ACAP Grade 7 Expressions and Equations Practice

Expressions and Equations skills

Use properties of operations to generate equivalent expressions

Solve real-life and mathematical problems using numerical and algebraic expressions and equations

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers

Use variables to represent quantities in real-world problems

Standards basis

Alabama Course of Study: Mathematics — Alabama

How the ACAP reports it

Alabama’s ACAP Summative is a state assessment tied to Alabama’s own K-12 mathematics standards and reporting structure rather than a national consortium blueprint. The publicly accessible assessment page does not expose a separate ACAP math blueprint in the fetched content, so the safest official coverage basis is Alabama’s mathematics standards organization into grade-level domains.

Blueprint & weighting

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

Official sources

Alabama Department of Education - Assessment
Alabama Office of Mathematics Improvement

8 free questions · 0/0 correct

Practice playeasy

A library reading room must keep noise at a level of at most $65.0$ decibels. A meter shows $68.5$ decibels. What is the minimum decrease needed in the noise level, in decibels, so that the room meets the rule?

The noise level must be at most $65.0$ decibels. The minimum decrease is $68.5 - 65.0 = 3.5\textsf{.}$

Practice playeasy

Solve for $k$ : $9k = -27$ .

Isolate $k$ : $k = -3$ .

Practice playmedium

At the start of the season, a soccer club roster was divided into three position groups. Exactly $\dfrac{1}{3}$ of the players were forwards, exactly $\dfrac{1}{2}$ were midfielders, and $9$ players were goalkeepers. How many players were on the roster?

Let $x$ be the roster size. Forwards and midfielders account for $\dfrac{1}{3}x + \dfrac{1}{2}x = \dfrac{5}{6}x$ . The goalkeepers are the remaining $\dfrac{1}{6}x = 9$ , so $x = 54$ .

Practice playeasy

In a school zone, a car must travel at a speed of at most $35.0$ miles per hour. A car is traveling at $38.2$ miles per hour. What is the minimum decrease needed in the car's speed, in miles per hour, so that it meets the speed limit?

The speed must be at most $35.0$ miles per hour. The minimum decrease is $38.2 - 35.0 = 3.2\textsf{.}$

Practice playeasy

What value of $n$ satisfies $5n - 8 = 17$ ?

Add $8$ to both sides: $5n = 25$ . Divide both sides by $5$ : $n = 5$ .

Practice playmedium

An arena concert used four seating sections. Exactly $\dfrac{1}{6}$ of the seats were in section A, exactly $\dfrac{1}{3}$ were in section B, $22$ seats were in section C, and $18$ seats were in section D. How many seats were in the arena for this concert?

Let $x$ be the total number of seats. Sections A and B account for $\dfrac{1}{6}x + \dfrac{1}{3}x = \dfrac{1}{2}x$ . Sections C and D total $22 + 18 = 40$ seats, so $\dfrac{1}{2}x = 40$ and $x = 80$ .

Practice playeasy

A shipping company accepts a package only if its mass is at least $2.50$ kilograms. A package has a mass of $2.15$ kilograms. What is the minimum increase needed in the package's mass, in kilograms, so that it can be accepted?