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

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?

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?

\( 4p + 2s = 100 \)

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?

The function \( j \) is given by \( j(x) = 50 \cdot k^x \), where \( k \) is a positive constant. If \( j(5) = 15625 \), what is \( j(0.5) \)?

If \( 45 \) is \( p \% \) of \( 90 \), what is \( p \% \) of \( 45 \)?

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

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

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?

Value: 7, 14, 21, 28, 35

Data set A frequency: 10, 8, 6, 4, 2

Data set B frequency: 2, 4, 6, 8, 10

Data set A and Data set B each contain 30 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?

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

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?

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 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?

\( 2.5d + 3.5b = 70 \)

Given the system of equations:

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

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

Triangles \( \triangle ABC \) and \( \triangle DEF \) are congruent, where \( A \) corresponds to \( D \), and \( B \) and \( E \) are right angles. If the measure of angle \( C \) is 55°, what is the measure of angle \( F \)?

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?

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

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 \(q\)?

The given equation describes the relationship between the number of cats, \( x \), and the number of dogs, \( y \), that can be cared for at a pet shelter on a given day. If the shelter cares for 24 dogs on a given day, how many cats can it care for on this day?

\( 3.5x + 7y = 140 \)

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

\( x - 4y = 3 \) and \( -2x + 8y = -6 \)

Square M has side lengths that are 15 times the side lengths of square N. The area of square M is \( k \) times the area of square N. What is the value of \( k \)?

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?

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?

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 \(b\)?

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

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

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

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 \( k \)?

If \(\frac{r}{s} = 6\) and \(\frac{48r}{ks} = 6\), what is the value of \(k\)?

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 \( \sin(J) \)?

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 \( d \)?

In the xy-plane, the equation \( 16x^2 + 192px + 16y^2 - 128py = -1024p^2 \)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 xy-plane, the equation \( 25x^2 + 250px + 25y^2 - 200py = -625p^2 \) 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 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)

A colony of microorganisms starts with a population of 4,000. After three hours, the population has grown to 32,000. Following the exponential growth formula \( P = C(2)^{rt} \), where \( t \) represents hours, determine the value of \( r \).

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 \( d \)?

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?

Given \(f(x) = 3x^2 + 24x + 59\), the function \(g\) is defined by \(g(x) = f(x - 4)\). For what value of \(x\) does \(g(x)\) reach its minimum?

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

For \(x > 0\), the function \(q\) is defined as follows: \(q(x)\) equals 130% of \(x\). Which of the following could describe this function?

If \( 39 \) is \( p \% \) of \( 65 \), what is \( p \% \) of \( 39 \)?

One of the factors of \(2x^3 + 18x^2 + 32x\) is \(x + b\), where \(b\) is a positive constant. What is the smallest possible value of \(b\)?

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

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 \(q\)?