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100+ Free VTCAP Math Grade 9 Practice Questions

Prepare for the Vermont Comprehensive Assessment Program Mathematics Grade 9 exam with instant access — no signup required.

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2026 Statistics

Key Facts: VTCAP Math Grade 9 Exam

39-45 (adaptive)

Operational items on the real test

VTCAP Test Specifications, Spring 2026

45 points

Operational points on the Grade 9 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

Grade 9

Highest grade Vermont assesses in mathematics

VTCAP Test Specifications, Spring 2026

100

Practice questions in this free bank

OpenExamPrep Bank

VTCAP Math Grade 9 is Vermont's untimed, computer-adaptive spring mathematics assessment for 9th graders — the last grade Vermont tests in math — worth 45 operational points and reported on a 1500-2000 scale with 1750 marking proficiency. This free bank is 100 English-language multiple-choice study questions; the official test is also offered in five translated languages and is adaptive rather than fixed-form.

Sample VTCAP Math Grade 9 Practice Questions

Try these sample questions to test your VTCAP Math Grade 9 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Solve for x: 2x + 7 = 19
A.x = 6
B.x = 13
C.x = 12
D.x = 5
Explanation: Subtract 7 from both sides: 2x = 12. Then divide by 2: x = 6.
2Solve for x: 5x - 4 = 21
A.x = 17/5
B.x = 5
C.x = 25
D.x = -5
Explanation: Add 4 to both sides: 5x = 25. Divide by 5: x = 5.
3Solve for x: -3x + 10 = 1
A.-11/3
B.-3
C.3
D.9
Explanation: Subtract 10 from both sides: -3x = -9. Divide by -3: x = 3.
4Solve the inequality: 4x - 3 > 9
A.x > 3
B.x < 3
C.x > 12
D.x > 1.5
Explanation: Add 3 to both sides: 4x > 12. Divide by 4: x > 3.
5Find the slope of the line passing through points (1, 3) and (4, 9).
A.1/2
B.2
C.6
D.3
Explanation: Slope m = (y2 - y1) / (x2 - x1) = (9 - 3) / (4 - 1) = 6 / 3 = 2.
6What is the y-intercept of the line y = -4x + 7?
A.-4
B.-7
C.7
D.(7, 0)
Explanation: In slope-intercept form y = mx + b, b represents the y-intercept. Here b = 7.
7Which equation represents a line with a slope of 3 and a y-intercept of -5?
A.y = -5x + 3
B.y = 3x - 5
C.y = 3x + 5
D.y = 5x - 3
Explanation: Using slope-intercept form y = mx + b with m = 3 and b = -5 gives y = 3x - 5.
8If f(x) = 4x - 9, what is the value of f(5)?
A.11
B.20
C.29
D.1
Explanation: Substitute x = 5: f(5) = 4(5) - 9 = 20 - 9 = 11.
9If g(x) = -x + 12, what is g(-4)?
A.8
B.-16
C.16
D.4
Explanation: Substitute x = -4: g(-4) = -(-4) + 12 = 4 + 12 = 16.
10Which set of ordered pairs represents a function?
A.{(1, 2), (1, 3), (2, 4)}
B.{(0, 1), (0, 2), (0, 3)}
C.{(1, 2), (2, 3), (3, 4)}
D.{(4, 5), (4, 6), (5, 7)}
Explanation: A relation is a function if every x-value (domain element) maps to exactly one y-value. In {(1, 2), (2, 3), (3, 4)}, all x-values (1, 2, 3) are distinct.

About the VTCAP Math Grade 9 Exam

The Vermont Comprehensive Assessment Program (VTCAP) Mathematics Grade 9 assessment evaluates student proficiency against a prioritized subset of the high school Common Core State Standards, spanning Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability. Grade 9 is the final grade at which Vermont assesses mathematics.

Assessment

The official VTCAP Grade 9 mathematics test is computer-adaptive, delivered in two sessions, and reports four content indicators: Number and Quantity/Algebra, Algebra/Functions, Geometry, and Statistics and Probability. Machine-scored items target 0-30% DOK 1, 25-80% DOK 2 and 0-5% DOK 3. Unlike Grades 3-8 there are no human-scored constructed responses; multi-part machine-scored items carry 2 or 3 points instead. Our practice bank provides 100 multiple-choice items at easy (30%), medium (50%) and hard (20%) difficulty and does not reproduce the adaptive engine or equation-entry items.

