100+ Free Vermont Comprehensive Assessment Program Mathematics Grade 7 Practice Questions
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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?
2What is the value of -8 + 15?
3Simplify the expression: 4x + 7x - 3x
4Two angles are complementary. If one angle measures 35°, what is the measure of the other angle?
5A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of randomly choosing a blue marble?
6What is 20% of 80?
7Convert the fraction 3/4 to a decimal.
8Solve for x: x + 9 = 23
9Find the area of a circle with a radius of 5 cm. (Use π ≈ 3.14)
10An event has a probability of 0.95. Which word best describes the likelihood of this event occurring?
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
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.
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.
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.
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.
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.
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
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.