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100+ Free Vermont Comprehensive Assessment Program Mathematics Grade 7 Practice Questions

Prepare for the Vermont Comprehensive Assessment Program Mathematics — Grade 7 exam with instant access — no signup required.

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2026 Statistics

Key Facts: Vermont Comprehensive Assessment Program Mathematics Grade 7 Exam

VT AOE

State Agency

Vermont Agency of Education

Grade 7

Target Grade

VTCAP Test Specifications, Spring 2026

40 (adaptive)

Operational Items

VTCAP Test Specifications, Spring 2026

1750 scale score

Proficiency Cut

VTCAP Score Interpretation Guide, Spring 2026

100 Practice Items

Practice Bank

OpenExamPrep Bank

Cognia

Assessment Vendor

Vermont AOE Portal

Comprehensive 100-question practice test for Vermont's VTCAP Grade 7 Mathematics assessment. Features authentic word problems, accurate calculations, multi-step problem solving, and detailed worked solutions. These are English-language multiple-choice study items; the official test is adaptive, is offered in five translated languages besides English, and includes human-scored constructed responses that multiple-choice practice cannot replace.

Sample Vermont Comprehensive Assessment Program Mathematics Grade 7 Practice Questions

Try these sample questions to test your Vermont Comprehensive Assessment Program Mathematics Grade 7 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A car travels 120 miles in 2 hours at a constant speed. What is the unit rate of the car in miles per hour?
A.50 mph
B.60 mph
C.70 mph
D.240 mph
Explanation: To find the unit rate in miles per hour, divide the total distance by the total time: 120 miles ÷ 2 hours = 60 miles per hour.
2What is the value of -8 + 15?
A.-23
B.-7
C.7
D.23
Explanation: When adding integers with different signs, subtract the smaller absolute value from the larger absolute value (15 - 8 = 7) and keep the sign of the number with the larger absolute value, which is positive 15. Thus, -8 + 15 = 7.
3Simplify the expression: 4x + 7x - 3x
A.8x
B.10x
C.11x
D.14x
Explanation: Combine like terms by adding and subtracting their coefficients: (4 + 7 - 3)x = (11 - 3)x = 8x.
4Two angles are complementary. If one angle measures 35°, what is the measure of the other angle?
A.55°
B.65°
C.145°
D.155°
Explanation: Complementary angles sum to 90°. To find the missing angle, subtract 35° from 90°: 90° - 35° = 55°.
5A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of randomly choosing a blue marble?
A.1/5
B.3/10
C.1/2
D.3/5
Explanation: The total number of marbles is 3 + 5 + 2 = 10. The number of blue marbles is 5. The probability is 5/10, which simplifies to 1/2.
6What is 20% of 80?
A.4
B.16
C.20
D.40
Explanation: Convert 20% to a decimal (0.20) and multiply by 80: 0.20 × 80 = 16.
7Convert the fraction 3/4 to a decimal.
A.0.34
B.0.70
C.0.75
D.0.80
Explanation: Divide the numerator by the denominator: 3 ÷ 4 = 0.75.
8Solve for x: x + 9 = 23
A.12
B.14
C.22
D.32
Explanation: Subtract 9 from both sides of the equation: x = 23 - 9 = 14.
9Find the area of a circle with a radius of 5 cm. (Use π ≈ 3.14)
A.15.7 cm²
B.31.4 cm²
C.78.5 cm²
D.314 cm²
Explanation: The formula for the area of a circle is A = πr². Substituting r = 5: A = 3.14 × 5² = 3.14 × 25 = 78.5 cm².
10An event has a probability of 0.95. Which word best describes the likelihood of this event occurring?
A.Impossible
B.Unlikely
C.Equally likely as not
D.Likely
Explanation: A probability of 0.95 is very close to 1 (certainty), so the event is described as highly likely.

About the Vermont Comprehensive Assessment Program Mathematics Grade 7 Exam

The VTCAP Grade 7 Mathematics assessment measures student proficiency in proportional reasoning, rational number operations, algebraic expressions and linear equations, geometric measurement, and statistics/probability.

