VTCAP Grade 9 Number and Quantity/Algebra. Practice it free.

High school number/quantity and algebra content reported as the 'Number and Quantity/Algebra' performance indicator; blueprint target: 8-12 points (18-27% of the grade 9 test). The grade 9 Performance Level Descriptors publish the assessed focus areas listed below; they are placed under this slash-named category by their CCSS conceptual category (Number and Quantity, Algebra). This Grade 9 reporting domain maps to 54 practice skills and 8 representative questions from the playable bank.

Grade 954 mapped skills
What the test measures

Number and Quantity/Algebra skills

  1. The Real Number System

  2. Quantities

  3. Seeing Structure in Expressions

  4. Creating Equations

  5. Reasoning with Equations and Inequalities

  6. Arithmetic with Polynomials and Rational Expressions

Standards basis

Common Core State Standards for Mathematics (CCSS-M) — Vermont

How the VTCAP reports it

Vermont administered the Smarter Balanced summative through spring 2022, then replaced it with the Cognia-developed Vermont Comprehensive Assessment Program (VTCAP) beginning spring 2023 — this landing slug predates the switch. VTCAP mathematics is an adaptive, CCSS-M-aligned assessment in grades 3-9. It is NOT a Smarter Balanced administration: its reporting categories are groupings of the CCSS grade-level domains (e.g. 'The Number System, Expressions and Equations'), not SBAC claims, though two cross-grade Mathematical Practices indicators ('Problem Solving, Reasoning, and Argument'; 'Modeling, Patterns, and Structure') echo the old claim structure. Per the test specifications, the grades 3-8 test may assess any CCSS-M standard at the grade; the grade 9 test assesses a prioritized subset of the high school CCSS-M within the conceptual categories of Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability (the assessed focus areas are published in the grade 9 Performance Level Descriptors).

Blueprint & weighting

VTCAP Test Specifications (Spring 2026) operational test blueprint, target percent of points per grade — Grade 3: OA 24-35%, NBT 10-14%, NF 16-20%, MD 22-29%, G 6-10%, constructed-response Mathematical Practices 12%. Grade 4: OA 20-31%, NBT 16-20%, NF 20-31%, MD 12-20%, G 6-10%, practices 12%. Grade 5: OA 14-22%, NBT 14-25%, NF 22-29%, MD 20-27%, G 8-16%, practices 12%. Grade 6: RP 15-22%, NS 15-22%, EE 15-22%, G 11-19%, SP 11-19%, practices 11%. Grade 7: RP 15-22%, NS 11%, EE 15-30%, G 11-19%, SP 19-22%, practices 11%. Grade 8: F 18-29%, NS 7%, EE 20-31%, G 18-29%, SP 18-22%, practices 11%. Grade 9 (all machine-scored): Number and Quantity/Algebra 18-27%, Algebra/Functions 31-40%, Geometry 20-29%, Statistics and Probability 13-20%; the two practices indicators are dual-aligned targets of >18% of points each. Identical figures appear in the Spring 2025 specifications.

Practice by skill

Topics mapped to this domain

Common factor group size (ACT)

Grade 910 questions

Fraction bounds extreme value (ACT)

Grade 910 questions

LCM word problems (ACT)

Grade 910 questions

Monomial expression multiplication (SAT)

Grade 920 questions

Polynomial combining like terms (ACT/SAT)

Grade 910 questions

Polynomial expression multiplication (SAT)

Grade 910 questions

Square and cube binomials

Grade 910 questions

Unit conversion word problems (ACT)

Grade 910 questions

Combining like square roots (ACT)

Grade 910 questions

Radical to exponent conversions

Grade 910 questions

Radical word problems (ACT)

Grade 910 questions

Rational exponents

Grade 915 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

At a summer camp, each camper received the same number of activity tokens and the same number of snack coupons. The camp issued 2828 activity tokens and 4242 snack coupons in all. Which could be the number of campers?

The number of campers must divide both 2828 and 4242. The common factors greater than 11 are 22, 77, and 1414. Only 77 appears among the choices: 28÷7=428 \div 7 = 4 tokens and 42÷7=642 \div 7 = 6 coupons per camper.

Practice playmedium

Given that 2≤m≤62 \le m \le 6, 1≤n≤41 \le n \le 4, and 5≤p≤105 \le p \le 10, what is the greatest possible value of m+np\dfrac{m + n}{p}?

