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

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

Given \(f(x) = 2x^2 + 8x + 6\), define the function \(g(x) = f(x + 1)\). For what value of \(x\) does \(g(x)\) reach its minimum?

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 \( k \)?

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)

A lake has an area of 5,904,900 square yards. What is the area, in square miles, of this lake? (1 mile = 1760 yards)

Starting with 5,000 bacteria, a biologist records 40,000 bacteria after five hours. If the growth follows \( P = C(2)^{rt} \), where \( P \) is the bacterial count and \( t \) is time in hours, what is the value of \( r \)?

Value: 5, 10, 15, 20, 25

Data set A frequency: 6, 8, 10, 8, 6

Data set B frequency: 7, 8, 9, 8, 7

Data set A and Data set B each contain 38 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 gardener used water to fill watering cans. The function h(x) = -2x + 20 approximates the volume, in liters, of water the gardener had remaining after filling x watering cans. Which statement is the best interpretation of the y-intercept of the graph of y=h(x) in the xy-plane in this context?

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 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 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 \( p \)?

The equation describes the relationship between the number of parrots, \( p \), and the number of snakes, \( s \), that can be cared for in a wildlife rehabilitation center. If the center cares for 10 snakes, how many parrots can it care for?

\( 4p + 2s = 100 \)

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?

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?

\( 5(x + 3) = 5x + 15 \). How many solutions does the given equation have?

The function \( f \) is defined by \( f(x) = 500(0.05)^x \). What is the value of \( f(0) \)?

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?

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 campus consists of a 5-acre sports field and a 40-acre academic zone. The total number of benches on the campus is 2,450. The equation 5𝑏 + 40𝑐 = 2,450 represents this situation. Which of the following is the best interpretation of 𝑏 in this context?

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?

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 \( \sin(E) \)?

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

Given the system of equations:

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

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

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?

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

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

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

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 \( d \)?

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

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 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?

The exponential function \( m \) is defined by \( m(x) = 16 \cdot q^x \), where \( q \) is a positive constant. If \( m(3) = 4096 \), what is \( m(\frac{1}{4}) \)?

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

| x | y |
|----|----|
| \(q\) | -10 |
| \(q - 9\) | -40 |

The y-intercept of the line is at \((q + 5, b)\), where \(q\) and \(b\) are constants. What is the value of \(b\)?

What percentage of \(700\) is \(350\)?

Given the system of equations:

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

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

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

A national park has an area of 10,240,000 square yards. What is the area, in square miles, of this park? (1 mile = 1760 yards)

The measure of angle P is \( \frac{5\pi}{6} \) radians. The measure of angle Q is \( \frac{\pi}{4} \) radians greater than the measure of angle P. What is the measure of angle Q, in degrees?

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?

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

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

In the equation \( y = x^2 - 16x + 40 \), which relates \( x \) and \( y \), for what value of \( x \) does \( y \) reach its minimum?

Given the system of equations:

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

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

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?

The population of a certain bacteria colony is initially 2,000. The population doubles every 30 minutes. Which equation represents the population \( p \) after \( x \) hours?

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 \(b\)?