MCAP Algebra II Number and Quantity Practice

Number and Quantity skills

N.RN.A Extend the properties of exponents to rational exponents.

N.Q.A Reason quantitatively and use units to solve problems.

N.CN.A Perform arithmetic operations with complex numbers.

N.CN.C Complex numbers in polynomial identities and equations.

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 playmedium

A drama club prepared scripts and prop kits for a showcase. Each cast member received the same number of scripts and the same number of prop kits. The club had $54$ scripts and $81$ prop kits in all. Which could be the number of cast members?

The number of cast members must divide both totals. The common factors of $54$ and $81$ greater than $1$ are $3$ , $9$ , and $27$ . Only $9$ appears among the choices: $54 \div 9 = 6$ scripts and $81 \div 9 = 9$ kits per member.

Practice playmedium

Given that $1 \le m \le 5$ , $3 \le n \le 7$ , and $8 \le p \le 12$ , what is the greatest possible value of $\dfrac{m}{n} \cdot \dfrac{1}{p}$ ?

Maximize $\dfrac{m}{n}$ with $m = 5$ and $n = 3$ , and maximize $\dfrac{1}{p}$ with $p = 8$ : $\dfrac{5}{3} \cdot \dfrac{1}{8} = \dfrac{5}{24}$ .

Practice playhard

A parking-garage gate opens every $9$ minutes, and a ferry docks every $15$ minutes. Both events occur together at noon. Over the next $90$ minutes, not counting noon, how many times do both events occur at the same time?

Both events coincide every least common multiple of $9$ and $15$ minutes. Since the GCF of $9$ and $15$ is $3\textsf{,}$ divide their product by the GCF to get that interval: $\dfrac{9 \times 15}{3}=45$ minutes. In $90$ minutes after noon, the shared times are at $45$ and $90$ minutes, so there are $2$ additional times.

Practice playeasy

A package weighs $4$ pounds. What is the weight of the package in ounces?
(Note: $1$ pound $= 16$ ounces)

Multiply by a conversion factor so the old unit cancels: $4\,\text{lb} \times \dfrac{16\,\text{oz}}{1\,\text{lb}} = 64\,\text{oz}$ .

Practice playmedium

What is $(3+2i)^{2}$ ?

Expand: $(3+2i)^{2}=9+12i+4i^{2}$ . Since $i^{2}=-1$ , this is $9+12i-4=5+12i\textsf{.}$

Practice playeasy

What is $i^{6}$ ?

$i^{6} = (i^{2})^{3} = (-1)^{3} = -1$ .

Practice playeasy

Given $i = \sqrt{-1}$ , what is $\sqrt{100} + \sqrt{-49}$ ?

$\sqrt{100} = 10$ and $\sqrt{-49} = 7i$ . So $\sqrt{100} + \sqrt{-49} = 10 + 7i$ .

Practice playeasy

Which expression is equivalent to $\sqrt{72}+\sqrt{98}$ ?

$\sqrt{72}=\sqrt{36 \cdot 2}=6\sqrt{2}$ and $\sqrt{98}=\sqrt{49 \cdot 2}=7\sqrt{2}$ . Adding like radical terms gives $6\sqrt{2}+7\sqrt{2}=13\sqrt{2}$ .

MCAP Algebra II Number and Quantity. Practice it free.

Number and Quantity skills

N.RN.A Extend the properties of exponents to rational exponents.

N.Q.A Reason quantitatively and use units to solve problems.

N.CN.A Perform arithmetic operations with complex numbers.

N.CN.C Complex numbers in polynomial identities and equations.

Topics mapped to this domain

Common factor group size (ACT)

Fraction bounds extreme value (ACT)

LCM word problems (ACT)

Unit conversion word problems (ACT)

Multiplying and squaring complex numbers (ACT)

Complex number operations

Rewriting complex numbers

Combining like square roots (ACT)

Radical to exponent conversions

Radical word problems (ACT)

Rational exponents

Simplifying square roots (ACT)

8 free questions · 0/0 correct

Turn number and quantity into game time.

More Algebra II domains