SAT Math: Advanced Math

$x=49$

$y = \sqrt{x} + 9$

The graphs of the given equations intersect at the point $(x,y)$ in the $xy$-plane. What is the value of $y$?

One solution to the equation $x^2 - 2x - 9 = 0$ can be written as 1 + \sqrt{k}, where $k$ is a constant. What is the value of $k$?

$$\begin{aligned} x^2 + y + 10 &= 10 \\ 8x + 16 - y &= 0 \end{aligned}$$The solution to the given system of equations is $(x, y)$. What is the value of $x$?

The function $f$ is defined by $f(x) = 4x^{-1}$. What is the value of $f(21)$?

Immanuel purchased a certain rare coin on January 1. The function $f(x) = 65(1.03)^x$, where 0 \le x \le 10, gives the predicted value, in dollars, of the rare coin $x$ years after Immanuel purchased it. What is the best interpretation of the statement “$f(8)$ is approximately equal to 82” in this context?

$$w^2 + 12w - 40 = 0$$ Which of the following is a solution to the given equation?