PSAT/NMSQT Algebra Practice — Sports Academy Games

What the test measures

Algebra skills

Linear equations in one variable
Linear equations in two variables
Linear functions
Systems of two linear equations in two variables
Linear inequalities in one or two variables

Standards basis

College Board SAT Suite content domains aligned to college- and career-ready math skills; Common Core State Standards–aligned at the content level — national

How the PSAT/NMSQT reports it

PSAT/NMSQT uses the same SAT Suite digital test design and shared math content domains as SAT and the other PSATs. College Board states these tests assess the same group of skills and knowledge, with content aligned to the SAT Suite’s domain framework rather than a state-specific blueprint.

Blueprint & weighting

College Board’s SAT Suite math content domains are used for reporting and preparation, but the primary sources retrieved here did not provide a PSAT/NMSQT-specific published item percentage by domain in accessible form.

Official sources

College Board PSAT/NMSQT page
College Board PSAT/NMSQT Testing Rules
College Board SAT Practice content domains

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

$|x + 8| = 21$

Which of the following gives both solutions to the given equation?

The equation means $x + 8 = 21$ or $x + 8 = -21$ . So $x = 13$ or $x = -29$ . Both solutions are $-29$ and $13\textsf{.}$

Practice playeasy

If $|2x + 10| = 26$ , what is the positive value of $x + 5$ ?

Rewrite $|2x + 10| = |2(x + 5)| = |2|\,|x + 5| = 2|x + 5|$ . Since $2|x + 5| = 26$ , divide by $2$ to get $|x + 5| = 13$ . The expression $x + 5$ equals $13$ or $-13$ ; the positive value is $13\textsf{.}$

Practice playeasy

If $6x = 54$ , what is the value of $x + 7$ ?

Divide both sides by $6$ : $x = 9$ . Then $x + 7 = 9 + 7 = 16\textsf{.}$

Practice playeasy

Solve for $x$ : $x - 3 > 4$ . The solution is $x > k$ . What is the value of $k$ ?

Add 3 to both sides: $x > 7$ , so $k = 7$ .

Practice playeasy

The equation $3u + 4v = 35$ gives the total number of stamps in $u$ packs of $3$ and $v$ packs of $4$ . If $v = 2$ , what is the value of $u$ ?

Substitute $v = 2$ : $3u + 4(2) = 35$ , so $3u + 8 = 35$ . Then $3u = 27$ and $u = 9$ .

Practice playeasy

What is the $y$ -intercept of the line $y = \dfrac{1}{2}x - 4$ ?

In $y = mx + b$ , the $y$ -intercept is $b = -4$ .

Practice playeasy

Which system of linear equations has no solution?

Both equations have slope $-3$ but different $y$ -intercepts ( $2$ and $5$ ), so the lines are parallel and the system has no solution.

Practice playeasy

A band competition allows an instrument case's length, width, and height to total at most $62.0$ inches. A case measures $65.4$ inches in total. What is the minimum decrease needed in that total, in inches, so that the case meets the rule?