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

Calculate percentages: Candidate L received \( \frac{600}{1000} = 0.6 \), or 60%. Candidate M received \( \frac{400}{1000} = 0.4 \), or 40%. If 7,500 people vote, Candidate L would receive \( 0.6 \times 7500 = 4500 \) votes, and Candidate M \( 0.4 \times 7500 = 3000 \) votes. The difference is \( 4500 - 3000 = 1500 \) votes.

To find the area in square miles, divide by \(1760^2\): \(23,184,000 / 3,097,600 = 7.48\) square miles.

Since \(g(x) = f(x+2) = 8(5)^{x+2} = 8 \cdot 25 \cdot (5)^x = 200(5)^x\), the correct answer is g(x) = 200(5)^x.

Rewrite \(f(x)\) in vertex form by completing the square, yielding \(f(x) = 3(x + 4)^2 - 5\). The minimum of \(f(x)\) is at \(x = -4\), so \(g(x) = f(x - 4)\) shifts this to \(x = 0\).

To find the surface area, first find the side length using \( V = s^3 \). Given \( V = 27000 \), find \( s = \sqrt[3]{27000} = 30 \). The surface area is given by \( 6s^2 \). Therefore, the surface area is \( 6(30)^2 = 5400 \) square units.

The volume of a cube is given by \( V = s^3 \). Here, \( V = 64000 \), so \( s = \sqrt[3]{64000} = 40 \). The surface area is \( 6s^2 \). Therefore, the surface area is \( 6(40)^2 = 9600 \) square units.

The minimum value of \( y \) occurs at \( x = \frac{-b}{2a} \), giving \( x = \frac{6}{2} = 3 \).

To isolate \(7m + 5n\), multiply both sides by \((7m + 5n)\) to get \(k = p(7m + 5n)\), then divide by \(p\) to find \(7m + 5n = \frac{k}{p}\).

Substitute \( (1, 5) \) into both inequalities. Both inequalities are satisfied.

Both sides simplify to \( 8z + 4 \), making the equation true for all values of z. Therefore, there are infinitely many solutions.

The two lines have the same slope but different intercepts, which means they are parallel and do not intersect at any point. Thus, the answer is zero points of intersection.

The decay factor is 0.75 per half-year, which means it decays by 25% every six months. Over a year, this represents a 25% drop, so \(q = 25\).

The rate of leakage is 7 milliliters per minute. Over one hour (60 minutes), the volume leaked is 7 * 60 = 420 milliliters. Converting to liters (1 liter = 1000 mL), the answer is 0.42 liters.

The minimum value of \( y \) occurs at \( x = \frac{-b}{2a} \). Here, \( a = 1 \) and \( b = -8 \), so \( x = \frac{8}{2} = 4 \).

To find \( p \), use the equation: \( 39 = \frac{p}{100} \times 65 \Rightarrow p = \frac{39 \times 100}{65} = 60 \). Then, calculate \( 60 \% \) of \( 39 \): \( \frac{60}{100} \times 39 = 23.4 \).

Using the slope \( \frac{1}{3} \) and point \( (-3, 5) \) in the point-slope formula, the resulting equation is \( y = \frac{1}{3}x + 6 \).

Calculate the slope with the given points and determine the equation of the line. Substitute \(x = p - 6\) to find \(b = -41\).

In the equation 3𝑠 + 50𝑡 = 8,000, the coefficient 3 corresponds to the trail, meaning 𝑠 represents the total number of streetlights per kilometer along the trail.

Since the triangles are similar, corresponding angles have the same trigonometric ratios. Thus, \( \sin(D) = \sin(A) = \frac{120}{125} \).

The vertex of the function \( f(x) = \frac{1}{4}(x - 8)^2 + 6 \) occurs at \( (8, 6) \). This represents the minimum height of the drone. The vertex form of a quadratic function, \( a(x - h)^2 + k \), indicates the vertex as \( (h, k) \). Since \( h = 8 \) and \( k = 6 \), the minimum height is 6 meters above the ground.

Testing each pair shows that only \( (4, 5) \) satisfies both equations.

To cover the walls twice, double the total area \(w\) to get \(2w\). Since each gallon covers 200 square feet, divide \(2w\) by 200 to get \(P = \frac{w}{100}\).

