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

The population of a certain bacteria colony is initially 2,000. The population doubles every 30 minutes. Which equation represents the population \( p \) after \( x \) hours?

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 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 \( p \)?

Consider the system of inequalities: \( y \leq -x + 4 \) and \( 2x + y \geq 1 \). Which point \( (x, y) \) is a solution to the system in the xy-plane?

The function \( f \) is defined by \( f(x) = 500(0.05)^x \). What is the value of \( f(0) \)?

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?

Value: 7, 14, 21, 28, 35

Data set A frequency: 10, 8, 6, 4, 2

Data set B frequency: 2, 4, 6, 8, 10

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?

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

\( 2x - 3y = 7 \) and \( 4x - 6y = 20 \)

Poll results:
Candidate P - 725 votes
Candidate Q - 275 votes

According to the poll of 1,000 voters, Candidate P received 725 votes, and Candidate Q received 275 votes. If 8,000 people vote in the election, how many more votes would Candidate P receive compared to Candidate Q?

A cube has a volume of 343 cubic units. What is the surface area, in square units, of the cube?

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 \( g(\frac{1}{2}) \)?

A national park has an area of 10,240,000 square yards. What is the area, in square miles, of this park? (1 mile = 1760 yards)

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

Triangles \( \triangle ABC \) and \( \triangle DEF \) are congruent, where \( A \) corresponds to \( D \), and \( B \) and \( E \) are right angles. If the measure of angle \( C \) is 55°, what is the measure of angle \( F \)?

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

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

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

| x | y |
|----|----|
| \(m\) | 10 |
| \(m + 3\) | -20 |

The y-intercept of the line is at \((m - 4, b)\), where \(m\) and \(b\) are constants. What is the value of \(b\)?

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?

\(k(x) = 4800(0.68)^{x/6}\)

The function \(k\) models the depreciation in the value of a computer, in dollars, after \(x\) months. If the computer's value decreases each year by \(p\)% of its value from the preceding year, what is the value of \(p\)?

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

\(x^2 - 8x + 7 = 0.\) 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 function \( f(x) = \frac{1}{16}(x - 5)^2 + 2 \) gives a roller coaster car's height above the ground \( f(x) \), in feet, \( x \) seconds after it started moving on a track, where \(\) 0 < x < 12 [/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?

The function \( f(x) = \frac{1}{9}(x - 7)^2 + 3 \) gives a metal ball's height above the ground \( f(x) \), in inches, \( x \) seconds after it started moving on a track, where \(\) 0 < x < 10 [/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?

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?

A proposal for a new library was included on an election ballot. A radio show stated that 3 times as many people voted in favor of the proposal as people who voted against it. A social media post reported that 15,000 more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?

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?

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

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

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 \( p \)?

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?

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 \(b\)?

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

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?

\(x^2 - 6x + 3 = 0.\) 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 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?

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 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)

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?

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

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

For \(x > 0\), the function \(q\) is defined as follows: \(q(x)\) equals 130% of \(x\). Which of the following could describe this function?

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?

The function \( j \) is given by \( j(x) = 50 \cdot k^x \), where \( k \) is a positive constant. If \( j(5) = 15625 \), what is \( j(0.5) \)?