HSPT Domain 3: Mathematics

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

A circle has an area of \(50\pi\) square units. What is the circumference of the circle?

What is the sum of the solutions to the equation \(2x^2 - 8x = 0\)?

If \(a\) and \(b\) are the roots of the quadratic equation \(x^2 - 5x + 6 = 0\), what is \(a + b\)?

What is the value of \(x\) in the equation \(\log_2(x) + \log_2(8) = 4\)?

In the geometric sequence \(4, 12, 36, ...\), what is the 5th term?

If the polynomial \(x^3 - 4x^2 + 5x - 2\) is divided by \(x - 2\), what is the remainder?

How many distinct integer solutions does the equation \(|2x - 4| = 8\) have?

What is the derivative of \(f(x) = x^3 - 3x^2 + 2x\) at \(x = 1\)?

A cylinder has a radius of 3 units and a height of 4 units. What is the volume of the cylinder?

If the sequence of numbers 2, 4, 8, 16, ... continues to double, what is the sum of the first 5 terms?

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

What is the inverse function of \(f(x) = \frac{3x - 4}{2}\)?

The sum of the interior angles of a polygon is 1260 degrees. How many sides does the polygon have?

If \(3^x = 81\) and \(4^y = 16\), what is \(x + y\)?

What is the 7th term of the arithmetic sequence 2, 5, 8, ...?

If the probability of selecting a red marble from a bag is \(\frac{1}{3}\) and the probability of selecting a blue marble is \(\frac{1}{4}\), what is the probability of selecting either a red or a blue marble?

A circle is inscribed in a square. The area of the square is 64 square units. What is the area of the circle?

In a right triangle, one angle measures \(30^\circ\). What is the measure of the other non-right angle?

If the lengths of the sides of a triangle are in the ratio 3:4:5, and the perimeter of the triangle is 24 units, what is the length of the longest side?