SAT practice test

SAT Algebra Practice Test

Linear equations, functions, systems, inequalities. 35% of Math. Here are 10 SAT algebra questions, each with the answer and the reason.

Updated 2026-11-14 by the Tigertest team. Original questions written to the digital SAT specifications. Not affiliated with College Board. Score estimates are unofficial.

1. 1.

   If $6(x - 1) = 2x + 14$, what is the value of $x$?

   • A.

     $2$

   • B.

     $3.75$

   • C.

     $5$

   • D.

     $20$

   Answer: C.

   Distribute first: $6x - 6 = 2x + 14$. Subtract $2x$ from both sides and add $6$ to both sides to get $4x = 20$, so $x = 5$. Check: $6(5 - 1) = 24$ and $2(5) + 14 = 24$. The choice $3.75$ comes from writing $6x - 1$ instead of $6x - 6$, forgetting to multiply the $-1$ by $6$. The choice $20$ stops at $4x = 20$ without dividing, and $2$ comes from subtracting $6$ instead of adding it ($4x = 8$).

2. 2.

   A line in the $xy$-plane passes through the point $(0, -2)$ and has slope $\frac{3}{4}$. Which of the following is an equation of the line?

   • A.

     $y = \frac{3}{4}x - 2$

   • B.

     $y = \frac{3}{4}x + 2$

   • C.

     $y = \frac{4}{3}x - 2$

   • D.

     $y = -2x + \frac{3}{4}$

   Answer: A.

   A point with $x$-coordinate $0$ is the $y$-intercept, so $b = -2$ in the slope-intercept form $y = mx + b$, and the slope is $m = \frac{3}{4}$, giving $y = \frac{3}{4}x - 2$. Check: $x = 0$ gives $y = -2$. The choice $y = \frac{3}{4}x + 2$ drops the sign of the intercept. The choice $y = \frac{4}{3}x - 2$ inverts the slope, and $y = -2x + \frac{3}{4}$ swaps the roles of the slope and the intercept.

3. 3.

   Which of the following ordered pairs $(x, y)$ is a solution to the system of inequalities $y > 2x - 1$ and $y \le -x + 5$?

   • A.

     $(1, 3)$

   • B.

     $(2, 3)$

   • C.

     $(3, 2)$

   • D.

     $(0, 6)$

   Answer: A.

   Test each pair in both inequalities. For $(1, 3)$: $3 > 2(1) - 1 = 1$ is true and $3 \le -1 + 5 = 4$ is true, so it is a solution. The pair $(2, 3)$ gives $3 > 3$, which is false because the first inequality is strict; points on that boundary line are not included. The pair $(0, 6)$ satisfies the first inequality, but $6 \le 5$ is false, and $(3, 2)$ fails the first inequality since $2 > 5$ is false.

4. 4.

   The function $C(m) = 0.25m + 40$ gives the monthly cost, in dollars, of a phone plan when $m$ minutes of calls are used. What is the best interpretation of the number $40$ in this context?

   • A.

     The cost, in dollars, of each minute of calls

   • B.

     The monthly cost, in dollars, when no call minutes are used

   • C.

     The number of minutes of calls included each month

   • D.

     The monthly cost, in dollars, when $40$ minutes of calls are used

   Answer: B.

   In $C(m) = 0.25m + 40$, the number $40$ is the value of $C$ when $m = 0$, so it is the monthly cost when no call minutes are used: the fixed charge. The number $0.25$ is the slope, the cost added for each additional minute, which rules out the choice about cost per minute. The choice about $40$ minutes confuses an input of the function with its constant term; $C(40) = 50$, not $40$.

5. 5.

   A drone's battery lasts $24$ minutes on a full charge. It takes $3$ minutes to fly to a survey site and $3$ minutes to fly back, and the drone must land with at least $4$ minutes of battery remaining. If the drone spends $t$ minutes filming at the site, which inequality represents all possible values of $t$?

   • A.

     $t + 6 \le 20$

   • B.

     $t + 6 \ge 20$

   • C.

     $t + 4 \le 24$

   • D.

     $t - 6 \le 20$

   Answer: A.

