SAT Math Hard practice

A line in the $xy$-plane has slope $-\frac{2}{3}$ and passes through the point $(6,1)$. What is the $y$-intercept of this line?

In the $xy$-plane, line $\ell$ has equation $3x-4y=12$. Line $m$ is perpendicular to $\ell$ and passes through $(0,5)$. Which equation represents line $m$?

In the unit circle, angle $\theta$ is in standard position and $\cos \theta =-\frac{\sqrt{2}}{2}$ with $\sin \theta >0$. In which quadrant does angle $\theta$ lie?

Which of the following is the complete solution set of $x^2+4x+5=0$ over the real numbers?

In a survey of 400 people, $35\%$ said they exercise daily. The margin of error is $\pm 4\%$. Which of the following is a reasonable estimate for the percentage of the entire population that exercises daily?

A scientist converts a measurement from feet to meters using the fact that $1$ foot $=0.3048$ meters. A room is $25$ feet long. What is the length in meters, rounded to the nearest tenth?

A sphere has a radius of $6$. What is its volume? (Leave in terms of $\pi$.)

The function $g$ is defined by $g(x)=\frac{3x+6}{x-2}$. For what value of $x$ is $g(x)$ undefined?

A study measured the heights of 50 adults. The mean height was 170 cm and the standard deviation was 8 cm. Which statement best describes a height of 186 cm?

The box plot below summarizes a data set. The minimum is 10, Q1 is 25, median is 40, Q3 is 55, and the maximum is 70. What is the interquartile range (IQR)?

For which value of $k$ does the system below have infinitely many solutions?

$$2x-ky=4$$
$$4x-6y=8$$

In right triangle $ABC$, angle $C$ is the right angle, $AC=8$, and $BC=6$. What is $\cos (A)$?

If $2^x=8^{x-2}$, what is the value of $x$?

A cylinder has radius $r=3$ and height $h=5$. What is its volume? (Leave in terms of $\pi$.)

The graph of $y=a(x-2{)}^2+5$ is a parabola. If it opens downward, which of the following could be the value of $a$?