PSAT Math Domain 2: Advanced Math

Given \(f(x) = 3x^2 - 2x + 7\), what is the derivative of \(f(x)\) with respect to \(x\)?

If the sum of two numbers is 10 and their product is 21, what is the value of the smaller number?

What is the area of a circle with a circumference of 12??

The function \(g(x) = 2\log(x) + 3\). What is the value of \(g(100)\)?

A rectangle has a length of \(2x + 3\) and a width of \(x - 1\). If its perimeter is 34, what is \(x\)?

If \(x^2 - y^2 = 21\), what is the value of \(x - y\)?

If \(f(x) = x^3 - 3x^2 + 2x\), what is the value of \(f'(x)\) at \(x = 3\)?

A sphere has a volume of \(36\pi\). What is the radius of the sphere?

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

If \(a + b = 3\) and \(a^2 - b^2 = 7\), what is the product \(a \times b\)?

If \(f(x) = x^3 + 2x^2 - x\), what is the second derivative \(f''(x)\)?

If \(x^3 - x = k\), what is the value of \(x\) when \(k = 6\)?

A quadratic equation is given as \(ax^2 + bx + c = 0\). If \(a = 2\), \(b = -8\), and \(c = 6\), what is the larger solution \(x\)?

If the geometric series has the first term \(a_1 = 2\) and a common ratio \(r = 3\), what is the fourth term in the series?

If \(f(x) = 3x^2 - 5x + 4\), what is the integral of \(f(x)\) with respect to \(x\)?