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

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 \(b\)?

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

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 \( a + b \)?

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

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?

Given the system of equations:

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

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

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 \( F \)?

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 \(b\)?

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?

A right triangle has legs with lengths of \( 5 , \text{cm} \) and \( 12 , \text{cm} \). 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 \( d \)?

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

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

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

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 |
|----|----|
| \(m\) | 10 |
| \(m + 3\) | -20 |

The y-intercept of the line is at \((m - 4, b)\), where \(m\) and \(b\) are constants. What is the 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?

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 \( O \)?

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 \( p \)?

Given the system of equations:

\( 15x + 2y = 90 \)
\( 5x + y = 60 \)

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

\(x^2 - 12x + 11 = 0.\) One solution to the given equation can be written as \(6 + \sqrt{k}\), where \(k\) is a constant. What is the value of \(k\)?

Poll results:
Candidate A - 600 votes
Candidate B - 400 votes

In a random poll of 1,000 voters, the above results were recorded. If 10,000 people vote in the election, by how many votes is Candidate A expected to win?

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

\( y = 4x + 8 \)
\( y = 4x - 2 \)

The function \( F(x) = \frac{9}{5}(x - 273.15) + 32 \) gives the temperature in degrees Fahrenheit that corresponds to a temperature of \( x \) kelvins. If a temperature increased by 2.10 kelvins, by how much did the temperature increase in degrees Fahrenheit?

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 \( p \)?

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 \( \sin(J) \)?

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

| x | y |
|----|----|
| \(p\) | -7 |
| \(p + 8\) | 21 |

The y-intercept of the line is at \((p - 6, b)\), where \(p\) and \(b\) are constants. What is the value of \(b\)?

A runner used water from a bottle during a marathon. The function j(x) = -0.5x + 10 approximates the volume, in liters, of water the runner had remaining after x kilometers of the marathon. Which statement is the best interpretation of the y-intercept of the graph of y=j(x) in the xy-plane in this context?

A construction worker used concrete to build foundations. The function k(x) = -8x + 64 approximates the amount of concrete, in cubic feet, the worker had remaining after building x foundations. Which statement is the best interpretation of the y-intercept of the graph of y=k(x) in the xy-plane in this context?

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

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?

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

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?

g(t) = 500 - 7t
The function g models the volume of liquid, in milliliters, in a bottle t minutes after it starts leaking. According to the model, what is the predicted volume, in liters, leaking from the bottle each hour?

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

Consider the system of inequalities: \( y \geq 2x + 3 \) and \( x + y \leq 7 \). Which point \( (x, y) \) is a solution to the system in the xy-plane?

A cube has a volume of 343 cubic units. What is the surface area, in square units, of the cube?

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

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

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?

\( 5x + 4y = 16 \) and \( -10x - 8y = -32 \)

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

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 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?

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