VTCAP Grade 9 Algebra/Functions Practice

VTCAP Grade 9 Algebra/Functions. Practice it free.

High 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). This Grade 9 reporting domain maps to 31 practice skills and 8 representative questions from the playable bank.

Grade 931 mapped skills

Algebra/Functions skills

Interpreting Functions

Building Functions

Linear, Quadratic, and Exponential Models

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.

Official sources

VTCAP Test Specifications, Spring 2026 (Vermont AOE / Cognia)
VTCAP Test Specifications, Spring 2025 (Vermont AOE / Cognia)
VTCAP Performance Level Descriptors: Mathematics, Grades 3-9 (Vermont AOE)

8 free questions · 0/0 correct

Practice playmedium

The first five terms of an arithmetic sequence are $8, 14, 20, 26, 32$ . What is the $18$ th term?

The common difference is $d = 6$ . With $a_1 = 8$ , the $18$ th term is $a_{18} = 8 + 17(6) = 110$ .

Practice playmedium

Which expression represents the inverse of $f(x)=\sqrt{x+2}$ ?

Set $y=\sqrt{x+2}$ . Swap: $x=\sqrt{y+2}$ . Square both sides: $x^{2}=y+2$ . Subtract $2$ : $y=x^{2}-2$ . So $f^{-1}(x)=x^{2}-2\textsf{.}$

Practice playmedium

The table defines functions for positive integers $x \leq 5$ .
$\begin{array}{c|c|c|c} x & j(x) & k(x) & l(x) \\ \hline 1 & 3 & 4 & 2 \\ 2 & 1 & 5 & 3 \\ 3 & 4 & 2 & 5 \\ 4 & 5 & 1 & 4 \\ 5 & 2 & 3 & 1 \end{array}$
If $j(k(l(x))) = 5$ , what is the value of $x$ ?

Work from the outside in. Since $j(4) = 5$ , we need $k(l(x)) = 4$ . Since $k(1) = 4$ , we need $l(x) = 1$ . From the table, $l(5) = 1$ , so $x = 5$ .

Practice playeasy

Which of the following describes the transformation from the graph of $f(x)$ to the graph of $y = f(x + 5)$ ?

Replacing $x$ with $x + 5$ is equivalent to $f(x - (-5))$ , so the input must be $5$ smaller to produce the same output and the graph shifts $5$ units left.

Practice playeasy

How does the graph of $y = f(x)$ move as a result of the transformation $y = f(x - 6) + 1$ ?

To shift right, $x$ gets larger but the height stays the same, so $6$ is subtracted inside $f$ . Adding $1$ outside $f$ is a separate move up.

Practice playeasy

The first term of a sequence is $9$ . Each term after the first is $3$ times the preceding term. If $a_n$ represents the $n$ th term, which equation gives $a_n$ in terms of $n$ ?

Following the pattern:
1st term, or $n = 1\textsf{:}$ $9 \cdot 3^{0}$
2nd term, or $n = 2\textsf{:}$ $9 \cdot 3^{1}$
3rd term, or $n = 3\textsf{:}$ $9 \cdot 3^{2}$
4th term, or $n = 4\textsf{:}$ $9 \cdot 3^{3}$
Since each term has an exponent that is $1$ less than the term number, the $n$ th term is $a_n = 9 \cdot 3^{n-1}$ .

Practice playeasy

The graph of $x + 3y = 9$ is translated up $6$ units on the coordinate plane. What is the $y$ -coordinate of the $y$ -intercept of the resulting graph?

An upward shift of $6$ replaces $y$ with $y - 6$ . At the $y$ -intercept, $x = 0$ , so $3(y - 6) = 9$ . Then $3y - 18 = 9$ , $3y = 27$ , and $y = 9$ .

Practice playeasy

Which rule combines $\log a + \log b$ into a single logarithm?

$\log a + \log b = \log(ab)$ is the product rule.

VTCAP Grade 9 Algebra/Functions. Practice it free.

Algebra/Functions skills

Interpreting Functions

Building Functions

Linear, Quadratic, and Exponential Models

Topics mapped to this domain

Arithmetic sequence nth term

Finding inverse functions (ACT)

Function table composition (ACT)

Function transformation descriptions

Function transformations

Geometric sequence equations

Linear graph translations

Logarithm rules

Piecewise function composition (ACT)

Sequences and series

Writing exponential equations from context (SAT)

Exponential functions in context (SAT)

8 free questions · 0/0 correct

Turn algebra/functions into game time.

More Grade 9 domains