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?

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 \(b\)?

f(x) = 7(2)^x. The function f is defined by the given equation. If g(x) = f(x + 4), which of the following equations defines the function g?

Given the system of equations:

\( 8x + 5y = 160 \)
\( 2x + y = 30 \)

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

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 150 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?

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

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

For \(x > 0\), the function \(p\) is defined as follows: \(p(x)\) equals 75% of \(x\). Which of the following could describe this function?

What percentage of \(500\) is \(250\)?

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?

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 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)

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?

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?

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

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

\(q = \frac{m}{10a + 3b}\). The given equation relates the distinct positive numbers \(q, m, a,\) and \(b\). Which equation correctly expresses \(10a + 3b\) in terms of \(q\) and \(m\)?

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?

\( 3y - 9 = 3(y - 3) \). How many solutions does the given equation have?

In the given equation, \( (7x + p)(5x^2 - 25)(4x^2 - 14x + 5p) = 0 \), where \( p \) is a positive constant. The sum of the solutions to the equation is \( 10 \). What is the value of \( p \)?

Triangle ABC is similar to triangle DEF, where angle A corresponds to angle D and angles B and E are right angles. If \( \sin(A) = \frac{120}{125} \), what is the value of \( \sin(D) \)?

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

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

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

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 \( d \)?

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 \( a + b \)?

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?

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 \( \sin(J) \)?

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?

66x = 66x. How many solutions does the given equation have?

Consider the system of inequalities: \( y \leq -x + 4 \) and \( 2x + y \geq 1 \). Which point \( (x, y) \) is a solution to the system in the xy-plane?

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?

In the given equation, \( (4x + p)(6x^2 - 36)(3x^2 - 18x + 9p) = 0 \), where \( p \) is a positive constant. The sum of the solutions to the equation is \( 8 \). 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 \(g\)?

Given the equation \( x(x + 1) - 56 = 4x(x - 7) \), what is the sum of the solutions to the given equation?

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

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 \(r\)?

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

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

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

Which ordered pair is a solution to the following equations:

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

A farm includes a 10-acre orchard and a 30-acre pasture. The total number of apple trees on the farm is 1,800. The equation 10𝑎 + 30𝑏 = 1,800 represents this situation. Which of the following is the best interpretation of 𝑎 in this context?

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

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 \( -\frac{5}{6} \) and passes through the point \( (-6, 4) \). Which of the following equations represents this line?

\(x^2 - 6x + 3 = 0.\) One solution to the given equation can be written as \(3 + \sqrt{k}\), where \(k\) is a constant. What is the value of \(k\)?

Triangles \( \triangle LMN \) and \( \triangle PQR \) are congruent, where \( L \) corresponds to \( P \), and \( M \) and \( Q \) are right angles. The measure of angle \( L \) is 30°. What is the measure of angle \( R \)?

Consider the system of inequalities: \( y \geq 4x - 1 \) and \( y \leq x + 5 \). Which point \( (x, y) \) is a solution to the system in the xy-plane?