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

The exponential function \( f \) is defined by \( f(x) = 8 \cdot d^x \), where \( d \) is a positive constant. If \( f(3) = 1024 \), what is \( f(-2) \)?

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?

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?

For the function f, the value of f(x) decreases by 30% for every increase in the value of x by 1. If f(0) = 100, which equation defines f?

Given the system of equations:

\( 8x + 5y = 160 \)
\( 2x + y = 30 \)

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

In similar triangles XYZ and PQR, angle X corresponds to angle P and angles Y and Q are right angles. If \( \sin(X) = \frac{5}{13} \), what is the value of \( \sin(P) \)?

The function \( f(x) = \frac{1}{8}(x - 6)^2 + 5 \) describes the height of a kite above the ground \( f(x) \), in feet, \( x \) seconds after it was launched, 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?

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?

If \(\frac{r}{s} = 6\) and \(\frac{48r}{ks} = 6\), what is the value of \(k\)?

Given the system of equations:

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

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

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 \( a + b \)?

In the given equation, \( (3x + p)(5x^2 - 45)(3x^2 - 16x + 6p) = 0 \), where \( p \) is a positive constant. The sum of the solutions to the equation is \( \frac{20}{3} \). What is the value of \( p \)?

A baker used dough to make loaves of bread. The function g(x) = -3x + 50 approximates the amount of dough, in pounds, the baker had remaining after making x loaves of bread. Which statement is the best interpretation of the y-intercept of the graph of y=g(x) in the xy-plane in this context?

Let \(f(x) = 5x^2 - 20x + 95\) and define \(g(x) = f(x + 3)\). For what value of \(x\) does \(g(x)\) reach its minimum?

Which ordered pair is a solution to the given system of equations:

\( y = (x + 3)(x - 5) \)
\( y = 4x - 10 \)

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

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

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

The equation below relates \( x \) and \( y \):

\( y = x^2 - 6x + 15 \)

For what value of \( x \) does \( y \) 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?

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?

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 \( F \)?

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?

Which ordered pair is a solution to the following equations:

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

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

Given the equation \( x(x + 2) - 10 = 3x(x - 5) \), what is the sum of the solutions to the given equation?

\(x^2 - 4x - 5 = 0.\) One solution to the given equation can be written as \(2 + \sqrt{k}\), where \(k\) is a constant. What is the value of \(k\)?

Which ordered pair is a solution to the given equations:

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

\(x = \frac{h}{3y + 8z}\). The given equation relates the distinct positive numbers \(x, h, y,\) and \(z\). Which equation correctly expresses \(3y + 8z\) in terms of \(x\) and \(h\)?

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

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 \( p \)?

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

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?

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

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 \(q\)?

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?

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?

\( 2.5d + 3.5b = 70 \)

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?

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?

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 \(b\)?

In the xy-plane, the equation \( 4x^2 + 64px + 4y^2 - 32py = -256p^2 \) 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 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?

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?