Hardest Digital SAT Questions in 2025

Question 1

The system of equations is given as:

$$\frac{9}{20}by + \frac{7}{15} = -\frac{9}{20}ax$$ $$\frac{x}{8} + \frac{y}{18} = \frac{a}{2} + \frac{5x}{12}$$

What is the value of $a - b$?

Question 2

The equation above gives the power in an electrical circuit, $P$, in Watts as a function of the voltage, $V$, in Volts and the resistance, $R$, in Ohms:

$$P = \frac{V^2}{R}$$

An electrical engineer is measuring two circuits. The first circuit has a voltage of $v$ Volts and a resistance of $r$ Ohms. The second circuit has a voltage of $12v$ Volts and a resistance of $3r$ Ohms. The numbers $v$ and $r$ are positive constants. Which of the following could represent the ratio of the power in the second circuit to the power in the first circuit?

Question 3

The table shows three values of $x$ and their corresponding values of $y$ for the linear relationship between $x$ and $y$. The $x$-intercept of the line occurs when $x = -4$. The number $d$ is a negative constant. The number $k$ is a constant. What is the value of $dk$?

$$\begin{array}{|c|c|} \hline x & y \\ \hline -7 & d + 3 \\ -4 & 4k + 6d \\ 1 - 3d & 8 \\ \hline \end{array}$$

Question 4

The function $f(x)$ is defined as:

$$f(x) = ax^2 - 7x + c$$

The graph of $y = f(x)$ is a parabola with a vertex at the point $(h, k)$, where $h$ and $k$ are constants. Given $f(-9) = f(-2)$ and $c > 0$, which of the following must be true?

I. $a < -\frac{3}{4}$
II. $k > 16$

Question 5

For the function $f(x)$, for each increase in $x$ by $\frac{1}{4}$, the value of $f(x)$ increases by a factor of $m$. Which equivalent form displays $m$ as a constant or a coefficient?

Question 6

The equation is given as:

$$23 - 7x = \sqrt{3k - 2x}$$

In the given equation, $k$ is a constant. The equation has exactly one real solution. What is the minimum possible value of $56k$?

Question 7

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the length of the third side. A triangle has side lengths of $4x + 20$, $2x + 8$, and $7x - 11$. Which inequality represents all possible values of $x$?

Question 8

The given quadratic function $54x^4 + 216x^2 + 210$ has factors in the form:

$$(k)(ax^2 + b)(cx^2 + d)$$

If $a, b, c, d,$ and $k$ are integers, what is the smallest possible value of $ab$?

Question 9

For the function $f(x)$, for each increase in the value of $x$ by $c$, where $c$ is a positive constant, the value of $f(x)$ increases by a factor of $27$. Which of the following equivalent forms of the function $f$ displays $\frac{1}{c}$ as a coefficient of $x$?

Question 10

The function $f(x)$ is given as:

$$f(x) = a((x+9)^2 - b)((x+9)^2 - c)$$

The graph $y = f(x)$ passes through $(-7, 15)$ and $(0, 299)$. To the nearest whole number, what is the value of $f(-4) + f(-15)$?