Time Limit

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

Passing Score

Not pass/fail. Grade 9 mathematics scale score ranges are Level 1 (1500-1654), Level 2 (1655-1749), Level 3 (1750-1861) and Level 4 (1862-2000); 1750 and above (Level 3+) indicates grade-level proficiency.

Exam Fee

Free for eligible Vermont public school students; VTCAP is state-mandated and state-funded. (Vermont Agency of Education (AOE) in partnership with Cognia)

VTCAP Math Grade 9 Exam Content Outline

31-40%

Algebra / Functions

Target 14-18 of 45 operational points. Function notation, quadratic graphs, factoring, the quadratic formula, exponential growth and decay, and sequences.

20-29%

Geometry

Target 9-13 of 45 operational points. Pythagorean theorem, distance formula, midpoint, transformations, perimeter, area, surface area, and volume.

18-27%

Number and Quantity / Algebra

Target 8-12 of 45 operational points. Quantities and units, radicals and rational exponents, multi-step equations and inequalities, absolute value, slope-intercept form, and systems of equations.

13-20%

Statistics and Probability

Target 6-10 of 45 operational points. Measures of central tendency and spread, box plots, scatter plots, trend lines, residual analysis, and two-way frequency tables.

How to Pass the VTCAP Math Grade 9 Exam

What You Need to Know

  • Passing score: Not pass/fail. Grade 9 mathematics scale score ranges are Level 1 (1500-1654), Level 2 (1655-1749), Level 3 (1750-1861) and Level 4 (1862-2000); 1750 and above (Level 3+) indicates grade-level proficiency.
  • Assessment: The official VTCAP Grade 9 mathematics test is computer-adaptive, delivered in two sessions, and reports four content indicators: Number and Quantity/Algebra, Algebra/Functions, Geometry, and Statistics and Probability. Machine-scored items target 0-30% DOK 1, 25-80% DOK 2 and 0-5% DOK 3. Unlike Grades 3-8 there are no human-scored constructed responses; multi-part machine-scored items carry 2 or 3 points instead. Our practice bank provides 100 multiple-choice items at easy (30%), medium (50%) and hard (20%) difficulty and does not reproduce the adaptive engine or equation-entry items.
  • Time limit: Untimed; scheduling estimate is two sessions totalling about 120-130 minutes
  • Exam fee: Free for eligible Vermont public school students; VTCAP is state-mandated and state-funded.

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 9 Study Tips from Top Performers

1Master solving multi-step linear equations, clearing fractions, and applying the distributive property.
2Understand slope as rate of change and be comfortable converting between slope-intercept, point-slope, and standard forms.
3Practice solving systems of equations using substitution, elimination, and graphing in real-world contexts.
4Review factoring quadratics, finding roots, and using the quadratic formula — Algebra/Functions is the largest reporting category at Grade 9.
5Understand exponential functions y = a(b)^x, distinguishing between growth (b > 1) and decay (0 < b < 1).
6Work on statistical measures like mean, median, interquartile range (IQR), and interpreting box plots and scatter plots.

Frequently Asked Questions

What is VTCAP Math Grade 9?

VTCAP Math Grade 9 is Vermont's statewide summative mathematics assessment for 9th grade students, administered annually each spring. Grade 9 is the highest grade at which Vermont assesses mathematics.

What content is tested on VTCAP Grade 9 Math?

A prioritized subset of the high school Common Core standards, reported as Number and Quantity/Algebra (18-27% of points), Algebra/Functions (31-40%), Geometry (20-29%), and Statistics and Probability (13-20%).

How is VTCAP Grade 9 Math scored?

On a 1500-2000 scale placed into four performance levels describing emerging (Level 1), partial (Level 2), satisfactory (Level 3) and thorough (Level 4) understanding. For Grade 9 mathematics, Level 3 begins at 1750 and Level 4 at 1862.

Is a calculator allowed on VTCAP Math Grade 9?

On some sessions but not others. Desmos calculators are embedded universal tools 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, Grade 9 students may use a graphing calculator.

How long is the VTCAP Grade 9 Math assessment?

Sessions are not timed. The published scheduling estimate is two sessions totalling about 120-130 minutes.

Is there a fee for taking the VTCAP Math test?

No, VTCAP is a state-funded assessment administered at no cost to Vermont public school students.

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.