   The time in the air is the trip out, the filming time, and the trip back: $3 + t + 3 = t + 6$ minutes. Landing with at least $4$ minutes left means the air time can be at most $24 - 4 = 20$ minutes, so $t + 6 \le 20$. The choice $t + 6 \ge 20$ reverses the direction; keeping battery in reserve limits the flight, it does not require a minimum. The choice $t + 4 \le 24$ ignores the $6$ minutes of travel, and $t - 6 \le 20$ subtracts the travel time instead of adding it.

6. 6.

   A line in the $xy$-plane has a slope of $-2$ and passes through the point $(0, 3)$. Which of the following is an equation of the line?

   • A.

     $y = -2x + 3$

   • B.

     $y = 2x + 3$

   • C.

     $y = 3x - 2$

   • D.

     $y = -2x - 3$

   Answer: A.

   In slope-intercept form $y = mx + b$, $m$ is the slope and $b$ is the $y$-intercept. The point $(0, 3)$ lies on the $y$-axis, so $b = 3$, and the slope is $m = -2$, which gives $y = -2x + 3$. The choice $y = 3x - 2$ swaps the slope and the intercept, and $y = 2x + 3$ drops the negative sign on the slope.

7. 7.

   The function $g$ is linear, $g(2) = 7$, and $g(5) = 1$. For what value of $x$ does $g(x) = -9$?

   • A.

     $-6$

   • B.

     $-1$

   • C.

     $8$

   • D.

     $10$

   Answer: D.

   The slope is $\frac{1 - 7}{5 - 2} = -2$, so $g(x) = -2x + b$. Using $g(2) = 7$ gives $-4 + b = 7$, so $b = 11$ and $g(x) = -2x + 11$. Setting $-2x + 11 = -9$ gives $-2x = -20$, so $x = 10$. The choice $-1$ comes from moving $11$ to the right side with the wrong sign, giving $-2x = 2$, and $8$ comes from treating $7$ as the $y$-intercept instead of $g(2)$.

8. 8.

   In the system of equations $ax + 6y = 15$ and $4x - 8y = 9$, $a$ is a constant. If the system has no solution, what is the value of $a$?

   • A.

     $-12$

   • B.

     $-3$

   • C.

     $-\frac{3}{4}$

   • D.

     $3$

   Answer: B.

   A system of two linear equations has no solution when the lines are parallel: same slope, different intercepts. In slope-intercept form, the first line has slope $-\frac{a}{6}$ and the second has slope $\frac{4}{8} = \frac{1}{2}$. Setting $-\frac{a}{6} = \frac{1}{2}$ gives $a = -3$. The first equation is then $-3x + 6y = 15$; multiplying the second equation by $-\frac{3}{4}$ gives $-3x + 6y = -\frac{27}{4}$, a different constant, so the lines are distinct and never meet. Choice D drops the negative sign from the slope of the first equation, and choice C is the ratio of the coefficients rather than the value of $a$.

9. 9.

   For the linear function $f$, $f(x + 3) - f(x) = 12$ for every value of $x$, and $f(5) = 11$. What is the value of $f(-1)$?

   • A.

     $-61$

   • B.

     $-13$

   • C.

     $-1$

   • D.

     $35$

   Answer: B.

   A linear function changes by a constant amount per unit of $x$. An increase of $3$ in $x$ raises $f$ by $12$, so the slope is $\frac{12}{3} = 4$. Going from $x = 5$ to $x = -1$ is a decrease of $6$ in $x$, so $f(-1) = 11 - 6(4) = -13$. Choice A uses $12$ as the slope instead of $12 \div 3$, and choice D adds $24$ instead of subtracting it, moving in the wrong direction along the line.

10. 10.

    $x + 2y = 11$

    $x - y = 2$

    Which ordered pair $(x, y)$ is the solution to the system of equations above?

    • A.

      $(5, 3)$

    • B.

      $(3, 5)$

    • C.

      $(7, 2)$

    • D.

      $(1, 5)$

    Answer: A.

    Subtract the second equation from the first: $(x + 2y) - (x - y) = 11 - 2$, so $3y = 9$ and $y = 3$. Then $x - 3 = 2$ gives $x = 5$, and the solution is $(5, 3)$. The choice $(3, 5)$ reverses the coordinates; it fails the first equation because $3 + 2(5) = 13$, not $11$. The choice $(7, 2)$ satisfies only the first equation, since $7 - 2 = 5$, not $2$.