Practice Test 11 - PSAT Math

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

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1. The graph shown represents the linear function $f$. Which of the following could define $f$?
2. Refer to the stacked bar chart. Which energy source experienced the greatest change in its percentage share of electricity generation from 2010 to 2020?
3. The coordinate plane shows an exponential curve that passes through the labeled points $(0,2)$ and $(1,4)$. The graph increases as $x$ increases and approaches $y=0$ as $x$ becomes very negative. Which equation matches the graph?
4. On the coordinate plane, the graph of a function $f(x)$ is shown as a V-shaped absolute value graph. A new function is defined by $g(x)=f(x-2)$. Which statement describes how the graph changes from $f$ to $g$? Watch the sign inside the parentheses: it is often reversed when interpreting shifts.
5. A water tank holds $0.75$ gallons. How many milliliters is this? Use $1\text{ gal}=4\text{ qt}$, $1\text{ qt}=2\text{ pt}$, $1\text{ pt}=2\text{ cups}$, and $1\text{ cup}=240\text{ mL}$.
6. A teacher notices that students who submit homework earlier tend to score higher on quizzes. The teacher says, "Submitting homework early improves quiz performance." Which statement is most appropriate?
7. A nutritionist tracked 30 clients for 8 weeks and found that clients who logged meals in a journal at least 5 days per week lost an average of 6.2 lb, while those who logged fewer days lost 3.1 lb. Clients chose whether to journal. Which statement is supported?
8. A gym charges a one-time sign-up fee plus a monthly fee. The total cost in dollars after $m$ months is modeled by $C=15+22m$. If the number of months $m$ increases by 3, by how much does $C$ change?
9. Refer to the figure. Diameter $\overline{PQ}$ of circle $O$ is perpendicular to chord $\overline{RS}$ at point $M$. If $RM=5\text{ cm}$, what is the length of $RS$?
10. A coordinate plane shows an absolute value graph opening downward with vertex at $(0,5)$. Which equation matches the graph?
11. A rectangular garden measures 18 feet by 9 feet. What is its area in square yards? Use $3\text{ ft}=1\text{ yd}$, and remember that area conversions require squaring the length conversion factor.
12. What are the solutions to the equation $x^2-7x+10=0$? Choose the pair of values of $x$ that makes the equation true.
13. In the figure shown, triangle $ABC$ is right-angled at $C$, and $CD$ is the altitude from $C$ to hypotenuse $AB$. If $AD = 4$ and $DB = 9$, what is the length of $AC$?
14. A random sample of 200 voters in a county was asked whether they support Candidate X. In the sample, 110 said "yes." A campaign ad claims, "Candidate X will win the county because 55% of voters support X." Which critique is most valid?
15. A coordinate plane graph shows the function $f(x)$ as an increasing exponential curve. The curve passes through the labeled points $(0,1)$ and $(1,2)$. Which equation matches the graph of $f(x)$?
16. A gym charges a one-time sign-up fee of $12 plus $8 per visit. You have at most $60 to spend this month. Let $v$ be the number of visits. Which inequality represents this situation, and what values of $v$ make it true?
17. The box plots shown display the distributions of test scores for Class X and Class Y. Which of the following statements is best supported by the box plots?
18. Which set contains every real solution to the equation $|x|+|x-2|=4\;?$
19. A random sample of 500 shoppers at a mall found that 40% planned to buy shoes that day. A report concludes, "40% of all residents in the city plan to buy shoes today." Which statement best evaluates the report?
20. Consider the polynomial $p(x)=(x^2-9)(x^3+2x)$. Without fully expanding, determine the degree of $p(x)$ and use that to reason about its possible number of real zeros. What is the degree of $p(x)$?

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