MCAP Algebra II 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.

F.TF.A Extend the domain of trigonometric functions using the unit circle.

F.TF.B Model periodic phenomena with trigonometric functions.

F.TF.C Prove and apply trigonometric identities.

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

If $\sin\theta = \dfrac{5}{13}$ and $\cos\theta = \dfrac{12}{13}\textsf{,}$ what is $\sin(2\theta)\textsf{?}$

$\sin(2\theta) = 2\sin\theta\cos\theta = 2 \cdot \dfrac{5}{13} \cdot \dfrac{12}{13} = \dfrac{120}{169}\textsf{.}$

Practice playeasy

The graph of $y = -2(x + 15)(x - 8)(x + 3)$ intercepts the $x$ -axis at which value of $x$ ?

Set $y = 0$ : $-2(x + 15)(x - 8)(x + 3) = 0$ . The constant $-2 \neq 0$ , so the zeros are $x = -15$ , $x = 8$ , and $x = -3$ . Among the choices, only $8$ is an x-coordinate of an x-intercept.

Practice playeasy

$f(x) = (x - 8)^2 + 1$

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. Here $h = 8$ , so the vertex is at $x = 8$ . Therefore, $f(x)$ reaches its minimum when $x = 8$ .

Practice playmedium

For the relation $y = 3x^2 - 30x + 70$ , find the value of $x$ at which $y$ is smallest.

The parabola opens upward, so 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 $a = 3$ and $b = -30$ , so $x = -\dfrac{-30}{2(3)} = \dfrac{30}{6} = 5$ . Therefore, $y$ is smallest when $x = 5$ .

Practice playmedium

A warehouse begins a clearance week with $640$ boxes. Each week, half of the boxes still in the warehouse are shipped out. Which equation gives the number of boxes, $b$ , still in the warehouse after $w$ weeks?

The warehouse starts with $640$ boxes, and each week the remaining amount is multiplied by $\dfrac{1}{2}$ . After $w$ weeks, $b = 640\left(\dfrac{1}{2}\right)^w$ .

Practice playeasy

The function $c$ is defined by $c(x) = 40(1.25)^{x}$ . The function models the number of colonies of bacteria $x$ hours after a culture is started. Which statement is the best interpretation of the growth factor $1.25$ in this context?

The growth factor is $1.25$ . Each time $x$ increases by $1$ , the number of colonies is multiplied by $1.25$ . That means each hour the number of colonies is $125\%$ of the previous hour's number, a $25\%$ increase.

Practice playeasy

The given equation represents the number of pages $p$ read, where $h$ represents the number of hours spent reading.

$p = 42h$

Which of the following is the best interpretation of $42$ in this context?

In $p = 42h$ , the number $42$ is the reading rate: $42$ pages for each hour spent reading.

Practice playmedium

A candle is $16$ inches tall when lit and burns down at a constant rate. Let $t$ be the time in hours and $h$ be the candle height in inches. The situation is modeled by $h = -0.5t + 16$ . Which is the best interpretation of the number $-0.5$ in this equation?

The slope is $-0.5$ inches per hour, so the candle loses $0.5$ inch of height each hour.

MCAP Algebra II 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.

F.TF.A Extend the domain of trigonometric functions using the unit circle.

F.TF.B Model periodic phenomena with trigonometric functions.

F.TF.C Prove and apply trigonometric identities.

Topics mapped to this domain

Trig identities

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)

Degree-radian conversion

Inverse trig domain and range

Unit circle trig values (SAT)

Arithmetic sequence nth term

8 free questions · 0/0 correct

Turn functions into game time.

More Algebra II domains