MCAP Algebra I Functions Practice — Sports Academy Games

Functions skills

F.IF.A Understand the concept of a function and use function notation.

F.IF.B Interpret functions that arise in applications in terms of the context.

F.IF.C Analyze functions using different representations.

F.BF.A Build a function that models a relationship between two quantities.

F.BF.B Build new functions from existing functions.

F.LE.A Construct and compare linear, quadratic, exponential models & solve problems.

F.LE.B Interpret expressions for functions in terms of the situation they model.

Standards basis

Maryland College and Career Ready Standards for Mathematics (MCCRSM) — Maryland

How the MCAP reports it

MCAP is Maryland's statewide successor to PARCC, built on the Maryland College and Career Ready Standards for Mathematics (which mirror CCSS-M) — it is not a Smarter Balanced administration despite the claims-style family resemblance. Each grade/course High Level Blueprint (September 2022) organizes the assessment into three subclaims: Content (23-24 one-point machine-scored items, listed per domain/conceptual category as MCCRSM cluster headings), Reasoning (6 items), and Modeling (6 items), the latter two defined by per-grade evidence statements and including constructed-response items. Cluster headings are transcribed verbatim from the blueprints, including their minor typographical deviations from the parallel CCSS-M headings; two evident misprints are normalized (a duplicated sentence fragment on 4.OA.C, and the domain codes printed as G.P.E / T.TF for G.GPE / F.TF). Since March 2025, grade 6-7 students enrolled in a high-school mathematics course may take the corresponding MCAP course assessment instead of the grade-level test.

Blueprint & weighting

Each High Level Blueprint (September 2022) publishes per-domain operational item counts. Content Subclaim (1-point machine-scored items): Grade 3 — OA 7, NBT 2, NF 7, Measurement 5, Geometry 2 (23 items); Grade 4 — OA 4, NBT 5, NF 10, Measurement 3, Geometry 1 (23); Grade 5 — OA 2, NBT 6, NF 9, Measurement 4, Geometry 2 (23); Grade 6 — RP 3, NS 8, EE 8, Geometry 2, SP 2 (23); Grade 7 — RP 8, NS 4, EE 5, Geometry 3, SP 3 (23); Grade 8 — NS 2, EE 10, Functions 5, Geometry 4, SP 2 (23); Algebra I — Number and Quantity 1, Algebra 12, Functions 9, Statistics 2 (24); Geometry — G.CO 7, G.SRT 8, G.C 3, G.GPE 3, G.GMD 1, G.MG 1 (23); Algebra II — Number and Quantity 3, Algebra 8, Functions 11, Statistics 1 (23). Every assessment adds 6 Reasoning Subclaim and 6 Modeling Subclaim operational items — four 1-point machine-scored each, plus two constructed-response items (two 3-point in grades 3-4; one 3-point and one 4-point in grades 5-8; two 4-point in Algebra I, Geometry, and Algebra II) — so a form carries 35 operational items (36 for Algebra I).

Official sources

MSDE — MCAP Mathematics (current program page: grades 3-8, Algebra I, Geometry, Algebra II)
MSDE — MCAP Overview / High Level Blueprints summary
MSDE — MCAP Grade 3 Mathematics High Level Blueprint (September 2022)

8 free questions · 0/0 correct

Practice playeasy

For what value of $x$ does the graph of $y = -5(x - 11)(x + 4)$ intercept the $x$ -axis?

Set $y = 0$ : $-5(x - 11)(x + 4) = 0$ . The constant $-5 \neq 0$ , so the zeros are $x = 11$ and $x = -4$ . Of the choices, $-4$ is an x-coordinate of an x-intercept.

Practice playeasy

$f(x) = (x + 3)^2 - 6$

The function $f$ is defined by the given equation. For what value of $x$ does $f(x)$ reach its minimum?

The equation is in vertex form $f(x) = a(x - h)^2 + k$ with $a = 1 > 0$ , so the graph opens upward and the minimum occurs at the vertex. Rewrite $(x + 3)^2$ as $(x - (-3))^2$ : the vertex is at $x = -3$ . Therefore, $f(x)$ reaches its minimum when $x = -3$ .

Practice playeasy

A parabola opens upward and is described by $y = x^2 - 18x + 65$ . At what $x$ -coordinate does $y$ attain its minimum?

Because this parabola opens upward, the smallest $y$ is at the vertex. For $y = ax^2 + bx + c$ , the $x$ -value at the vertex is $x = -\dfrac{b}{2a}$ . Here $a = 1$ and $b = -18$ , so $x = -\dfrac{-18}{2(1)} = \dfrac{18}{2} = 9$ . Therefore, $y$ reaches its minimum when $x = 9$ .

Practice playmedium

An online course begins with $5{,}000$ students enrolled. Each week, a model estimates that $10\%$ of the students still enrolled withdraw. Which equation defines this model, where $e(w)$ is the estimated number of students still enrolled $w$ weeks after the course begins?

The starting enrollment is $5{,}000$ , and a $10\%$ weekly withdrawal means $90\%$ remain, so multiply by $0.90$ each week: $e(w) = 5{,}000(0.90)^w$ .

Practice playeasy

The function $v$ is defined by $v(y) = 18{,}000(0.88)^{y}$ . The function models the value, in dollars, of a used scooter $y$ years after it is purchased. Which statement is the best interpretation of $18{,}000$ in this context?

When $y = 0$ , $v(0) = 18{,}000$ . So $\text{\char36}18{,}000$ is the value of the scooter when it is purchased.

Practice playeasy

A bike rental shop charges a flat fee plus an hourly rate. The total cost $C$ , in dollars, after $h$ hours is modeled by $C = 6h + 10$ . Which of the following is the best interpretation of $6$ in this context?

In $C = 6h + 10$ , the $6$ multiplies hours, so $6$ is the hourly rental rate in dollars.

Practice playmedium

A furniture order has $76$ screws to assemble tables and chairs. The builder uses the equation $8t + 5c = 76$ to figure out how many tables, $t$ , and how many chairs, $c$ , can be assembled. Which is the best interpretation of the number $5$ in this equation?

Each chair uses $5$ screws, so $5$ is the number multiplied by the number of chairs ordered.

Practice playeasy

The first five terms of an arithmetic sequence are $1, 4, 7, 10, 13$ . What is the $16$ th term?

The common difference is $d = 3$ . With $a_1 = 1$ , the $16$ th term is $a_{16} = 1 + 15(3) = 46$ .

MCAP Algebra I Functions. Practice it free.

Functions skills

F.IF.A Understand the concept of a function and use function notation.

F.IF.B Interpret functions that arise in applications in terms of the context.

F.IF.C Analyze functions using different representations.

F.BF.A Build a function that models a relationship between two quantities.

F.BF.B Build new functions from existing functions.

F.LE.A Construct and compare linear, quadratic, exponential models & solve problems.

F.LE.B Interpret expressions for functions in terms of the situation they model.

Topics mapped to this domain

Factored polynomial x-intercepts (SAT)

Quadratic minimum from vertex form

Quadratic minimum x-value

Writing exponential equations from context (SAT)

Interpreting exponential parameters

Interpreting linear parameters

Linear coefficient interpretations (SAT/PSAT 8/9/10)

Arithmetic sequence nth term

Finding inverse functions (ACT)

Function table composition (ACT)

Function transformation descriptions

Function transformations

8 free questions · 0/0 correct

Turn functions into game time.

More Algebra I domains