Assessment

The official VTCAP Grade 7 mathematics test is computer-adaptive, delivered in two sessions, and reports three content indicators — Ratios and Proportional Relationships; The Number System with Expressions and Equations; Geometry with Statistics and Probability — plus 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-entry items, or the four constructed-response tasks.

Time Limit

Untimed; scheduling estimate is two sessions totalling about 115-125 minutes

Passing Score

Not pass/fail. Grade 7 mathematics scale score ranges are Level 1 (1500-1685), Level 2 (1686-1749), Level 3 (1750-1810) and Level 4 (1811-2000); 1750 and above (Level 3+) indicates grade-level proficiency.

Exam Fee

No fee to public school students (Vermont Agency of Education (AOE) & Cognia)

Vermont Comprehensive Assessment Program Mathematics Grade 7 Exam Content Outline

15-30%

Expressions & Equations

Target 8-16 of 54 operational points. Linear expression simplification, factoring, expanding, multi-step equations (px + q = r and p(x + q) = r), and two-step linear inequalities.

19-22%

Statistics & Probability

Target 10-12 of 54 operational points. Population sampling, comparing distributions using mean/MAD/median/IQR, theoretical and experimental probability, compound events, and tree diagrams.

15-22%

Ratios & Proportional Relationships

Target 8-12 of 54 operational points. Unit rates, ratio tables, constant of proportionality, graphing proportions, percents, discounts, markups, tax, tip, simple interest, and percent error.

11-19%

Geometry

Target 6-10 of 54 operational points. Scale drawings, area and circumference of circles, angle relationships (complementary, supplementary, vertical), surface area, volume, and 3D cross-sections.

11%

Rational Numbers & The Number System

Target 6 of 54 operational points. Addition, subtraction, multiplication, and division of signed integers and fractions, number line models, absolute value distance, and fraction-decimal conversions.

11%

Constructed Response — Mathematical Practices

6 of 54 operational points scored on the Mathematical Practices rubric across the four human-scored constructed-response items.

How to Pass the Vermont Comprehensive Assessment Program Mathematics Grade 7 Exam

What You Need to Know

  • Passing score: Not pass/fail. Grade 7 mathematics scale score ranges are Level 1 (1500-1685), Level 2 (1686-1749), Level 3 (1750-1810) and Level 4 (1811-2000); 1750 and above (Level 3+) indicates grade-level proficiency.
  • Assessment: The official VTCAP Grade 7 mathematics test is computer-adaptive, delivered in two sessions, and reports three content indicators — Ratios and Proportional Relationships; The Number System with Expressions and Equations; Geometry with Statistics and Probability — plus 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-entry items, or the four constructed-response tasks.
  • Time limit: Untimed; scheduling estimate is two sessions totalling about 115-125 minutes
  • Exam fee: No fee to public school 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

Vermont Comprehensive Assessment Program Mathematics Grade 7 Study Tips from Top Performers

1Master integer sign rules (+ and -) and operations with positive and negative fractions.
2Set up proportions using cross-multiplication or unit rates for percent and scaling word problems.
3Practice solving two-step equations and remembering to flip the inequality sign when multiplying or dividing by a negative number.
4Know circle formulas: Circumference C = pi * d = 2 * pi * r and Area A = pi * r^2.

Frequently Asked Questions

What is VTCAP Math Grade 7?

VTCAP is Vermont's annual spring assessment program measuring 7th grade mathematics proficiency against the Common Core State Standards, administered by the Vermont Agency of Education with Cognia.

Are calculators allowed on VTCAP Grade 7 Math?

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.

How are VTCAP Math performance levels defined?

On a 1500-2000 scale in four performance levels describing emerging (Level 1), partial (Level 2), satisfactory (Level 3) and thorough (Level 4) understanding. For Grade 7 mathematics, Level 3 begins at 1750 and Level 4 at 1811.

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.