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

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?

\( 6m + 2t = 180 \)

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?

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?

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?

In the given equation, \( (4x + p)(6x^2 - 36)(3x^2 - 18x + 9p) = 0 \), where \( p \) is a positive constant. The sum of the solutions to the equation is \( 8 \). What is the value of \( p \)?

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 half-life of a radioactive substance is 3 years. The initial quantity of the substance is 5 grams. Which equation best represents the quantity \( Q \) of the substance remaining after \( x \) minutes?

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?

\( 1.5a + 4.5c = 90 \)

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

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

Given the system of equations:

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

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

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

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?

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?

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?

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?

\(x(nx - 72)\) = -36. In the given equation, n is an integer constant. If the equation has no real solution, what is the least possible value of n?

\(x^2 - 12x + 11 = 0.\) 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 \( \frac{7}{8} \) and passes through the point \( (4, -1) \). Which of the following equations represents this line?

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?

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

Which ordered pair is a solution to the given equations:

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

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?

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

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

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

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?

A cube has a volume of 474,552 cubic units. What is the surface area, in square units, of the cube?

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?

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?

A line in the xy-plane has a slope of \( -\frac{5}{6} \) and passes through the point \( (-6, 4) \). Which of the following equations represents this line?

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 \( p \)?

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?

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

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 \( d \)?

For \(x > 0\), the function \(g\) is defined as follows: \(g(x)\) equals 150% of \(x\). Which of the following could describe this function?

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?

For \(x > 0\), the function \(p\) is defined as follows: \(p(x)\) equals 75% of \(x\). Which of the following could describe this function?

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 \( p \) 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 \( a + b \)?

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?

If \( 120 \) is \( p \% \) of \( 200 \), what is \( p \% \) of \( 120 \)?

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 \( U \)?

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?