ATDH Domain 3: Quantitative Reasoning

If the sum of the interior angles of a polygon is 1,800 degrees, how many sides does the polygon have?

A researcher uses a solution with a 15\% concentration of a certain substance. If she needs 2 liters of a 45\% concentration, how much of the 15\% solution should she use if she plans to evaporate the water to increase the concentration to the desired level?

In a sequence, the nth term is given by the formula \(3n^2 - 2n + 1\). What is the 5th term?

A cylindrical tank with a radius of 4 meters and a height of 10 meters is filled with water. If water is drawn from the tank, lowering its height to 4 meters, what volume of water, in cubic meters, was drawn from the tank?

A loan of \$5,000 is made with an annual interest rate of 8\% compounded quarterly. What is the balance after 1 year?

If the odds against an event are 5 to 3, what is the probability that the event will occur?

A set of data has a mean of 50 and a standard deviation of 5. If all values in the set are increased by 10, what will be the new mean and standard deviation?

What is the sum of the infinite series \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots\)?

If \(f(x) = 2x^3 - x^2 + 3x - 5\), what is \(f(-2)\)?

A rectangle's length is three times its width. If the perimeter is 64 cm, what are the rectangle's dimensions?

A car travels 150 miles in 2.5 hours. What is its average speed in miles per hour?

What is the probability of drawing a red card or a king from a standard deck of 52 playing cards?

Given a right triangle, if one angle measures \(45^\circ\), what is the ratio of the lengths of the sides adjacent to the \(45^\circ\) angle?

What is the sum of the solutions to the equation \(x^2 - 4x + 4 = 0\)?

A sequence is defined as \(a_n = 3^n + 2^n\). What is \(a_4\)?

If \(3x - 7 < 2(x + 4)\), what is the range of possible values for \(x\)?

A circle has a circumference of \(31.4\) meters. What is its area in square meters? (Use \(\pi \approx 3.14\))

What is the coefficient of \(x^3\) in the expansion of \((2x - 1)^4\)?

If the logarithm of 8 to the base \(x\) equals 2, what is the value of \(x\)?

A rectangle's length is twice its width, and its area is \(128\) square cm. What is the perimeter of the rectangle?

In how many ways can 5 books be arranged on a shelf if two of the books must stay together?

A tank is filled by Pipe A in 3 hours and by Pipe B in 6 hours. When both pipes are opened together, how long will it take to fill the tank?

If \(5^x = 125\) and \(5^y = 1/25\), what is the value of \(x + y\)?

What is the smallest positive integer value of \(n\) for which \(2^n > 1,000\)?

If \(x^3 - 6x^2 + 11x - 6 = 0\), what are the sum and product of its roots?

A set contains all integers \(x\) such that \(2 < x^2 < 50\). How many elements are in the set?

What is the remainder when \(2^{23}\) is divided by 7?

If the interquartile range of a data set is 15 and the range is 30, what is the minimum possible number of elements in the set?

What is the equation of the circle with center at \((3,-4)\) and passing through the point \((7, -8)\)?

A geometric sequence has a first term of 2 and a common ratio of 3. What is the fifth term?

If \(tan(\theta) = \frac{3}{4}\), what is \(sin(2\theta)\)?

A survey conducted on a sample of 1000 people found that 60\% prefer tea over coffee. If the margin of error is 4\%, what is the confidence interval for the population proportion who prefer tea?

A triangle has sides of length 5, 12, and 13. What is its area?

What is the derivative of \(f(x) = x^3 - 3x^2 + 5x - 7\) at \(x = 2\)?

If a fair die is rolled twice, what is the probability that the sum of the two rolls is 9?

A particle moves along a line so that its position at time \(t\) is given by \(s(t) = 3t^3 - 15t^2 + 18t\). At what time \(t\) is the velocity zero?

Calculate the integral of the function \(f(x) = x^2 e^x\).

If the sum of an infinite geometric series is 8 and the first term is 1, what is the common ratio?

What is the least positive integer solution to the congruence \(7x \equiv 1 \mod 26\)?

A line intersects the \(x\)-axis at \((4,0)\) and the \(y\)-axis at \((0,2)\). What is the area of the triangle formed by the line and the coordinate axes?