Digital SAT Practice Questions

The polynomial \( P(x) = x^4 + ax^3 + bx^2 + cx + d \) has strictly real coefficients. It is given that \( P(1 + i) = 0 \) and \( P(2) = 0 \). When \( P(x) \) i...

A radioactive isotope decays exponentially such that its mass decreases by \( p \\% \) every \( h \) hours. If the mass of the isotope decreases by \( q \\% \) ...

A circle with center \( O \) has a radius of \( 6 \). A secant line from a point \( P \) located outside the circle intersects the circle at points \( A \) and ...

The quadratic equation \( 3x^2 - kx + 12 = 0 \) has two distinct real roots, \( r_1 \) and \( r_2 \). If it is given that \( \frac{r_1}{r_2} + \frac{r_2}{r_1} =...

In evolutionary biology, the Baldwin effect posits that phenotypic plasticity—an organism’s ability to alter its physical traits in response to environmental ch...

Text 1 Proponents of high-frequency algorithmic trading (HFT) argue that its implementation has effectively democratized modern financial markets. By executing ...

Historical sociologists frequently conceptualize the rise of the modern European nation-state as a linear, inevitable progression from the fractured tribalism o...

Hidden beneath the expansive, two-mile-thick ice sheets of Antarctica and completely isolated from the global biosphere for millions of years ________ a vast, i...

While analyzing the original text of the 18th-century border treaty, the historian realized that the document was riddled with ________ language. These carefull...

Let \( P(x) = x^4 + ax^3 + bx^2 + cx + d \), where \( a, b, c, \) and \( d \) are real constants. When the polynomial \( P(x) \) is divided by \( x^2 + 1 \), th...

In the \( xy \)-plane, the circle with equation \[ x^2 + (y - 3)^2 = 10 \] intersects the parabola with equation \[ y = x^2 + k \] at exactly three distinct poi...

The solution to the equation \[ 2^{x+2} \cdot 3^{x-1} = 5^{2x} \] is \( x \). Which of the following expressions is equivalent to \( x \)?...

Acute triangle \( ABC \) is inscribed in a circle with a radius of \( 12 \). If \( \sin(A) = \frac{3}{4} \) and the measure of angle \( B \) is \( 30^\circ \), ...

A merchant sells two types of gems: rubies and sapphires. A ruby costs $120 and a sapphire costs $85. The merchant sold a total of \( N \) gems for exactly $4,1...

In paleoclimatology, reconstructing ancient ocean pH often relies on measuring the boron isotope ratio (\(^{11}\text{B}/^{10}\text{B}\)) found in the fossilized...

Text 1 For decades, literary historians have posited that the sheer psychological devastation of World War I was the singular catalyst for literary modernism. T...

In 1932, while observing the astonishingly agile flight patterns of tiny insects like the Encarsia formosa wasp, ______ Which choice completes the text so that ...

The introduction of the cane toad to Australia in 1935 was officially intended to eradicate the cane beetle, a pest devastating the country's lucrative sugarcan...

A team of biochemists is evaluating a newly synthesized enzyme designed to accelerate the degradation of polyethylene terephthalate (PET) plastics. They hypothe...

The system of equations is given by \[ y = cx^2 - 4x + 7 \] \[ y = 2x + k \] where \( c \) and \( k \) are constants. If the system has exactly one real solutio...

In the \( xy \)-plane, a circle with center \( O \) passes through the origin and has a radius of \( 4 \). Points \( A \) and \( B \) lie on the circle such tha...

What is the sum of all valid solutions to the equation below? \[ \frac{x}{x - 3} - \frac{2}{x + 3} = \frac{18}{x^2 - 9} \]...

A microbiologist is observing two bacterial cultures, Culture A and Culture B. Culture A initially contains \( 10,000 \) bacteria and grows by \( p\% \) every \...

The polynomial \( P(x) = ax^3 + bx^2 + cx + d \) has a remainder of \( 5 \) when divided by \( (x - 2) \), and a remainder of \( -3 \) when divided by \( (x + 1...