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

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

If \(\frac{m}{n} = 3\) and \(\frac{18m}{pn} = 3\), what is the value of \(p\)?

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

\(w = \frac{g}{2p + 9q}\). The given equation relates the distinct positive numbers \(w, g, p,\) and \(q\). Which equation correctly expresses \(2p + 9q\) in terms of \(w\) and \(g\)?

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?

5x + 7y = 20 + n

14y = 10x - 35

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

One gallon of paint will cover 180 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?

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

\( x - 4y = 3 \) and \( -2x + 8y = -6 \)

One of the factors of \(4x^3 + 32x^2 + 96x\) is \(x + b\), where \(b\) is a positive constant. What is the smallest possible value of \(b\)?

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)

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 \( \sin(P) \)?

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?

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?

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?

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?

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?

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 \( O \)?

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?

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

What percentage of \(400\) is \(120\)?

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 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 given equation describes the relationship between the number of cats, \( x \), and the number of dogs, \( y \), that can be cared for at a pet shelter on a given day. If the shelter cares for 24 dogs on a given day, how many cats can it care for on this day?

\( 3.5x + 7y = 140 \)

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?

Poll results:
Candidate X - 350 votes
Candidate Y - 450 votes

In a poll of 800 voters, Candidate X received 350 votes, and Candidate Y received 450 votes. If 5,600 people vote in the election, how many more votes is Candidate Y expected to receive compared to Candidate X?

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?

For the function q, the value of q(x) decreases by 45% for every increase in the value of x by 1. If q(0) = 14, which equation defines q?

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

| x | y |
|----|----|
| \(n\) | 12 |
| \(n - 6\) | -18 |

The y-intercept of the line is at \((n + 2, b)\), where \(n\) and \(b\) are constants. What is the value of \(b\)?

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 \( p \)?

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 \( F \)?

If \(f(x) = x^2 - 10x + 25\), and \(g(x) = f(x - 2)\), for what value of \(x\) does \(g(x)\) reach its minimum?

\( 10a - 3 = 10(a - 0.3) + 0 \). How many solutions does the given equation have?

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 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?

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?

Which ordered pair is a solution to the following equations:

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

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

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?

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?

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

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 \(b\)?

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

\( 7x + 2y = 15 \) and \( 3.5x + y = 8 \)

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

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

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

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?