Practice Test 6 - PSAT Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

A line passes through $(2, -1)$ and $(2, 5)$ . Which of the following best describes this relation?
A photo is enlarged so that all lengths are multiplied by the same scale factor. In the original photo, the width is $9\text{ cm}$ and the height is $13.5\text{ cm}$ . In the enlarged photo, the width is $15\text{ cm}$ . What is the height of the enlarged photo?
A coordinate plane shows a square-root curve that begins at $(0,-3)$ and increases to the right, passing through $(4,-1)$ . Which equation matches the graph?
On the coordinate plane, the graph of a parabola opens upward and has vertex at $(2,-1)$ . It passes through the point $(0,3)$ . Which equation matches this graph? (Watch for confusing a horizontal shift with a vertical shift, since both can place the curve near the same points.)
The coordinate plane shows the graph of $f(x)$ , an absolute value function with vertex at $(0,0)$ and points $(1,2)$ and $(-1,2)$ . A new function is defined by $g(x)=f(x-3)$ . Which description matches the transformation from $f$ to $g$ ? (Do not confuse $x-3$ with $x+3$ .)
A $30^\circ$ - $60^\circ$ - $90^\circ$ triangle has a longer leg of length $12\sqrt{3}$ . What is the length of the hypotenuse?
A multiple-choice quiz has 5 questions, each with 4 answer choices, and a student guesses randomly on every question. What is the probability that the student answers exactly 3 questions correctly?
A coordinate plane shows a V-shaped graph with vertex at $(3,-2)$ and opening upward. Which is the range of the function shown? Express your answer using interval notation.
A line on the coordinate plane passes through $(0,-4)$ and $(5,6)$ . What is the y-intercept of the line?
A jar contains 6 red marbles, 5 blue marbles, and 4 green marbles (15 total). One marble is chosen at random. Given that the marble is not green, what is the probability it is blue?
A storage container is a right circular cone with radius $4\text{ in}$ and height $9\text{ in}$ . What is the volume of the cone? (Use $\pi$ in your answer.)
A coordinate plane graph shows an exponential curve that passes through $(0,1)$ and increases to the right. It also appears to pass near $(1,2)$ and $(2,4)$ . Which equation best matches the graph? (If the scale is misread, $2^x$ and $3^x$ can look similar for small $x$ .)
A dot plot (shown as a bar-style frequency graph) summarizes the number of pets owned by 20 students. The counts are: 0 pets: 5 students, 1 pet: 7 students, 2 pets: 6 students, 3 pets: 2 students. What is the mode of the distribution?
The graph of a polynomial is shown on the coordinate plane. It crosses the x-axis at $x=-1$ and $x=3$ and has no other x-intercepts in the window. How many real zeros does the polynomial have, based on the x-intercepts shown?
A video is 2 hours 18 minutes long. How many seconds is this? (Students may assume $60\text{ s}=1\text{ min}$ and $60\text{ min}=1\text{ hr}$ .)
A box plot is described by the five-number summary for Dataset X: min 4, $Q_1=6$ , median 9, $Q_3=12$ , max 20. What is the interquartile range (IQR), and which value would be considered farthest above the center based on the maximum? Choose the option that correctly gives the IQR and identifies the farthest-above-center value.
Consider the system $\begin{cases}2x-3y=6\\4x-6y=12\end{cases}.$ How many ordered pairs (x, y) satisfy both equations?
A length of 450 meters is to be reported in yards. Which value is closest? (1 yard = 0.9144 meter)
A right triangle has legs of length $9\text{ cm}$ and $12\text{ cm}$ . A rectangle is formed using the triangle's hypotenuse as the rectangle's length and using a width of $5\text{ cm}$ . What is the area of the rectangle?
Two savings plans start with the same $2{,}000 deposit. • Plan F grows linearly: $F(t)=2{,}000+150t$ . • Plan G grows exponentially: $G(t)=2{,}000(1.04)^t$ . For approximately how many years will the two balances be equal?

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