Practice Test 1 - PSAT Math

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

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1. In a circle, an inscribed angle intercepts an arc measuring $110^\circ$. What is the measure of the inscribed angle, in degrees?
2. A box contains 4 math books and 6 history books. Two books are chosen at random without replacement. What is the probability that the second book chosen is a math book given that the first book chosen is a history book?
3. A class has $x$ juniors and $y$ seniors with the constraint $x+y=180$. If there are $x=95$ juniors, how many seniors $y$ are there?
4. Solve the equation $\dfrac{2x-1}{3}=\dfrac{x+5}{2}$. What is the value of $x$?
5. Solve the equation $|x|=|x-6|$. Interpret absolute value as distance on the number line.
6. The function $u(x)=3|x-4|+2$ is nonlinear. What is the minimum value of $u(x)$? Use the vertex of the absolute value graph.
7. A new app had 800 downloads on day 0. • Plan A: The total number of downloads increases by 60 each day. • Plan B: The total number of downloads increases by 9\% each day. After 20 days, which statement about the total downloads is true?
8. A coordinate plane graph shows a function with a horizontal asymptote at $y=2$. The curve passes through $(0,3)$ and decreases toward $y=2$ as $x$ increases. Which equation best matches the graph? (If you miss the asymptote, you might choose an unshifted exponential.)
9. A lab mixture has $x$ milliliters of solution A. After adding 12 mL, the total becomes 45 mL, modeled by $x+12=45$. What is the value of $x$?
10. If $|3x-7|=2,$ what is the sum of all real solutions for $x$?
11. The equation $9x-6y=30$ relates $x$ and $y$. Which equation is equivalent and solved for $x$?
12. Which value is equivalent to $\dfrac{4^{x+2}}{4^{x-1}}$ ?
13. What is the $x$-coordinate of the solution to the system? $\begin{cases} 5x + y = 7\\ 2x - y = 8 \end{cases}$
14. Which expression is equivalent to $\bigl(3x^{2}-4x+1\bigr)-\bigl(2x^{2}+x-5\bigr)$ ?
15. The graph of a polynomial $g(x)$ crosses the $x$-axis at $x=-2$ and touches (bounces off) the $x$-axis at $x=3$. Which could be an algebraic form for $g(x)$ with the least possible degree and a positive leading coefficient?
16. In the figure shown, $PA$ is tangent to circle $O$ at point $A$, and $PBC$ is a secant passing through the circle with $B$ and $C$ on the circle. If $PB = 4$ and $BC = 12$, what is the length of $PA$?
17. 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?
18. A car uses $3.2$ gallons of gasoline to travel $96$ miles. At this consumption rate, how many miles can the car travel on $5$ gallons?
19. A lab protocol requires 2,750 milliliters of solution. How many liters is this? (Use $1000\text{ mL}=1\text{ L}$.)
20. The graph in the figure shows the system $\begin{cases} y = -2x + 7 \\ y = kx + 1 \end{cases}$ where $k$ is a constant. If the solution to the system is the point shown at $(2, 3)$, which of the following systems has NO solution?

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