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

The function \( h \) is defined by \( h(x) = 10 \cdot c^x \), where \( c \) is a positive constant. If \( h(4) = 810 \), what is \( h(-1) \)?

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

A city park has an area of 23,184,000 square yards. What is the area, in square miles, of this park? (1 mile = 1760 yards)

A wildlife reserve has a 4-hectare bird sanctuary and a 25-hectare forest. The total number of nests in the reserve is 1,150. The equation 4𝑛 + 25𝑚 = 1,150 represents this situation. Which of the following is the best interpretation of 𝑛 in this context?

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

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

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?

Value: 10, 15, 20, 25, 30

Data set A frequency: 3, 5, 7, 9, 11

Data set B frequency: 11, 9, 7, 5, 3

Data set A and Data set B each contain 35 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?

Poll results:
Angel Cruz - 483 votes
Terry Smith - 320 votes

The table above shows the results of a poll. A total of 803 voters selected at random were asked which candidate they would vote for in the upcoming election. According to the poll, if 6,424 people vote in the election, by how many votes would Angel Cruz be expected to win?

For \(x > 0\), the function \(f\) is defined as follows: \(f(x)\) equals 120% of \(x\). Which of the following could describe this function?

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

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 \(b\)?

\(p = \frac{k}{7m + 5n}\). The given equation relates the distinct positive numbers \(p, k, m,\) and \(n\). Which equation correctly expresses \(7m + 5n\) in terms of \(p\) and \(k\)?

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

q(t) = 600 - 10t
The function q models the amount of liquid, in liters, in a tank t minutes after it begins draining. According to the model, what is the predicted amount of liquid, in milliliters, draining from the tank every 2 hours?

If \(\frac{c}{d} = 2\) and \(\frac{40c}{qd} = 2\), what is the value of \(q\)?

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

| x | y |
|----|----|
| \(p\) | -7 |
| \(p + 8\) | 21 |

The y-intercept of the line is at \((p - 6, b)\), where \(p\) and \(b\) are constants. What is the value of \(b\)?

The exponential function \( g \) is defined by \( g(x) = 25 \cdot b^x \), where \( b \) is a positive constant. If \( g(2) = 625 \), what is \( g(\frac{1}{2}) \)?

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

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

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

Square P has side lengths that are 20 times the side lengths of square Q. The area of square P is \( k \) times the area of square Q. What is the value of \( k \)?

A gardener used water to fill watering cans. The function h(x) = -2x + 20 approximates the volume, in liters, of water the gardener had remaining after filling x watering cans. Which statement is the best interpretation of the y-intercept of the graph of y=h(x) in the xy-plane in this context?

A garden contains a 6-square-meter vegetable patch and a 12-square-meter flower bed. The total number of plants in the garden is 216. The equation 6𝑣 + 12𝑓 = 216 represents this situation. Which of the following is the best interpretation of 𝑣 in this context?

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

A line in the xy-plane has a slope of \( \frac{1}{3} \) and passes through the point \( (-3, 5) \). Which of the following equations represents this line?

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

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 \( F(x) = \frac{9}{5}(x - 180) + 5 \) 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?

\(x(mx - 40\) = -25. In the given equation, m is an integer constant. If the equation has no real solution, what is the least possible value of m?

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

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

Value: 8, 16, 24, 32, 40

Data set A frequency: 5, 5, 10, 5, 5

Data set B frequency: 6, 8, 6, 8, 6

Data set A and Data set B each contain 30 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?

h(t) = 200 - 5t
The function h models the amount of water, in gallons, in a container t hours after it begins to leak. According to the model, what is the predicted amount of water, in pints, leaking from the container each day?

\(x^2 - 8x + 7 = 0.\) One solution to the given equation can be written as \(4 + \sqrt{k}\), where \(k\) is a constant. What is the value of \(k\)?

In the xy-plane, the equation \( 16x^2 + 192px + 16y^2 - 128py = -1024p^2 \)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 \( \triangle XYZ \) 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 \( C \)?

Which ordered pair is a solution to the following equations:

\( y = (x + 5)(x - 3) \)
\( y = 6x - 15 \)

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) = 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?

Starting with 5,000 bacteria, a biologist records 40,000 bacteria after five hours. If the growth follows \( P = C(2)^{rt} \), where \( P \) is the bacterial count and \( t \) is time in hours, what is the value of \( r \)?

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

| x | y |
|----|----|
| \(q\) | -10 |
| \(q - 9\) | -40 |

The y-intercept of the line is at \((q + 5, b)\), where \(q\) and \(b\) are constants. What is the value of \(b\)?

\(h(x) = 12000(0.82)^{x/4}\)

The function \(h\) gives the value, in dollars, of a machine after \(x\) months of operation. If the machine’s value decreases each year by \(r\)% of its value from the preceding year, what is the value of \(r\)?

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

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