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

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

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\(x(rx - 120) = -64.\) In the given equation, r is an integer constant. If the equation has no real solution, what is the least possible value of r?

2 / 44

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 \( a + b \)?

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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?

4 / 44

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

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

5 / 44

One of the factors of \(4x^3 + 32x^2 + 96x\) is \(x + b\), where \(b\) is a positive constant. What is the smallest possible value of \(b\)?

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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?

7 / 44

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

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 \(p\)?

8 / 44

\(q = \frac{m}{10a + 3b}\). The given equation relates the distinct positive numbers \(q, m, a,\) and \(b\). Which equation correctly expresses \(10a + 3b\) in terms of \(q\) and \(m\)?

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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?

10 / 44

In the given equation, \( (4x + p)(6x^2 - 36)(3x^2 - 18x + 9p) = 0 \), where \( p \) is a positive constant. The sum of the solutions to the equation is \( 8 \). What is the value of \( p \)?

11 / 44

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)

12 / 44

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?

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

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 \(m\)?

14 / 44

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?

15 / 44

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?

16 / 44

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

\( y = \frac{1}{2}x + 5 \)
\( y = -\frac{1}{2}x + 5 \)

17 / 44

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 \( k \)?

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\(p = \frac{k}{7m + 5n}\). The given equation relates the distinct positive numbers \(p, k, m,\) and \(n\). Which equation correctly expresses \(7m + 5n\) in terms of \(p\) and \(k\)?

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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 \( k \)?

20 / 44

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?

21 / 44

For \(x > 0\), the function \(f\) is defined as follows: \(f(x)\) equals 120% of \(x\). Which of the following could describe this function?

22 / 44

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

23 / 44

A cube has a volume of 343 cubic units. What is the surface area, in square units, of the cube?

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The number of cells in a lab experiment is given by \( j(t) = 100,000 \cdot (1.03)^{t/350} \), where \( t \) is in minutes. How much time, in hours, will it take for the cell count to double?

25 / 44

Which ordered pair is a solution to the following equations:

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

26 / 44

For the function q, the value of q(x) decreases by 45% for every increase in the value of x by 1. If q(0) = 14, which equation defines q?

27 / 44

What percentage of \(700\) is \(350\)?

28 / 44

Which ordered pair is a solution to the following equations:

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

29 / 44

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?

30 / 44

\(t = \frac{n}{5x + 6y}\). The given equation relates the distinct positive numbers \(t, n, x,\) and \(y\). Which equation correctly expresses \(5x + 6y\) in terms of \(t\) and \(n\)?

31 / 44

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

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

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

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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?

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

36 / 44

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?

37 / 44

Which ordered pair is a solution to the given equations:

\( y = (x + 4)(x - 2) \)
\( y = 5x - 4 \)

38 / 44

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 \( \sin(E) \)?

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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?

40 / 44

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

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

41 / 44

Given the system of equations:

\( 18x + y = 81 \)
\( 3x + y = 27 \)

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

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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 \( d \)?

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\(w = \frac{g}{2p + 9q}\). The given equation relates the distinct positive numbers \(w, g, p,\) and \(q\). Which equation correctly expresses \(2p + 9q\) in terms of \(w\) and \(g\)?

44 / 44

The function \( f(x) = \frac{1}{4}(x - 8)^2 + 6 \) gives the height of a drone above the ground \( f(x) \), in meters, \( x \) seconds after it started flying, where \(\) 0 < x < 15 [/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?

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