SAT Math Randomized Questions - 2 Full Math Practice Tests - Answers and Detailed Explanations at the END

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 \( a + b \)?

Which ordered pair is a solution to the following equations:

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

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

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?

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?

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 \( \sin(E) \)?

Given the equation \( x(2x - 3) + 15 = 5x(3 - x) \), what is the sum of the solutions to the given equation?

For \(x > 0\), the function \(f\) is defined as follows: \(f(x)\) equals 120% of \(x\). Which of the following could describe this function?

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?

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

The measure of angle X is \( \frac{\pi}{6} \) radians. The measure of angle Y is \( \frac{\pi}{3} \) radians greater than the measure of angle X. What is the measure of angle Y, in degrees?

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?

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 \( k \)?

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?

Which ordered pair is a solution to the following equations:

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

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?

Two similar triangles GHI and JKL have corresponding angles G and J, with angles H and K being right angles. If \( \sin(G) = \frac{24}{25} \), what is the value of \( \sin(J) \)?

2x - 3y = 10 + k

5y = 6x - 3

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

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 \( r \).

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 \( p \)?

Given the system of equations:

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

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

7x - 4y = 8

14y = kx + 16

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

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?

\( 2.5d + 3.5b = 70 \)

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

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 \(q\)?

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

The equation \( y = x^2 - 12x + 35 \) relates \( x \) and \( y \). For what value of \( x \) does \( y \) reach its minimum?

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

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

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?

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

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 \( p \)?

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

Which ordered pair is a solution to the given equations:

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

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

\(x(mx - 40\) = -25. In the given equation, m is an integer constant. If the equation has no real solution, what is the least possible value of m?

Square X has side lengths that are 50 times the side lengths of square Y. The area of square X is \( k \) times the area of square Y. What is the value of \( k \)?

The function \( f \) is defined by \( f(x) = 180(0.3)^x \). What is the value of \( f(0) \)?

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?

Given the system of equations:

\( 20x + 3y = 150 \)
\( 4x + y = 30 \)

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

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?

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

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

Square P has side lengths that are 20 times the side lengths of square Q. The area of square P is \( k \) times the area of square Q. What is the value of \( k \)?

The growth of a bacterial culture is described by \( b(t) = 15,000 \cdot (1.06)^{t/100} \), with \( t \) in minutes. How much time, in hours, does it take for the bacteria count to double?

For the function k, the value of k(x) increases by 50% for every increase in the value of x by 1. If k(0) = 80, which equation defines k?