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

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

The function \( h \) is defined by \( h(x) = 10 \cdot c^x \), where \( c \) is a positive constant. If \( h(4) = 810 \), what is \( h(-1) \)?

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

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 \( f \) is defined by \( f(x) = 5x - 15 \). The graph of \( y = f(x) \) 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 \( a + b \)?

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?

The function \( f \) is defined by \( f(x) = 400(0.5)^x \). What is the value of \( f(0) \)?

f(x) = 8(5)^x. The function f is defined by the given equation. If g(x) = f(x + 2), which of the following equations defines the function g?

If \(\frac{c}{d} = 2\) and \(\frac{40c}{qd} = 2\), what is the value of \(q\)?

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

\( 7x + 2y = 15 \) and \( 3.5x + y = 8 \)

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?

Caleb used juice to make popsicles. The function f(x) = -5x + 30 approximates the volume, in fluid ounces, of juice Caleb had remaining after making x popsicles. Which statement is the best interpretation of the y-intercept of the graph of y=f(x) in the xy-plane in this context?

Value: 10, 15, 20, 25, 30

Data set A frequency: 3, 5, 7, 9, 11

Data set B frequency: 11, 9, 7, 5, 3

Data set A and Data set B each contain 35 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?

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

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 \(q\)?

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?

The equation below relates \( x \) and \( y \):

\( y = x^2 - 6x + 15 \)

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

One gallon of paint will cover 300 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?

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?

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?

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

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

| x | y |
|----|----|
| \(r\) | 8 |
| \(r + 4\) | -24 |

The y-intercept of the line is at \((r - 2, b)\), where \(r\) and \(b\) are constants. What is the value of \(b\)?

Poll results:
Candidate L - 600 votes
Candidate M - 400 votes

A poll was conducted with 1,000 voters. If 7,500 people vote in the election, by how many votes is Candidate L expected to win?

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)

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?

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

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 \(q\)?

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

The population of a city was 50,000 in the year 2020, and it increases by 2% per year. Which equation best represents the population \( p \) of the city after \( x \) seconds?

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 line in the xy-plane has a slope of \( \frac{7}{8} \) and passes through the point \( (4, -1) \). Which of the following equations represents this line?

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

\( y = 7x - 10 \)
\( y = 7x + 5 \)

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 \(b\)?

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)

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?

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 \(b\)?

The function \( f(x) = \frac{1}{9}(x - 7)^2 + 3 \) gives a metal ball's height above the ground \( f(x) \), in inches, \( x \) seconds after it started moving on a track, where \(\) 0 < x < 10 [/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?

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 \( p(t) = 75,000 \cdot (1.02)^{t/250} \) represents the population of a certain type of bacteria \( t \) minutes after observation. How much time, in hours, does it take for this bacterial population to double?

The measure of angle S is \( \frac{2\pi}{3} \) radians. The measure of angle T is \( \frac{\pi}{4} \) radians greater than the measure of angle S. What is the measure of angle T, in degrees?

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?

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 \( \sin(E) \)?

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

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?

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

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?