The volume of a cube is \( V = s^3 \). Given \( V = 343 \), find \( s = \sqrt[3]{343} = 7 \). The surface area formula is \( 6s^2 \). Therefore, the surface area is \( 6(7)^2 = 294 \) square units.

Let the number of people who voted in favor of the measure be z. According to the problem, 4 times as many people voted against, so the number against is 4z. The survey states that 12,000 more people voted against, so the equation is 4z = z + 12,000. Solving for z gives 4,000.

The two lines are parallel because their slopes are equal. Dividing the first equation by 2 yields \( 3.5x + y = 7.5 \). Since this differs from the second equation, the lines are parallel and do not intersect.

To cover the walls twice, double the total area \(w\) to get \(2w\). Since each gallon covers 180 square feet, divide \(2w\) by 180 to get \(P = \frac{w}{90}\).

Sum the solutions for each factor individually, then equate it to the given total of 15 to determine \( p \).

With the slope \( \frac{7}{8} \) and point \( (4, -1) \), apply the point-slope formula to find the equation \( y = \frac{7}{8}x - \frac{23}{8} \).

Only \( (3, 3) \) is a solution that satisfies both equations.

Expanding the left side gives \( 5x + 15 \), which matches the right side. Therefore, the equation is true for all values of x, leading to infinitely many solutions.

The half-life is 3 years, so the remaining quantity after \( x \) minutes is \( Q = 5 \cdot \left(\frac{1}{2}\right)^{\frac{x}{3 \cdot 365 \cdot 24 \cdot 60}} \).

Since \(g(x) = f(x+1) = 6(10)^{x+1} = 6 \cdot 10 \cdot (10)^x = 60(10)^x\), the correct answer is g(x) = 60(10)^x.

Using the point-slope form \( y - y_1 = m(x - x_1) \) with the slope \( m = \frac{3}{5} \) and point \( (2, -4) \), the resulting equation is \( y = \frac{3}{5}x - \frac{22}{5} \).

Let the number of people who voted in favor of the policy be x. According to the problem, 5 times as many people voted against it, so the number against is 5x. The article states that 40,000 more people voted against it, so the equation is 5x = x + 40,000. Solving for x gives 10,000.

Since the function decreases by 45%, it retains 55% of its value at each step. Thus, the multiplier for the decay is 0.55. Therefore, the correct equation is \( q(x) = 14(0.55)^x \).

In the function h(x) = -2x + 20, the y-intercept (where x = 0) represents the initial amount of water the gardener had before filling any watering cans. When x = 0, h(0) = 20, indicating that the gardener started with 20 liters of water.

To convert from square yards to square miles, divide the area by \(1760^2\): \(5,904,900 / 3,097,600 = 1.91\) square miles.

To find the doubling time, set \( b(t) = 2 \cdot b(0) \) and solve for \( t \): \( 15,000 \cdot (1.06)^{t/100} = 30,000 \). Use logarithms to isolate \( t \) and convert to hours.

To find the surface area, find the side length first. The volume of the cube is \( V = s^3 \). Given \( V = 729 \), \( s = \sqrt[3]{729} = 9 \). The surface area formula is \( 6s^2 \). Therefore, the surface area is \( 6(9)^2 = 486 \) square units.

Since both sides of the equation are identical, the equation is true for all values of x. Therefore, there are infinitely many solutions.

Let the number of people who voted against the proposal be x. According to the problem, 3 times as many people voted in favor, so the number in favor is 3x. The social media post states that 15,000 more people voted in favor, so the equation is 3x = x + 15,000. Solving for x gives 7,500.

The spill rate is 6 ounces per second. Over 30 seconds (half a minute), the volume spilled is 6 * 30 = 180 ounces.

The population triples every hour, so the growth factor per hour is 3. Since there are 24 hours in a day, the population after \( x \) days is \( p = 1,000 \cdot 3^{24x} \).

From \(\frac{x}{y} = 8\), we know \(x = 8y\). Substitute into \(\frac{56x}{my} = 8\) to get \(\frac{56(8y)}{my} = 8\). Simplify to \(\frac{448y}{my} = 8\), cancel \(y\) and solve to find \(m = 56\).