PSAT 8/9 Algebra Practice — Sports Academy Games

What the test measures

Algebra skills

Linear equations in 1 variable
Linear equations in 2 variables
Linear functions
Systems of 2 linear equations in 2 variables
Linear inequalities in 1 or 2 variables

Standards basis

Common Core State Standards (CCSS-M) / college-and-career-readiness aligned SAT Suite math framework — national

How the PSAT 8/9 reports it

PSAT 8/9 uses the SAT Suite’s shared digital math framework and the same four content domains as the other suite tests, with PSAT 8/9 adjusted for a younger grade band. College Board notes that PSAT 8/9 does not test trigonometry.

Blueprint & weighting

PSAT 8/9 Math has 44 questions total over 2 modules and 70 minutes total. Published question distribution is Algebra 16–18, Advanced Math 7–9, Problem-Solving and Data Analysis 9–11, and Geometry 4–6; College Board also summarizes these as approximately 42.5%, 20%, 25%, and 12.5%, respectively.

Official sources

College Board PSAT 8/9
College Board Math Specifications - SAT Suite of Assessments
College Board PSAT 8/9 Student Guide PDF

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

The equation $2p + 5q = 39$ gives the total weight, in pounds, of $p$ small boxes and $q$ large boxes. If $q = 3$ , what is the value of $p$ ?

Substitute $q = 3$ : $2p + 5(3) = 39$ , so $2p + 15 = 39$ . Then $2p = 24$ and $p = 12$ .

Practice playeasy

$|2x + 10| = 16$

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

The equation means $2x + 10 = 16$ or $2x + 10 = -16$ . So $2x = 6$ or $2x = -26$ , and $x = 3$ or $x = -13$ . Both solutions are $-13$ and $3\textsf{.}$

Practice playeasy

If $|5x + 10| = 35$ , what is the positive value of $x + 2$ ?

Rewrite $|5x + 10| = |5(x + 2)| = |5|\,|x + 2| = 5|x + 2|$ . Since $5|x + 2| = 35$ , divide by $5$ to get $|x + 2| = 7$ . The expression $x + 2$ equals $7$ or $-7$ ; the positive value is $7\textsf{.}$

Practice playeasy

If $12x = 60$ , what is the value of $5x$ ?

Divide both sides by $12$ : $x = 5$ . Then $5x = 5 \cdot 5 = 25\textsf{.}$

Practice playeasy

Solve for $x$ : $2x < 5$ . The solution is $x < k$ . What is the value of $k$ ?

Divide both sides by 2: $x < \dfrac{5}{2}$ , so $k = \dfrac{5}{2}$ .

Practice playmedium

The minimum value of $t$ is $3$ less than twice another number $m\textsf{.}$ Which inequality shows the possible values of $t\textsf{?}$

A minimum means $t$ must be at least that value, so use $\ge\textsf{.}$ Twice $m$ minus $3$ is $2m - 3\textsf{,}$ giving $t \ge 2m - 3\textsf{.}$

Practice playmedium

$\begin{cases} x + y \le 10 \\ x \ge y - 2 \end{cases}$
The point $(x, y)$ is a solution to the system of inequalities in the coordinate plane. If $y = 6$ , which of the following could be a value of $x$ ?