SAT Randomized Questions - 1 Full Math Practice Test - Answers and Detailed Explanations at the END

\(x^2 - 6x + 3 = 0.\) One solution to the given equation can be written as \(3 + \sqrt{k}\), where \(k\) is a constant. What is the value of \(k\)?

One of the factors of \(2x^3 + 18x^2 + 32x\) is \(x + b\), where \(b\) is a positive constant. What is the smallest possible value of \(b\)?

The function \( F(x) = \frac{9}{5}(x - 273.15) + 32 \) gives the temperature in degrees Fahrenheit that corresponds to a temperature of \( x \) kelvins. If a temperature increased by 2.10 kelvins, by how much did the temperature increase in degrees Fahrenheit?

In the xy-plane, the equation \( 36x^2 + 432px + 36y^2 - 288py = -1296p^2 \)represents a circle. The length of the radius of the circle is np, where n and p are positive constants. What is the value of n?

Which ordered pair is a solution to the given equations:

\( y = (x - 4)(x + 1) \)
\( y = 3x - 7 \)

The growth of a bacterial culture is described by \( b(t) = 15,000 \cdot (1.06)^{t/100} \), with \( t \) in minutes. How much time, in hours, does it take for the bacteria count to double?

In the equation \( y = x^2 - 16x + 40 \), which relates \( x \) and \( y \), for what value of \( x \) does \( y \) reach its minimum?

5x + 7y = 20 + n

14y = 10x - 35

In the given system of equations, n is a constant. If the system has no solution, what is the value of n?

A wildlife reserve has an area of 8,673,280 square yards. What is the area, in square miles, of this reserve? (1 mile = 1760 yards)

66x = 66x. How many solutions does the given equation have?

f(x) = 6(10)^x. The function f is defined by the given equation. If g(x) = f(x + 1), which of the following equations defines the function g?

The function \( f \) is defined by \( f(x) = 300(0.2)^x \). What is the value of \( f(0) \)?

The population of a certain bacteria colony is initially 2,000. The population doubles every 30 minutes. Which equation represents the population \( p \) after \( x \) hours?

g(t) = 500 - 7t
The function g models the volume of liquid, in milliliters, in a bottle t minutes after it starts leaking. According to the model, what is the predicted volume, in liters, leaking from the bottle each hour?

The function \( F(x) = \frac{9}{5}(x - 250) + 20 \) gives the temperature in degrees Fahrenheit that corresponds to a temperature of \( x \) kelvins. If a temperature increased by 1.50 kelvins, by how much did the temperature increase in degrees Fahrenheit?

The measure of angle X is \( \frac{\pi}{6} \) radians. The measure of angle Y is \( \frac{\pi}{3} \) radians greater than the measure of angle X. What is the measure of angle Y, in degrees?

The number of cells in a lab experiment is given by \( j(t) = 100,000 \cdot (1.03)^{t/350} \), where \( t \) is in minutes. How much time, in hours, will it take for the cell count to double?

The function \( q \) is defined by \( q(x) = -7x + 21 \). The graph of \( y = q(x) \) in the xy-plane has an x-intercept at \( (a, 0) \) and y-intercept at \( (0, b) \), where \( a \) and \( b \) are constants. What is the value of \( a + b \)?

Given the equation \( 2x(x - 4) + 12 = 6x(2 - x) \), what is the sum of the solutions to the given equation?

Given the system of equations:

\( 15x + 2y = 90 \)
\( 5x + y = 60 \)

The solution to the system is \( (x, y) \). What is the value of \( y \)?

A community consists of a 3-kilometer trail and a 50-kilometer network of roads. The total number of streetlights in the community is 8,000. The equation 3𝑠 + 50𝑡 = 8,000 represents this situation. Which of the following is the best interpretation of 𝑠 in this context?

In the xy-plane, the equation \( 4x^2 + 64px + 4y^2 - 32py = -256p^2 \) represents a circle. The length of the radius of the circle is np, where n and p are positive constants. What is the value of n?

