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

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?

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

| x | y |
|----|----|
| \(m\) | 10 |
| \(m + 3\) | -20 |

The y-intercept of the line is at \((m - 4, b)\), where \(m\) and \(b\) are constants. What is the value of \(b\)?

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 line in the xy-plane has a slope of \( \frac{3}{5} \) and passes through the point \( (2, -4) \). Which of the following equations represents this line?

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?

Which ordered pair is a solution to the following equations:

\( y = (x - 1)(x + 2) \)
\( y = 3x - 3 \)

A small business owner budgets $2,200 to purchase candles. The owner must purchase a minimum of 200 candles to maintain the discounted pricing. If the owner pays $4.90 per candle to purchase small candles and $11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?

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

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?

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?

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 \( k \)?

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 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?

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

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 \(m\)?

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

\( 5x + 4y = 16 \) and \( -10x - 8y = -32 \)

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

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

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 \( F(x) = \frac{9}{5}(x - 180) + 5 \) gives the temperature in degrees Fahrenheit that corresponds to a temperature of \( x \) kelvins. If a temperature increased by 3.00 kelvins, by how much did the temperature increase in degrees Fahrenheit?

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

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

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 M is \( \frac{3\pi}{4} \) radians. The measure of angle N is \( \frac{\pi}{6} \) radians greater than the measure of angle M. What is the measure of angle N, in degrees?

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 \( C \)?

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

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

Which ordered pair is a solution to the following equations:

\( y = (x + 5)(x - 3) \)
\( y = 6x - 15 \)

A wildlife reserve has a 4-hectare bird sanctuary and a 25-hectare forest. The total number of nests in the reserve is 1,150. The equation 4𝑛 + 25𝑚 = 1,150 represents this situation. Which of the following is the best interpretation of 𝑛 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 \(k\)?

The exponential function \( f \) is defined by \( f(x) = 8 \cdot d^x \), where \( d \) is a positive constant. If \( f(3) = 1024 \), what is \( f(-2) \)?

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

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 \( f \) 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 \( a + b \)?

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?

The function \( f \) is defined by \( f(x) = 300(0.2)^x \). What is the value of \( f(0) \)?

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?

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?

In the given equation, \( (5x + p)(4x^2 - 32)(2x^2 - 10x + 2p) = 0 \), where \( p \) is a positive constant. The sum of the solutions to the equation is \( 15 \). What is the value of \( p \)?

What percentage of \(250\) is \(62.5\)?

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

The equation describes the relationship between the number of rabbits, \( m \), and the number of guinea pigs, \( t \), that a pet care center can accommodate. If the center cares for 30 guinea pigs, how many rabbits can it care for?

\( 6m + 2t = 180 \)

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)

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?

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

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 \(p\)?

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 \( k \)?

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?

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?