NJSLA Algebra II Quantities Practice

Quantities skills

N.Q.A.1-3 Units, quantities, and precision

Standards basis

New Jersey Student Learning Standards for Mathematics (NJSLS-M), aligned to Common Core State Standards for Mathematics (CCSS-M) — New Jersey

How the NJSLA reports it

NJSLA math is built on the New Jersey Student Learning Standards for Mathematics, which closely follow the Common Core domain structure and progressions. The assessment is organized by grade-level and end-of-course reporting aligned to those standards rather than by a separate proprietary framework.

Blueprint & weighting

NJDOE publishes statewide assessment administration information and grade/course coverage, but no official public math-domain weighting blueprint was located in the retrieved primary materials.

Official sources

New Jersey Department of Education - Assessment
New Jersey Department of Education - 2023 NJSLS-Mathematics
NJDOE - Statewide Assessment Testing Schedule 2026-27

8 free questions · 0/0 correct

Practice playmedium

Teen volunteers at a food drive packed supply bags so that each volunteer received the same number of water bottles and the same number of granola bars to distribute. The drive had $56$ water bottles and $84$ granola bars in all. Which could be the number of volunteers?

The number of volunteers must divide both totals. Common factors of $56$ and $84$ greater than $1$ include $2$ , $4$ , $7$ , $14$ , and $28$ . Only $14$ appears among the choices: $56 \div 14 = 4$ bottles and $84 \div 14 = 6$ bars per volunteer.

Practice playmedium

Given that $3 \le m \le 8$ , $1 \le n \le 2$ , and $4 \le p \le 6$ , what is the least possible value of $\dfrac{m}{n + p}$ ?

Minimize $m$ with $m = 3$ , and maximize $n + p$ with $n = 2$ and $p = 6$ : $\dfrac{3}{2 + 6} = \dfrac{3}{8}$ .

Practice playhard

Bus route A leaves the station every $20$ minutes, and bus route B leaves every $30$ minutes. Both buses leave together at noon. Over the next $3$ hours, not counting the noon departure, how many times do both buses leave the station at the same time?

Both buses leave together every least common multiple of $20$ and $30$ minutes. Since the GCF of $20$ and $30$ is $10\textsf{,}$ divide their product by the GCF to get that interval: $\dfrac{20 \times 30}{10}=60$ minutes. In $180$ minutes after noon, the shared departures are at $60\textsf{,}$ $120\textsf{,}$ and $180$ minutes, so there are $3$ additional times.

Practice playeasy

A running track is $2$ kilometers long. What is the length of the track in meters?
(Note: $1$ kilometer $= 1{,}000$ meters)

Multiply by a conversion factor so the old unit cancels: $2\,\text{km} \times \dfrac{1{,}000\,\text{m}}{1\,\text{km}} = 2{,}000\,\text{m}$ .

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 $2 \le m \le 5$ and $3 \le n \le 8$ , what is the greatest possible value of $\dfrac{1}{m} + \dfrac{1}{n}$ ?

Each term $\dfrac{1}{m}$ and $\dfrac{1}{n}$ is greatest when its denominator is least: $\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{5}{6}$ .

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.