Practice Test 12 - PSAT Math

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

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1. The function $p(x)=\dfrac{4}{x-1}+2$ is graphed on a coordinate plane. What is the equation of the vertical asymptote of $p$?
2. Refer to the figure. $\triangle ABC$ is a right triangle with $\angle C = 90^{\circ}$. If $AC = 6\text{ cm}$ and $BC = 8\text{ cm}$, what is the length of $AB$ in centimeters?
3. The graph of a polynomial crosses the x-axis at $x=-3$ and touches (but does not cross) at $x=2$. Which factored form is most consistent with this information if the polynomial has degree $3$ and a positive leading coefficient?
4. Solve $-6(x-2)>18$. What is the solution?
5. At a point, two lines intersect forming vertical angles. One of the angles is labeled $(5x-15)^\circ$, and its vertical angle is labeled $(3x+25)^\circ$. What is the value of $x$?​​
6. A delivery truck can carry at most 1,200 pounds. The truck already has 350 pounds loaded, and each box weighs 55 pounds. Let $x$ be the number of boxes added. Which inequality shows the possible values of $x$?
7. Solve for all real values of $x$ that satisfy $\sqrt{2x+3}=x-1$.
8. A city tested a new bus schedule on 6 routes for one month and compared average rider wait times to the previous month on the same routes. Weather was unusually mild during the test month. Average wait time decreased on 5 of the 6 routes. Which claim is best supported by the data and study design?
9. A coordinate plane graph shows a rational function $r(x)$ with a vertical asymptote at $x=1$ and a horizontal asymptote at $y=0$. The curve passes through the labeled point $(2,1)$. Which equation matches the graph of $r(x)$?
10. A circular track has radius $14$ m. A runner completes $\tfrac{3}{8}$ of a lap. What distance does the runner travel along the track? (Use $\pi$ in your answer.)
11. A triangle has side lengths $7$ cm, $9$ cm, and $x$ cm. If the triangle is possible, which of the following could be the value of $x$?
12. A printing company charges $45 to set up a job plus $0.15 per flyer. Another company charges $30 to set up plus $0.20 per flyer. For how many flyers $f$ will the total costs be equal?
13. Based on the graph shown, which statement best compares $f$ and $g$?
14. In the figure, a rectangle with dimensions $12 \times 18$ has a semicircle removed from one of its longer sides (diameter along the side). The diameter of the semicircle equals the shorter dimension of the rectangle. What is the perimeter of the resulting shape?
15. A cylindrical water tank has radius $0.6\text{ m}$ and height $2.5\text{ m}$. What is the volume of the tank in cubic meters? Use $\pi=3.14$.
16. In the coordinate plane, points $A(-2,1)$, $B(4,1)$, and $C(4,6)$ form triangle $ABC$. What is the length of segment $AC$?
17. A scientist tested a fertilizer by applying it to 10 randomly selected plants and leaving 10 similar plants untreated. After 4 weeks, treated plants averaged 18 cm growth while untreated averaged 14 cm. All plants were kept under the same light and water. What is the most appropriate conclusion?
18. What is the $y$-intercept of the line represented by $7x-5y=35$?
19. Which of the following lists all real solutions to the equation $x^{2}-7x+12=0$ ?
20. The graph of $y = f(x)$ shown consists of line segments. What is the value of $f^{-1}(2) + f^{-1}(-1)$?

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