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

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

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 \(r\)?

The measure of angle A is \( \frac{\pi}{4} \) radians. The measure of angle B is \( \frac{3\pi}{8} \) radians greater than the measure of angle A. What is the measure of angle B, in degrees?

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 \( \sin(D) \)?

Value: 8, 16, 24, 32, 40

Data set A frequency: 5, 5, 10, 5, 5

Data set B frequency: 6, 8, 6, 8, 6

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?

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?

\( 2.5d + 3.5b = 70 \)

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?

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?

A researcher initially measures 8,000 units of a certain substance. Six hours later, the substance's quantity has increased to 64,000 units. Assuming exponential growth, the formula \( P = C(2)^{rt} \) represents the amount of substance, where \( C \) is a constant and \( P \) is the quantity after \( t \) hours. What is the value of \( r \)?

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?

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?

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?

A garden contains a 6-square-meter vegetable patch and a 12-square-meter flower bed. The total number of plants in the garden is 216. The equation 6𝑣 + 12𝑓 = 216 represents this situation. Which of the following is the best interpretation of 𝑣 in this context?

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

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 \( d \)?

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

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 \(q\)?

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

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

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

f(x) = 5(3)^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?

\( 8z + 4 = 4(2z + 1) \). How many solutions does the given equation have?

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?

Square C has side lengths that are 8 times the side lengths of square D. The area of square C is \( k \) times the area of square D. What is the value of \( k \)?

Given the equation \( 2x(x - 4) + 12 = 6x(2 - x) \), what is the sum of the solutions to the given equation?

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?

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 \(b\)?

Triangles \( \triangle XYZ \) and \( \triangle ABC \) are congruent, where \( X \) corresponds to \( A \), and \( Y \) and \( B \) are right angles. If the measure of angle \( Z \) is 70°, what is the measure of angle \( C \)?

For \(x > 0\), the function \(h\) is defined as follows: \(h(x)\) equals 80% of \(x\). Which of the following could describe this function?

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

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

The exponential function \( g \) is defined by \( g(x) = 25 \cdot b^x \), where \( b \) is a positive constant. If \( g(2) = 625 \), what is \( g(\frac{1}{2}) \)?

A cube has a volume of 64,000 cubic units. What is the surface area, in square units, of the cube?

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

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

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

The equation \( y = x^2 - 12x + 35 \) relates \( x \) and \( y \). For what value of \( x \) does \( y \) reach its minimum?

A cube has a volume of 27,000 cubic units. What is the surface area, in square units, of the cube?

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

A cube has a volume of 474,552 cubic units. What is the surface area, in square units, of the cube?

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 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?

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)

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

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

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

If \(f(x) = x^2 - 10x + 25\), and \(g(x) = f(x - 2)\), for what value of \(x\) does \(g(x)\) reach its minimum?

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 \( k \)?

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)

Given the equation \( x(x + 2) - 10 = 3x(x - 5) \), what is the sum of the solutions to the given equation?