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

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

The function \( f \) is defined by \( f(x) = 250(0.4)^x \). What is the value of \( f(0) \)?

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

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 \(q\)?

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 \(b\)?

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:
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?

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

One of the factors of \(6x^3 + 24x^2 + 30x\) is \(x + b\), where \(b\) is a positive constant. What is the smallest possible value of \(b\)?

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 \( a + b \)?

\(m(x) = 7500(0.70)^{x/12}\)

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

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 \( O \)?

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 \( k \)?

In a lab experiment, a cell culture begins with 3,000 cells. Eight hours later, the cell count increases to 24,000. Using the formula \( P = C(2)^{rt} \), where \( C \) and \( r \) are constants, and \( P \) is the number of cells \( t \) hours after the initial count, find the value of \( r \).

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?

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?

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

In triangles ABC and DEF, which are similar, angle B corresponds to angle E, and angles A and D are right angles. If \( \sin(B) = \frac{9}{15} \), what is the value of \( \sin(E) \)?

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?

The value of an investment is initially $10,000 and it increases by 8% every month. Which equation represents the value \( V \) of the investment after \( x \) years?

One of the factors of \(3x^3 + 27x^2 + 54x\) is \(x + b\), where \(b\) is a positive constant. What is the smallest possible value of \(b\)?

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

If \( 50 \) is \( p \% \) of \( 80 \), what is \( p \% \) of \( 50 \)?

f(x) = 5(3)^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?

Which ordered pair is a solution to the following equations:

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

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 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?

\( 4p + 2s = 100 \)

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?

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?

\(q = \frac{m}{10a + 3b}\). The given equation relates the distinct positive numbers \(q, m, a,\) and \(b\). Which equation correctly expresses \(10a + 3b\) in terms of \(q\) and \(m\)?

Square R has side lengths that are 12 times the side lengths of square S. The area of square R is \( k \) times the area of square S. What is the value of \( k \)?

Which ordered pair is a solution to the following equations:

\( y = (x - 1)(x + 2) \)
\( y = 3x - 3 \)

One gallon of paint will cover 250 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?

If \( 45 \) is \( p \% \) of \( 90 \), what is \( p \% \) of \( 45 \)?

A line in the xy-plane has a slope of \( \frac{3}{5} \) and passes through the point \( (2, -4) \). Which of the following equations represents this line?

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

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

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

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

The exponential function \( m \) is defined by \( m(x) = 16 \cdot q^x \), where \( q \) is a positive constant. If \( m(3) = 4096 \), what is \( m(\frac{1}{4}) \)?

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?

\(t = \frac{n}{5x + 6y}\). The given equation relates the distinct positive numbers \(t, n, x,\) and \(y\). Which equation correctly expresses \(5x + 6y\) in terms of \(t\) and \(n\)?

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 \( F(x) = \frac{9}{5}(x - 200) + 10 \) gives the temperature in degrees Fahrenheit that corresponds to a temperature of \( x \) kelvins. If a temperature increased by 4.50 kelvins, by how much did the temperature increase in degrees Fahrenheit?

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

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

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?

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?