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

The value of an investment is initially $10,000 and it increases by 8% every month. Which equation represents the value \( V \) of the investment after \( x \) years?

The given equation relates the variables \( x \) and \( y \):

\( y = x^2 - 10x + 13 \)

For what value of \( x \) does \( y \) reach its minimum?

What percentage of \(400\) is \(120\)?

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

\( 5x + 4y = 16 \) and \( -10x - 8y = -32 \)

If \( 39 \) is \( p \% \) of \( 65 \), what is \( p \% \) of \( 39 \)?

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

\( 7x + 2y = 15 \) and \( 3.5x + y = 8 \)

Given the equation \( x(x + 1) - 56 = 4x(x - 7) \), what is the sum of the solutions to the given equation?

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

\( y = \frac{1}{2}x + 5 \)
\( y = -\frac{1}{2}x + 5 \)

A cube has a volume of 27,000 cubic units. What is the surface area, in square units, of the cube?

Triangle ABC is similar to triangle DEF, where angle A corresponds to angle D and angles B and E are right angles. If \( \sin(A) = \frac{120}{125} \), what is the value of \( \sin(D) \)?

The population of a city was 50,000 in the year 2020, and it increases by 2% per year. Which equation best represents the population \( p \) of the city after \( x \) seconds?

f(t) = 250 - 3t
The function f models the volume of liquid, in liters, in a tank t seconds after it starts draining. According to the model, what is the predicted volume, in milliliters, draining from the tank each minute?

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?

A cube has a volume of 729 cubic units. What is the surface area, in square units, of the cube?

In the given equation, \( (7x + p)(5x^2 - 25)(4x^2 - 14x + 5p) = 0 \), where \( p \) is a positive constant. The sum of the solutions to the equation is \( 10 \). What is the value of \( p \)?

\(x(px - 90) = -49.\) In the given equation, p is an integer constant. If the equation has no real solution, what is the least possible value of p?

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?

For \(x > 0\), the function \(h\) is defined as follows: \(h(x)\) equals 80% of \(x\). Which of the following could describe this function?

For the function f, the value of f(x) decreases by 30% for every increase in the value of x by 1. If f(0) = 100, which equation defines f?

For the function p, the value of p(x) decreases by 60% for every increase in the value of x by 1. If p(0) = 50, which equation defines p?

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?

A line in the xy-plane has a slope of \( \frac{3}{5} \) and passes through the point \( (2, -4) \). Which of the following equations represents this line?

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?

\(t = \frac{n}{5x + 6y}\). The given equation relates the distinct positive numbers \(t, n, x,\) and \(y\). Which equation correctly expresses \(5x + 6y\) in terms of \(t\) and \(n\)?

Triangles \( \triangle JKL \) and \( \triangle MNO \) are congruent, where \( J \) corresponds to \( M \), and \( K \) and \( N \) are right angles. The measure of angle \( L \) is 40°. What is the measure of angle \( O \)?

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)

\(f(x) = 3(6)^x.\) The function f is defined by the given equation. If \(g(x) = f(x + 3)\), which of the following equations defines the function g?

What percentage of \(250\) is \(62.5\)?

What percentage of \(700\) is \(350\)?

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

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

In a lab experiment, a cell culture begins with 3,000 cells. Eight hours later, the cell count increases to 24,000. Using the formula \( P = C(2)^{rt} \), where \( C \) and \( r \) are constants, and \( P \) is the number of cells \( t \) hours after the initial count, find the value of \( r \).

A construction worker used concrete to build foundations. The function k(x) = -8x + 64 approximates the amount of concrete, in cubic feet, the worker had remaining after building x foundations. Which statement is the best interpretation of the y-intercept of the graph of y=k(x) in the xy-plane in this context?

The function \( F(x) = \frac{9}{5}(x - 180) + 5 \) gives the temperature in degrees Fahrenheit that corresponds to a temperature of \( x \) kelvins. If a temperature increased by 3.00 kelvins, by how much did the temperature increase in degrees Fahrenheit?

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 equation describes the relationship between the number of rabbits, \( m \), and the number of guinea pigs, \( t \), that a pet care center can accommodate. If the center cares for 30 guinea pigs, how many rabbits can it care for?

\( 6m + 2t = 180 \)

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?

In the xy-plane, the equation \( 9x^2 + 144px + 9y^2 - 96py = -576p^2 \) 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?

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?

One gallon of paint will cover 180 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?

Consider the system of inequalities: \( y \geq 4x - 1 \) and \( y \leq x + 5 \). Which point \( (x, y) \) is a solution to the system in the xy-plane?

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?

A right triangle has legs with lengths of \( 9 , \text{cm} \) and \( 12 , \text{cm} \). If the length of the hypotenuse, in cm, can be written in the form \( 3\sqrt{d} \), where \( d \) is an integer, what is the value of \( d \)?

Consider the system of inequalities: \( y \leq 3x + 4 \) and \( y \geq -x - 5 \). Which point \( (x, y) \) is a solution to the system in the xy-plane?