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

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

The function \( F(x) = \frac{9}{5}(x - 300) + 25 \) gives the temperature in degrees Fahrenheit that corresponds to a temperature of \( x \) kelvins. If a temperature increased by 5.00 kelvins, by how much did the temperature increase in degrees Fahrenheit?

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

f(t) = 250 - 3t
The function f models the volume of liquid, in liters, in a tank t seconds after it starts draining. According to the model, what is the predicted volume, in milliliters, draining from the tank each minute?

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 \( p \)?

\(f(x) = 3(6)^x.\) The function f is defined by the given equation. If \(g(x) = f(x + 3)\), which of the following equations defines the function g?

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

\(x^2 - 10x + 2 = 0.\) One solution to the given equation can be written as \(5 + \sqrt{k}\), where \(k\) is a constant. What is the value of \(k\)?

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 \( d \)?

The half-life of a radioactive substance is 3 years. The initial quantity of the substance is 5 grams. Which equation best represents the quantity \( Q \) of the substance remaining after \( x \) minutes?

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?

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?

Which ordered pair is a solution to the following equations:

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

\(x(px - 90) = -49.\) In the given equation, p is an integer constant. If the equation has no real solution, what is the least possible value of p?

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

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

For \(f(x) = -3x^2 + 12x - 5\), let \(g(x) = f(x - 6)\). For what value of \(x\) does \(g(x)\) reach its maximum?

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?

\(j(x) = 3050(0.90)^{x/3}\)

The function \(j\) models the value, in dollars, of a vehicle after \(x\) months. If the value of the vehicle decreases each year by \(m\)% of its value from the preceding year, what is the value of \(m\)?

A field has an area of 1,549,000 square yards. What is the area, in square miles, of this field? (1 mile = 1760 yards)

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?

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?

Which ordered pair is a solution to the given equations:

\( y = (x + 4)(x - 2) \)
\( y = 5x - 4 \)

For the function p, the value of p(x) decreases by 60% for every increase in the value of x by 1. If p(0) = 50, which equation defines p?

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

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 \(r\)?

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?

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

\( y = \frac{1}{2}x + 5 \)
\( y = -\frac{1}{2}x + 5 \)

The function \( f(x) = \frac{1}{6}(x - 10)^2 + 4 \) describes the height of a basketball above the court \( f(x) \), in feet, \( x \) seconds after it was thrown, where \(\) 0 < x < 20 [/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?

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?

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)

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

\( 8z + 4 = 4(2z + 1) \). How many solutions does the given equation have?

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?

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?

A community consists of a 3-kilometer trail and a 50-kilometer network of roads. The total number of streetlights in the community is 8,000. The equation 3𝑠 + 50𝑡 = 8,000 represents this situation. Which of the following is the best interpretation of 𝑠 in this context?

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 \( d \)?

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

\( 2x - 3y = 7 \) and \( 4x - 6y = 20 \)

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

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

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

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 \( k \)?

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

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 \(p\)?

The function \( r \) is defined by \( r(x) = 8x - 16 \). The graph of \( y = r(x) \) 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 \( a + b \)?

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