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

For the function g, the value of g(x) increases by 20% for every increase in the value of x by 1. If g(0) = 30, which equation defines g?

\(x(mx - 40\) = -25. In the given equation, m is an integer constant. If the equation has no real solution, what is the least possible value of m?

The function \( g(t) = 20,000 \cdot (1.05)^{t/300} \) gives the number of cells in a population \( t \) minutes after an initial observation. How much time, in hours, does it take for the number of cells to double?

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 measure of angle X is \( \frac{\pi}{6} \) radians. The measure of angle Y is \( \frac{\pi}{3} \) radians greater than the measure of angle X. What is the measure of angle Y, in degrees?

In a recent referendum, 4 times as many people voted against a measure as those who voted in favor of it. A survey indicated that 12,000 more people voted against it than in favor. How many people voted in favor of the measure?

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

What percentage of \(400\) is \(120\)?

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 \( d \)?

A proposal for a new library was included on an election ballot. A radio show stated that 3 times as many people voted in favor of the proposal as people who voted against it. A social media post reported that 15,000 more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?

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?

\(x = \frac{h}{3y + 8z}\). The given equation relates the distinct positive numbers \(x, h, y,\) and \(z\). Which equation correctly expresses \(3y + 8z\) in terms of \(x\) and \(h\)?

Square X has side lengths that are 50 times the side lengths of square Y. The area of square X is \( k \) times the area of square Y. What is the value of \( k \)?

Let \(f(x) = 5x^2 - 20x + 95\) and define \(g(x) = f(x + 3)\). For what value of \(x\) does \(g(x)\) reach its minimum?

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?

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 following equation relates the variables \( x \) and \( y \):

\( y = x^2 - 8x + 18 \)

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?

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

The equation describes the relationship between the number of fish, \( a \), and the number of turtles, \( c \), that a pet shop can care for. If the shop can care for 12 turtles on a given day, how many fish can it care for?

\( 1.5a + 4.5c = 90 \)

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?

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

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

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

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

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 \( U \)?

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

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

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

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

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?

\( 3x + 5y = 25 \) and \( 6x + 10y = 50 \)

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?

The function \( g \) is defined by \( g(x) = -2x + 10 \). The graph of \( y = g(x) \) 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 \( a + b \)?

Given the system of equations:

\( 10x + 6y = 120 \)
\( 2x + y = 15 \)

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

If \(\frac{x}{y} = 8\) and \(\frac{56x}{my} = 8\), what is the value of \(m\)?

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

One gallon of paint will cover 200 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?

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 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?

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?

For the function k, the value of k(x) increases by 50% for every increase in the value of x by 1. If k(0) = 80, which equation defines k?

A right triangle has legs with lengths of \( 16 , \text{cm} \) and \( 30 , \text{cm} \). If the length of the hypotenuse, in cm, can be written in the form \( 2\sqrt{d} \), where \( d \) is an integer, what is the value of \( d \)?

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

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

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 \(m\)?

The equation describes the relationship between the number of hamsters, \( d \), and the number of birds, \( b \), that can be kept in a pet shop. If the shop can keep 8 birds, how many hamsters can it keep?

\( 2.5d + 3.5b = 70 \)

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?