Digital ACT Practice Questions

Three geochemists debate the primary trigger of the Cretaceous-Paleogene (K-Pg) boundary mass extinction 66 million years ago. Scientist 1 The extinction was ca...

For the imaginary unit \( i = \sqrt{-1} \), which of the following expressions is equivalent to: \[ \frac{5 + 2i}{3 - 4i} \]?...

Matrix \( A \) is defined as \( \begin{pmatrix} 2k & 4 \\ 3 & k-1 \end{pmatrix} \). For which of the following values of \( k \) will Matrix \( A \) have no mat...

In triangle \( \triangle PQR \), the length of \( PQ = 7 \), \( QR = 10 \), and the measure of \( \angle PQR = 120^\circ \). What is the exact length of side \(...

**Study on Enzyme Catalase Kinetics** An aqueous solution of catalase was incubated with hydrogen peroxide (\( H_2O_2 \)) at various temperatures and pH levels....

Astronomer Maria Mitchell, who discovered Comet 1847 VI using a two-inch reflecting **telescope, was awarded a gold medal** by the King of Denmark for her break...

A quadratic function \( f(x) = ax^2 + bx + c \) has a minimum value of \( -4 \) at \( x = 1 \). If \( f(0) = -3 \), what is the value of \( a+b+c \)?...

A study investigates the effect of two different herbicides (Herbicide X and Herbicide Y) on the growth of a specific weed species (Weed Z) under varying soil p...

A small, specialized library contains a collection of 6 distinct historical fiction novels and 4 distinct non-fiction biographies. A student, unaware of the spe...

In $\triangle ABC$, the length of side $a$ is $8$ cm, the length of side $b$ is $11$ cm, and the measure of angle $C$ between them is $60^\circ$. What is the ex...

If $i = \sqrt{-1}$, what is the value of the complex expression $\frac{5 - 3i}{2 + 4i}$ in standard form $a + bi$?...

An ellipse centered at the origin in the standard $(x,y)$-coordinate plane has a major horizontal axis of length $14$ and a minor vertical axis of length $8$. W...

A committee of $4$ students is to be randomly selected from a pool of $7$ seniors and $5$ juniors. What is the probability that the committee contains exactly $...

If $\log_2(x) + \log_2(x - 6) = 4$, what is the real solution for $x$?...

Vectors $\mathbf{u} = \langle 3, -4 \rangle$ and $\mathbf{v} = \langle k, 6 \rangle$ are perpendicular in the standard coordinate plane. What is the value of th...

Given the $2 \times 2$ matrix $M = \begin{bmatrix} x & 3 \\ 4 & x - 1 \end{bmatrix}$, for what positive value of $x$ is the determinant of $M$ equal to $8$?...

In an arithmetic sequence, the $4^{\text{th}}$ term is $19$ and the $10^{\text{th}}$ term is $49$. What is the $25^{\text{th}}$ term of this sequence?...

What is the remainder when the polynomial $P(x) = 2x^4 - 5x^3 + 3x - 7$ is divided by $(x - 2)$?...

If $\sin(\theta) = -\frac{5}{13}$ and $\tan(\theta) > 0$, what is the exact value of $\cos(\theta)$?...

A circle has equation $(x + 3)^2 + (y - 5)^2 = 36$. Which of the following represents the circumference of this circle?...

How many distinct real solutions does the equation $3^{2x} - 10 \cdot 3^x + 9 = 0$ have?...

What is the sum of the infinite geometric series $18 - 12 + 8 - \frac{16}{3} + \cdots$?...

If $f(x) = 2x^2 - 3x + 1$ and $g(x) = x + 4$, what is the value of $(f \circ g)(-2)$?...

The volume of a sphere is $288\pi$ cubic units. What is the surface area, in square units, of this sphere?...