Practice Test 7 - PSAT Math

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

A coordinate plane shows two points on a line modeling a taxi fare: $(1, 9)$ and $(5, 21)$ . If $x$ is miles and $y$ is cost in dollars, what is the cost per mile (slope)?
For the linear equation $4x-3y=12,$ what is the value of $y$ when $x=-6$ ?
Based on the graph of $y = f(x)$ shown, how many solutions are there to the equation $f(f(x)) = 0$ on the interval shown?
A marathon race is 26.2 miles long. What is this distance in kilometers? (1 mile = 1.609 kilometers)
In a survey, 35% of students chose option A. If 280 students took the survey, how many students chose option A?
The table gives the summary statistics for the weights (in pounds) of dogs in two shelters. If the data for both shelters were combined into a single data set, which of the following could NOT be the median of the combined set?
A rectangular poster measures $18$ inches by $2.5$ feet. What is the area of the poster in square inches? Use $1\text{ ft}=12\text{ in}$ .
A teacher recorded quiz scores (out of 10) for 9 students: 6, 7, 7, 8, 8, 8, 9, 9, 10. What is the median of the scores? Be careful to identify the middle value in the ordered list rather than averaging two middle values.
A student recorded the number of minutes it took to finish 9 practice problems on different days. The times (in minutes) were: 7, 8, 8, 9, 9, 10, 10, 11, 30. What is the median of this data set, and which measure of center (mean or median) is more affected by the outlier 30? Choose the option that correctly answers both parts.
Based on the table shown, the value of function $h$ at selected $x$ -values is given. If $h$ is an exponential function of the form $h(x) = a \cdot b^{x}$ , what is the value of $h(5)$ ?
The formula for the surface area, $A$ , of a right circular cylinder is $A = 2\pi r^2 + 2\pi rh$ , where $r$ is the radius of the base and $h$ is the height of the cylinder. Which of the following equations correctly expresses the height, $h$ , in terms of $A$ and $r$ ?
Refer to the figure. $\triangle DEF$ is isosceles with $DE = DF$ . If $\angle E = 4x + 6$ degrees and $\angle F = 6x - 8$ degrees, what is the measure of $\angle D$ ?
A storage bin can hold no more than 60 pounds. A box weighs 12 pounds and each book weighs 3 pounds. Let $b$ be the number of books. Which inequality models the constraint?
A coordinate plane shows a rational function with vertical asymptote at $x=3$ and it passes through $(4,-2)$ . The branches approach $y=0$ for large $|x|$ . Which equation matches?
A student writes $3x+9=12$ and mistakenly divides only $3x$ by 3. What is the correct value of $x$ for $3x+9=12$ ?
Which expression is equivalent to $\dfrac{3}{2-\sqrt{5}}$ after rationalizing the denominator?
A line passes through $(7, -2)$ and $(1, 10)$ . What is the equation of the line in slope-intercept form?
The polynomial $g(x)=x^3-6x^2+11x-6$ has zeros at $x=1,2,3$ . Which expression is $g(x)$ written in completely factored form? A plausible wrong path is to miss a sign and use $(x+1)$ instead of $(x-1)$ .
In the $xy$ -plane, the graph of line $\ell$ is shown. Line $k$ (not shown) is parallel to line $\ell$ and passes through the point $(4,-1)$ . What is the $y$ -intercept of line $k$ ?
A student mixes $x$ liters of a 10% salt solution with $y$ liters of a 30% salt solution to make 12 liters of mixture. The constraint is $x+y=12$ . If $x$ increases by 2 liters, how must $y$ change to keep the total volume 12 liters?

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