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

Given the equation \( x(2x + 3) - 9 = 4x(x - 6) \), what is the sum of the solutions to the given equation?

If \( 75 \) is \( p \% \) of \( 150 \), what is \( p \% \) of \( 75 \)?

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 \(b\)?

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

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 \(p\)?

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 function \( h \) is defined by \( h(x) = 10 \cdot c^x \), where \( c \) is a positive constant. If \( h(4) = 810 \), what is \( h(-1) \)?

Square C has side lengths that are 8 times the side lengths of square D. The area of square C is \( k \) times the area of square D. What is the value of \( k \)?

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 \(b\)?

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 \( k \)?

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?

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

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

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

\( 3x + 5y = 25 \) and \( 6x + 10y = 50 \)

A scientist observes an initial population of 1,500 cells. Twelve hours later, the population grows to 24,000. Using the exponential growth formula \( P = C(2)^{rt} \), where \( P \) is the cell count at \( t \) hours, determine the value of \( r \).

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

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

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?

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?

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

p(t) = 350 - 6t
The function p represents the volume of liquid, in ounces, in a glass t seconds after it starts spilling. According to the model, what is the predicted volume, in fluid ounces, spilling from the glass every half minute?

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?

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

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?

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

\( y = 7x - 10 \)
\( y = 7x + 5 \)

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?

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 population of a certain bacteria colony is initially 1,000. The population triples every hour. Which equation represents the population \( p \) after \( x \) days?

A community poll reported that twice as many residents voted in favor of building a new park as those who voted against it. It was also reported that 6,000 more residents voted in favor than those who voted against. How many residents voted against the proposal?

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?

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

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

\(h(x) = 12000(0.82)^{x/4}\)

The function \(h\) gives the value, in dollars, of a machine after \(x\) months of operation. If the machine’s value decreases each year by \(r\)% of its value from the preceding year, what is the value of \(r\)?

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?

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?

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?

One gallon of paint will cover 200 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?

Which ordered pair is a solution to the following equations:

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

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 \( k \)?

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 \( p \)?

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 \( d \)?

A right triangle has legs with lengths of \( 9 , \text{cm} \) and \( 12 , \text{cm} \). If the length of the hypotenuse, in cm, can be written in the form \( 3\sqrt{d} \), where \( d \) is an integer, what is the value of \( d \)?

\(x(rx - 120) = -64.\) In the given equation, r is an integer constant. If the equation has no real solution, what is the least possible value of r?

The function \( g \) is defined by \( g(x) = -2x + 10 \). The graph of \( y = g(x) \) 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 \( a + b \)?

\(x^2 - 10x + 2 = 0.\) 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 function \( q \) is defined by \( q(x) = -7x + 21 \). The graph of \( y = q(x) \) 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 \( a + b \)?