Practice Test 5 - PSAT Math

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

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1. A researcher compares average test anxiety scores for students who attended an optional mindfulness session and those who did not. Attendees have lower average anxiety. The session was optional. Which statement is best supported?
2. Solve for $x$: $7x-3=2x+\dfrac{17}{2}$. What is the value of $x$?
3. A line passes through $(3, -7)$ and has slope $4$. Which equation is the line in point-slope form?
4. A researcher reports that in a sample of 70 adults, those who own pets report higher happiness scores. The researcher concludes, "Owning a pet increases happiness." Which statement best evaluates this conclusion?
5. Which expression equals $\dfrac{5}{2+\sqrt3}$ when the denominator is rationalized?
6. A water pump drains a tank at a constant rate. It removes 18 gallons every 4 minutes. At this rate, how many minutes will it take to drain 63 gallons?
7. The scatterplot shows the relationship between the weight, $w$, in pounds, of 15 adult dogs and their daily food intake, $f$, in ounces. Based on the line of best fit shown, what is the best interpretation of the slope?
8. Which of the following is equivalent to $\bigl(2a^{3}b^{2}\bigr)^{2}\bigl(4ab^{5}\bigr)^{-1}$ for nonzero $a$ and $b$ ?
9. A theater must sell at least 120 tickets to break even. It has already sold 45 tickets. Let $t$ be the additional tickets sold. Which inequality shows how many more tickets must be sold?
10. A small lab has two solutions of salt water. Solution A is $10\%$ salt and Solution B is $25\%$ salt. The lab wants to make 40 liters of a mixture that is $16\%$ salt. Let $x$ be liters of A and $y$ be liters of B. What is $(x,y)$?
11. A rectangular screen is 15 inches wide and 20 inches tall. What is the length of the diagonal of the screen, in inches?
12. A shipping label lists a package weight as 3.75 pounds, but the post office scale shows ounces. Using $16\text{ oz}=1\text{ lb}$, what is the package weight in ounces?
13. If $2x+5=\dfrac{3}{2}(x-1)$, what is the value of $x$? Multiply to clear the fraction before isolating $x$.
14. A teacher wants to estimate the proportion of students in a district who own a calculator. She surveys 30 students from her own class and finds 28 own one. Which statement best describes the problem with using this result for the entire district?
15. The graph shown shows the value $V$ of two different investments, $P$ and $Q$, over time $t$ (in years). Investment $P$ grows linearly and investment $Q$ grows exponentially. Approximately how many years after $t=0$ will investment $Q$ first exceed investment $P$?
16. The graph shown is of the function $y = a\sin(b(x - h))$ for positive constants $a$ and $b$. What is the value of $\dfrac{a}{b}$?
17. A student writes $y=200(1.06)^t$ to model a quantity that starts at 200 and increases by 6 each day. Which is the best critique of the student's model?
18. A grocery store sells almonds in bulk. A customer pays $7.80 for $1.2$ pounds of almonds. At the same price per pound, how much will $3.5$ pounds cost? Watch out for using $7.80 as a unit price without dividing by $1.2$.
19. A gym membership costs a one-time sign-up fee plus $25 per month. After 4 months, the total cost is $145. Assuming a linear model, what is the sign-up fee?
20. Solve the inequality $-\dfrac{1}{2}x+4<1$. For what values of $x$ is it true?

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