VTCAP Grade 8 Functions Practice — Sports Academy Games

What the test measures

Functions skills

Define, evaluate, and compare functions
Use functions to model relationships between quantities

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)

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

What is the slope of the line $y = \dfrac{3}{2}x + 2$ ?

In $y = mx + b$ , the slope is $m = \dfrac{3}{2}$ .

Practice playmedium

Consider the linear function $t$ given by $t(x) = nx + 150$ , where $n$ is a constant. Knowing that $t(10) = 80$ , determine $t(20)$ .

Substitute $x = 10$ : $10n + 150 = 80$ , so $10n = -70$ and $n = -7$ . The rule is $t(x) = -7x + 150$ , so $t(20) = -7(20) + 150 = -140 + 150 = 10$ .

Practice playeasy

An amusement park charges $\text{\char36}12$ for admission and $\text{\char36}3$ for each ride. Let $x$ be the number of rides and $y$ be the total cost in dollars. Which equation models the situation?

Admission is the starting cost ( $\text{\char36}12$ ) and each ride adds $\text{\char36}3$ , so $y = 3x + 12\textsf{.}$

Practice playeasy

What is the slope of the line through $(1, 2)$ and $(3, 8)$ ?

Slope $= \dfrac{8 - 2}{3 - 1} = \dfrac{6}{2} = 3\textsf{.}$

Practice playeasy

What is the $y$ -intercept of the line $y = \dfrac{3}{4}x - 5$ ?

In $y = mx + b$ , the $y$ -intercept is $b = -5$ .

Practice playmedium

For the function $v(x) = 6x + k$ with constant $k$ , it is known that $v(7) = 30$ . What number does $v(4)$ equal?

Substitute $x = 7$ : $6(7) + k = 30$ , so $42 + k = 30$ and $k = -12$ . The rule is $v(x) = 6x - 12$ , so $v(4) = 6(4) - 12 = 24 - 12 = 12$ .

Practice playeasy

Elena already has $\text{\char36}75$ in her savings account and deposits $\text{\char36}20$ each week. Let $x$ be the number of weeks and $y$ be the account balance in dollars. Which equation models the situation?