Practice Test 9 - PSAT Math

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

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1. A ramp rises 3 feet vertically over a horizontal distance of 10 feet, forming a right triangle. What is the length of the ramp, in feet?
2. A streaming service bills $9 plus $x$ dollars per movie. If the bill for 5 movies is $24, then $9+5x=24$. What is $x$?
3. A recipe that yields 8 servings calls for 3 cups of flour. Assuming the recipe scales proportionally, how many cups of flour are needed to prepare 14 servings?
4. A designer models the edge of a ramp with $y=x^2-4x+3$ and a support beam with $y=x-1$. At what points do the graphs intersect? Solve the system algebraically.
5. Simplify and write in simplest radical form: $\dfrac{\sqrt{45}}{\sqrt{5}}$.
6. Which of the following is equivalent to $\sqrt{50}-2\sqrt{8}+\sqrt{2}$ ?
7. If $2(x-4)+k$ is equivalent to $2x+3$, what is the value of $k$? (Assume the expressions are equal for all $x$.)
8. The table shown lists the enrollment at a community college for five consecutive years. Which of the following statements best describes the data?
9. A projectile is launched vertically so that its height, in feet, after $t$ seconds is given by $h(t)=-16t^{2}+64t+80.$ After how many seconds does the projectile reach its maximum height?
10. For which values of $m$ does the equation $x^{2}+(m-3)x+m=0$ have two distinct real solutions?
11. The figure shows two triangles sharing vertex $P$, with $\triangle APB \sim \triangle CPD$. The side lengths are $AP=6$, $PB=8$, $CP=9$, and segment $AB=10$. What is the length of segment $CD$?
12. In the diagram, two parallel lines are cut by a transversal. The angle labeled $x$ is adjacent to an angle of $88^\circ$ at the same intersection, forming a linear pair. What is $x$?
13. A water tank holds $2.4$ liters. How many milliliters is this? (Use $1000\text{ mL}=1\text{ L}$.)
14. The cubic polynomial $p(x)=x^{3}+ax^{2}+bx+8$ has zeros at $x=-4$ and $x=1.$ What is the value of $a$?
15. A container holds 2.5 liters of juice. How many cubic centimeters of juice does the container hold? (1 liter = 1,000 cubic centimeters)
16. Refer to the figure. A bowl is shaped like a hemisphere with radius $7\text{ cm}$. What is the volume of the bowl, in cubic centimeters?
17. A gym requires members to be at least 16 years old and younger than 65 to use the weight room without supervision. Let $x$ be a member's age. Which compound inequality represents this policy?
18. A number line graph shows an open circle at $-2$ with shading to the right. Which inequality matches the graph?
19. A computer generates a 3-character code. The first character is a letter chosen uniformly from A, B, or C. The second character is a digit chosen uniformly from 1, 2, 3, or 4. The third character is a letter chosen uniformly from A, B, or C. What is the probability the code starts and ends with the same letter?
20. Consider the system of equations $\begin{cases}3x-2y=7\\6x-4y=14\end{cases}$ A student claims the system has one solution because there are two equations and two variables. How many solutions does this system actually have?

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