Triangles \( \triangle ABC \) and \( \triangle DEF \) are congruent, where \( A \) corresponds to \( D \), and \( B \) and \( E \) are right angles. If the measure of angle \( C \) is 55°, what is the measure of angle \( F \)?

Value: 12, 16, 20, 24, 28

Data set A frequency: 4, 6, 8, 6, 4

Data set B frequency: 2, 5, 10, 5, 2

Data set A and Data set B each contain 28 values. The table shows the frequencies of the values for each data set. Which of the following statements best compares the means of the two data sets?

Given the equation \( x(x + 2) - 10 = 3x(x - 5) \), what is the sum of the solutions to the given equation?

Triangles \( \triangle PQR \) and \( \triangle STU \) are congruent, where \( P \) corresponds to \( S \), and \( Q \) and \( T \) are right angles. The measure of angle \( P \) is 25°. What is the measure of angle \( U \)?

A community poll reported that twice as many residents voted in favor of building a new park as those who voted against it. It was also reported that 6,000 more residents voted in favor than those who voted against. How many residents voted against the proposal?

At how many points do the graphs of the given equations intersect in the xy-plane?

\( y = 7x - 10 \)
\( y = 7x + 5 \)

In the given equation, \( (2x + p)(3x^2 - 15)(5x^2 - 20x + 3p) = 0 \), where \( p \) is a positive constant. The sum of the solutions to the equation is \( \frac{25}{2} \). What is the value of \( p \)?

Given \(f(x) = 2x^2 + 8x + 6\), define the function \(g(x) = f(x + 1)\). For what value of \(x\) does \(g(x)\) reach its minimum?

One of the factors of \(4x^3 + 32x^2 + 96x\) is \(x + b\), where \(b\) is a positive constant. What is the smallest possible value of \(b\)?

At how many points do the graphs of the given equations intersect in the xy-plane?

\( 3x + 5y = 25 \) and \( 6x + 10y = 50 \)

\(x^2 - 12x + 11 = 0.\) One solution to the given equation can be written as \(6 + \sqrt{k}\), where \(k\) is a constant. What is the value of \(k\)?

f(x) = 8(5)^x. The function f is defined by the given equation. If g(x) = f(x + 2), which of the following equations defines the function g?

f(x) = 5(3)^x. The function f is defined by the given equation. If g(x) = f(x + 3), which of the following equations defines the function g?

For the function k, the value of k(x) increases by 50% for every increase in the value of x by 1. If k(0) = 80, which equation defines k?

One gallon of paint will cover 250 square feet of a surface. A room has a total wall area of \(w\) square feet. Which equation represents the total amount of paint \(P\), in gallons, needed to paint the walls of the room twice?

The function \( f \) is defined by \( f(x) = 180(0.3)^x \). What is the value of \( f(0) \)?

Given the system of equations:

\( 8x + 5y = 160 \)
\( 2x + y = 30 \)

The solution to the system is \( (x, y) \). What is the value of \( y \)?

The function \( f \) is defined by \( f(x) = 400(0.5)^x \). What is the value of \( f(0) \)?

Given \(f(x) = 3x^2 + 24x + 59\), the function \(g\) is defined by \(g(x) = f(x - 4)\). For what value of \(x\) does \(g(x)\) reach its minimum?

The function \( p(t) = 75,000 \cdot (1.02)^{t/250} \) represents the population of a certain type of bacteria \( t \) minutes after observation. How much time, in hours, does it take for this bacterial population to double?

An election poll showed that 5 times as many people voted against a certain policy as those who voted in favor of it. A news article claimed that 40,000 more people voted against it than in favor. Based on this information, how many people voted in favor of the policy?

Triangles \( \triangle XYZ \) and \( \triangle ABC \) are congruent, where \( X \) corresponds to \( A \), and \( Y \) and \( B \) are right angles. If the measure of angle \( Z \) is 70°, what is the measure of angle \( C \)?