SAT Math Randomized Questions - 3 Full Math Practice Tests - Answers and Detailed Explanations at the END

\(g(x) = 8000(0.75)^{x/6}\)

The function \(g\) gives the value, in dollars, of a certain piece of equipment after \(x\) months of use. If the value of the equipment decreases each year by \(q\)% of its value from the preceding year, what is the value of \(q\)?

Consider the system of inequalities: \( y \geq 2x + 3 \) and \( x + y \leq 7 \). Which point \( (x, y) \) is a solution to the system in the xy-plane?

A vote on a school funding bill showed that 3 times as many voters voted against the bill as those who voted in favor. It was also reported that 18,000 more voters voted against it than in favor. How many voters voted against the bill?

In the xy-plane, the equation \( 25x^2 + 250px + 25y^2 - 200py = -625p^2 \) 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?

The equation describes the relationship between the number of fish, \( a \), and the number of turtles, \( c \), that a pet shop can care for. If the shop can care for 12 turtles on a given day, how many fish can it care for?

\( 1.5a + 4.5c = 90 \)

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?

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

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

The function \( r \) is defined by \( r(x) = 8x - 16 \). The graph of \( y = r(x) \) 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 \( a + b \)?

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

A line in the xy-plane has a slope of \( -2 \) and passes through the point \( (3, 7) \). Which of the following equations represents this line?

The function \( f(x) = \frac{1}{4}(x - 8)^2 + 6 \) gives the height of a drone above the ground \( f(x) \), in meters, \( x \) seconds after it started flying, where \(\) 0 < x < 15 [/latex]. Which of the following is the best interpretation of the vertex of the graph of [latex] y = f(x) [/latex] in the [latex] xy [/latex]-plane?

Poll results:
Candidate L - 600 votes
Candidate M - 400 votes

A poll was conducted with 1,000 voters. If 7,500 people vote in the election, by how many votes is Candidate L expected to win?

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?

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?

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

The table below gives the coordinates of two points on a line in the xy-plane:

| x | y |
|----|----|
| \(r\) | 8 |
| \(r + 4\) | -24 |

The y-intercept of the line is at \((r - 2, b)\), where \(r\) and \(b\) are constants. What is the value of \(b\)?

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

What percentage of \(500\) is \(250\)?

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?

Given the system of equations:

\( 20x + 3y = 150 \)
\( 4x + y = 30 \)

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

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 following equation relates the variables \( x \) and \( y \):

\( y = x^2 - 8x + 18 \)

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

The function \( f \) is defined by \( f(x) = 5x - 15 \). The graph of \( y = f(x) \) 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 \( a + b \)?

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

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

In a recent referendum, 4 times as many people voted against a measure as those who voted in favor of it. A survey indicated that 12,000 more people voted against it than in favor. How many people voted in favor of the measure?

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

A right triangle has legs with lengths of \( 7 , \text{cm} \) and \( 24 , \text{cm} \). If the length of the hypotenuse, in cm, can be written in the form \( \sqrt{d} \), where \( d \) is an integer, what is the value of \( d \)?

\( 3y - 9 = 3(y - 3) \). How many solutions does the given equation have?

Given the system of equations:

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

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

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?

One gallon of paint will cover 200 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?

Caleb used juice to make popsicles. The function f(x) = -5x + 30 approximates the volume, in fluid ounces, of juice Caleb had remaining after making x popsicles. Which statement is the best interpretation of the y-intercept of the graph of y=f(x) in the xy-plane in this context?

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

The equation \( y = x^2 - 12x + 35 \) relates \( x \) and \( y \). For what value of \( x \) does \( y \) reach its minimum?

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 \( O \)?

f(x) = 7(2)^x. The function f is defined by the given equation. If g(x) = f(x + 4), which of the following equations defines the function g?

A baker used dough to make loaves of bread. The function g(x) = -3x + 50 approximates the amount of dough, in pounds, the baker had remaining after making x loaves of bread. Which statement is the best interpretation of the y-intercept of the graph of y=g(x) in the xy-plane in this context?

If \(\frac{r}{s} = 6\) and \(\frac{48r}{ks} = 6\), what is the value of \(k\)?

Consider the system of inequalities: \( y \geq -2x - 1 \) and \( x + 7 \geq y \). Which point \( (x, y) \) is a solution to the system in the xy-plane?

If \(\frac{x}{y} = 8\) and \(\frac{56x}{my} = 8\), what is the value of \(m\)?

\(x(qx - 64) = -20.\) In the given equation, q is an integer constant. If the equation has no real solution, what is the least possible value of q?

A researcher initially measures 8,000 units of a certain substance. Six hours later, the substance's quantity has increased to 64,000 units. Assuming exponential growth, the formula \( P = C(2)^{rt} \) represents the amount of substance, where \( C \) is a constant and \( P \) is the quantity after \( t \) hours. What is the value of \( r \)?

A cube has a volume of 64,000 cubic units. What is the surface area, in square units, of the cube?