = (y2 - y1)/(x2 - x1) and interpreting y-intercept as initial value.
3Apply the Pythagorean theorem a² + b² = c² to right triangles and find distance between points on a coordinate grid using √((x2 - x1)² + (y2 - y1)²).
4Apply exponent rules (product, quotient, power rules, negative exponent a⁻ⁿ = 1/aⁿ) and perform arithmetic in scientific notation.
5Calculate 3D volume using formulas V = πr²h (cylinder), V = (1/3)πr²h (cone), and V = (4/3)πr³ (sphere).

Frequently Asked Questions

What is the VTCAP Grade 8 Mathematics exam?

The VTCAP Grade 8 Math exam is Vermont's statewide summative assessment measuring Grade 8 student achievement against state mathematics standards.

What mathematical domains are evaluated on the test?

Expressions & Equations (20-31% of the 55 operational points), Functions (18-29%), Geometry (18-29%), Statistics & Probability (18-22%) and The Number System (7%), plus 6 points (11%) scored on the Mathematical Practices rubric via constructed responses.

Are calculators allowed on the VTCAP Grade 8 Math test?

On some sessions but not others. Desmos calculators are a universal tool in the online platform, and the Test Administrator's Manual scripts both a calculator-permitted session and a no-calculator session. On paper-based accommodated forms, Grades 6-8 may use scientific calculators only.

What languages is the VTCAP mathematics test available in?

For the 2025-2026 testing cycle the VTCAP mathematics and science assessments are available in Arabic, Chinese, French, Spanish and Swahili as computer-based fixed-form translations, in addition to English. No other translated forms are offered.

How are the questions in this practice bank formatted?

Every question includes 4 plausible options, a single correct answer index, a full step-by-step math explanation, and individual explanations for why each incorrect option is wrong.

What is the difficulty breakdown of the 100 items?

The 100 items are distributed as ~30% easy (30 items), ~50% medium (50 items), and ~20% hard (20 items).