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

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?

\(x^2 - 10x + 2 = 0.\) One solution to the given equation can be written as \(5 + \sqrt{k}\), where \(k\) is a constant. What is the value of \(k\)?

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)

\( 8z + 4 = 4(2z + 1) \). How many solutions does the given equation have?

A scientist observes an initial population of 1,500 cells. Twelve hours later, the population grows to 24,000. Using the exponential growth formula \( P = C(2)^{rt} \), where \( P \) is the cell count at \( t \) hours, determine the value of \( r \).

The measure of angle M is \( \frac{3\pi}{4} \) radians. The measure of angle N is \( \frac{\pi}{6} \) radians greater than the measure of angle M. What is the measure of angle N, in degrees?

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?

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?

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

The equation describes the relationship between the number of parrots, \( p \), and the number of snakes, \( s \), that can be cared for in a wildlife rehabilitation center. If the center cares for 10 snakes, how many parrots can it care for?

\( 4p + 2s = 100 \)

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

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

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 given equation, \( (5x + p)(4x^2 - 32)(2x^2 - 10x + 2p) = 0 \), where \( p \) is a positive constant. The sum of the solutions to the equation is \( 15 \). What is the value of \( p \)?

Triangles \( \triangle LMN \) and \( \triangle PQR \) are congruent, where \( L \) corresponds to \( P \), and \( M \) and \( Q \) are right angles. The measure of angle \( L \) is 30°. What is the measure of angle \( R \)?

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?

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?

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

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 \(r\)?

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)

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 measure of angle P is \( \frac{5\pi}{6} \) radians. The measure of angle Q is \( \frac{\pi}{4} \) radians greater than the measure of angle P. What is the measure of angle Q, in degrees?

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?

Value: 5, 10, 15, 20, 25

Data set A frequency: 6, 8, 10, 8, 6

Data set B frequency: 7, 8, 9, 8, 7

Data set A and Data set B each contain 38 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?

For \(f(x) = -3x^2 + 12x - 5\), let \(g(x) = f(x - 6)\). For what value of \(x\) does \(g(x)\) reach its maximum?

A farm includes a 10-acre orchard and a 30-acre pasture. The total number of apple trees on the farm is 1,800. The equation 10𝑎 + 30𝑏 = 1,800 represents this situation. Which of the following is the best interpretation of 𝑎 in this context?

The function \( p \) is defined by \( p(x) = 3x + 9 \). The graph of \( y = p(x) \) 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 \( a + b \)?

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

The function \( h(t) = 45,000 \cdot (1.04)^{t/200} \) represents the number of organisms in a culture \( t \) minutes after starting. How much time, in hours, is needed for the culture's population to double?

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?

\( 6m + 2t = 180 \)

A line in the xy-plane has a slope of \( \frac{7}{8} \) and passes through the point \( (4, -1) \). Which of the following equations represents this line?

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

The equation describes the relationship between the number of hamsters, \( d \), and the number of birds, \( b \), that can be kept in a pet shop. If the shop can keep 8 birds, how many hamsters can it keep?

\( 2.5d + 3.5b = 70 \)

4x + my = 12

2x = 5 - 3y

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

Given the system of equations:

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

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

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?

Square M has side lengths that are 15 times the side lengths of square N. The area of square M is \( k \) times the area of square N. What is the value of \( k \)?

The function \( g(t) = 20,000 \cdot (1.05)^{t/300} \) gives the number of cells in a population \( t \) minutes after an initial observation. How much time, in hours, does it take for the number of cells to double?

Given the system of equations:

\( 18x + y = 81 \)
\( 3x + y = 27 \)

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

A colony of microorganisms starts with a population of 4,000. After three hours, the population has grown to 32,000. Following the exponential growth formula \( P = C(2)^{rt} \), where \( t \) represents hours, determine the value of \( r \).

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?

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 \( U \)?

One of the factors of \(5x^3 + 35x^2 + 60x\) is \(x + b\), where \(b\) is a positive constant. What is the smallest possible value of \(b\)?

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?

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?

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?