MCA High School / MCA EOC Number and Quantity Practice

Number and Quantity skills

Reason quantitatively and use units to solve problems

Perform arithmetic operations with complex numbers

Represent complex numbers and their operations on the complex plane

Use properties of rational and irrational numbers

Standards basis

Minnesota Academic Standards in Mathematics (2007; assessed by MCA-III in grades 3-8 and 11 through 2026-27. 2022 standards phase in with MCA-IV beginning 2027-28) — Minnesota

How the MCA reports it

Minnesota’s MCA math is a state assessment tied to Minnesota Academic Standards in Mathematics rather than a separate national framework. The official public resources available here point to Minnesota-specific standards implementation, and absent a test blueprint, the coverage map should be organized by the state’s grade-level math domains that closely parallel CCSS-M. Note: the current MCA-III assesses the 2007 Minnesota standards in grades 3-8 and 11; Minnesota administers a single comprehensive high-school (grade 11) math test, NOT Algebra I / Geometry / Algebra II end-of-course exams — the 'High School / MCA EOC' band below is the grade-11 HS administration. (MCA-IV on the 2022 standards begins 2027-28.)

Blueprint & weighting

MCA uses the Independent / state-specific framework (by grade domains structure).

Official sources

Minnesota Department of Education MCA page
Minnesota Academic Standards in Mathematics implementation reference
MCA-III Mathematics Test Specifications, Grades 3-8 and 11

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

$(-1+5i)(2-3i)=$

Expand: $(-1+5i)(2-3i)=-2+3i+10i-15i^{2}$ . Since $i^{2}=-1$ , this is $-2+13i+15=13+13i\textsf{.}$

Practice playeasy

What is $|8 + 15i|$ ?

$|8 + 15i| = \sqrt{8^2 + 15^2} = \sqrt{289} = 17$ .

Practice playmedium

Given $i = \sqrt{-1}$ , what is $\sqrt{121} - \sqrt{-9}$ ?

$\sqrt{121} = 11$ and $\sqrt{-9} = 3i$ . So $\sqrt{121} - \sqrt{-9} = 11 - 3i$ .

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.