Maximize the numerator with m=6m = 6 and n=4n = 4, and minimize the denominator with p=5p = 5: 6+45=2\dfrac{6 + 4}{5} = 2.

Practice playmedium

A cafe sells muffins in packs of 88 and bagels in packs of 14.14\textsf{.} What is the least number of muffins the cafe can buy so that it also buys exactly that many bagels?

The cafe needs the least common multiple of 88 and 1414 so the muffin and bagel totals match. Since the GCF of 88 and 1414 is 2,2\textsf{,} divide their product by the GCF: 8×142=56.\dfrac{8 \times 14}{2}=56\textsf{.} So the least matching total is 56.56\textsf{.}

Practice playeasy

Which expression is equivalent to (7p)(pq)(2q)?(7p)(pq)(2q)\textsf{?}

Multiply the coefficients: 7⋅1⋅2=14.7 \cdot 1 \cdot 2 = 14\textsf{.} Add the exponents on pp and on qq: p1+1q1+1=p2q2.p^{1+1} q^{1+1} = p^{2} q^{2}\textsf{.} So the product is 14p2q2.14p^{2}q^{2}\textsf{.}

Practice playmedium

Simplify: (9x2−4x)−(3x2−4x+5).(9x^2 - 4x) - (3x^2 - 4x + 5)\textsf{.}

Distribute the minus sign: (9x2−4x)−3x2+4x−5.(9x^2 - 4x) - 3x^2 + 4x - 5\textsf{.} Combine x2x^2 terms: 9x2−3x2=6x2.9x^2 - 3x^2 = 6x^2\textsf{.} The xx terms cancel: −4x+4x=0.-4x + 4x = 0\textsf{.} The constant is −5.-5\textsf{.} Result: 6x2−5.6x^2 - 5\textsf{.}

Practice playeasy

Which expression is equivalent to (x−1)(x−6)(x - 1)(x - 6)?

Expand: (x−1)(x−6)=x2−6x−x+6=x2−7x+6(x - 1)(x - 6) = x^2 - 6x - x + 6 = x^2 - 7x + 6.

Practice playeasy

Which expression is equivalent to (3x−2)2(3x - 2)^{2}?

(3x−2)2=(3x)2−2(3x)(2)+22=9x2−12x+4(3x - 2)^{2} = (3x)^{2} - 2(3x)(2) + 2^{2} = 9x^{2} - 12x + 4.

Practice playeasy

A hiking trail segment is 55 yards long. What is the length of the segment in inches?
(Note: 11 yard =3= 3 feet and 11 foot =12= 12 inches)

Multiply by conversion factors so the old units cancel: 5 yd×3 ft1 yd×12 in1 ft=180 in5\,\text{yd} \times \dfrac{3\,\text{ft}}{1\,\text{yd}} \times \dfrac{12\,\text{in}}{1\,\text{ft}} = 180\,\text{in}.

Keep practicing

Turn number and quantity/algebra into game time.

The VTCAP placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Related Common Core standards
HSA.APR.A.1HSN.RN.A.2HSN.RN.A.1HSA.SSE.A.2HSA.CED.A.3HSA.CED.A.2HSA.CED.A.1HSA.CED.A.4
Source and test overview
All VTCAP prepOfficial test source
Reporting categories

More Grade 9 domains

Algebra/FunctionsHigh school function content reported as the 'Algebra/Functions' performance indicator; blueprint target: 14-18 points (31-40% of the grade 9 test). The grade 9 Performance Level Descriptors publish the assessed focus areas listed below; they are placed under this slash-named category by their CCSS conceptual category (Functions, spanning linear, quadratic, and exponential function algebra).8 QsPractice →GeometryHigh school geometry content reported as the 'Geometry' performance indicator; blueprint target: 9-13 points (20-29% of the grade 9 test). The grade 9 Performance Level Descriptors publish the assessed focus areas listed below (congruence, transformations, constructions, and coordinate arguments with slope, distance, perimeter, and area).8 QsPractice →Statistics and ProbabilityHigh school statistics content reported as the 'Statistics and Probability' performance indicator; blueprint target: 6-10 points (13-20% of the grade 9 test). The grade 9 Performance Level Descriptors publish the assessed focus area listed below (one-variable displays, center and spread, two-way tables, scatterplots, fitted functions, correlation, and causation).8 QsPractice →