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sat_multiple_choice_math_may_23

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The graph of the polynomial function $f$, where $y=f(x)$, has $x$-intercepts of $(-6,0)$ and $(6,0)$. Which of the following must be true?

A) $f(-6)=0$ B) $f(6)=-6$ C) $f(-6)=6$ D) $f(0)=-6$

A

$$\begin{gathered} y=4 x+6 \\-5 x-y=21\end{gathered}$$ What is the solution $(x, y)$ to the given system of equations?

A) $(-3,-6)$ B) $\left(-\frac{5}{3},-\frac{2}{3}\right)$ C) $(3,18)$ D) $(15,66)$

A

$\lvert x-10 \rvert = 0$ What are all the possible solutions to the given equation?

A) -10 B) 0 C) 10 D) -10 and 10

C

$$q=s(r-1)^2$$ The given equation relates the positive numbers $q, r$, and $s$. Which equation gives $r$ in terms of $q$ and $s$, when $r>1$?

A) $r=1+\sqrt{\frac{q}{s}}$ B) $r=1+\frac{\sqrt{q}}{s}$ C) $r=-1-\sqrt{\frac{q}{s}}$ D) $r=-1-\frac{\sqrt{q}}{s}$

A

In the relationship between variables $x$ and $y$, each increase of $1$ in the value of $x$ decreases the value of $y$ by 2. When $x=0$, $y=5$. Which equation represents this relationship?

A) $y=-\frac{1}{2}x+5$ B) $y=-\frac{1}{2}x-5$ C) $y=-2x-5$ D) $y=-2x+5$

D

An isosceles right triangle has a hypotenuse of length 4 inches. What is the perimeter, in inches, of this triangle?

A) $2\sqrt{2}$ B) $4\sqrt{2}$ C) $4+4\sqrt{2}$ D) $4+8\sqrt{2}$

C

How many solutions does the equation $4(x-2) = -2(x+4)$ have?

A) Zero B) Exactly one C) Exactly two D) Infinitely many

B

$R(t) = 1,830 - 790(2.71)^{-.18t}$ The function $R$ gives the predicted average rating, expressed as a number of points, in the German chess federation database for a player based on the number of years, $t$, the player has participated in professional chess tournaments. Which of the following represents the predicted average rating of a player who has just entered their first professional chess tournament?

A) $R(-0.18)$ B) $R(0)$ C) $R(790)$ D) $R(1,830)$

B

Alice took 60 minutes to complete a task on her first trial. The time it took Alice to complete the task decreased by 10% of the previous time for each additional trial. Approximately how many minutes will it take Alice to complete the task on her fifth trial?

A) 50 B) 42 C) 39 D) 35

C

$$ \begin{aligned} & y<\frac{2}{5} x+3 \\& y>\frac{1}{2} x-6\end{aligned}$$ In which of the following tables are all the values of $x$ and their corresponding values of $y$ solutions to the system of inequalities shown?

A) \begin{tabular}{|r|r|} \hline$x$ & $y$ \\\hline-2 & -8 \\\hline 0 & -4 \\\hline 4 & 4 \\\hline\end{tabular} B) \begin{tabular}{|c|c|}\hline$x$ & $y$ \\\hline-2 & -8 \\\hline 0 & 4 \\\hline 4 & 4 \\\hline\end{tabular} C) \begin{tabular}{|r|r|}\hline$x$ & $y$ \\\hline-2 & 3 \\\hline 0 & 2 \\\hline 4 & -3 \\\hline\end{tabular} D) \begin{tabular}{|r|r|}\hline$x$ & $y$ \\\hline-2 & 2 \\\hline 0 & -3 \\\hline 4 & 3 \\\hline\end{tabular}

D

Which of the following is equivalent to $(\sqrt{32})(\sqrt[5]{64})$?

A) $6\left(\sqrt[7]{2^5}\right)$ B) $6\left(\sqrt[10]{2^7}\right)$ C) $8\left(\sqrt[7]{2^5}\right)$ D) $8\left(\sqrt[10]{2^7}\right)$

D

An object has a mass of 3,300 milligrams. What is the mass of the object in grams? (1 gram = 1,000 milligrams)

A) 0.33 B) 3.30 C) 33.00 D) 330.00

B

On average, one square inch of human skin contains 650 sweat glands. A certain area of skin contains 1,170 sweat glands. Based on this information, which of the following is closest to the size of this area, in square inches?

A) 0.44 B) 0.56 C) 0.80 D) 1.80

D

The table give the heights, in feet, of 5 peaks in the Rocky Mountains and 5 peaks in the Appalachian Mountains. \begin{tabular}{|l|l|l|l|l|} \hline $\begin{array}{l}\text { Rocky } \\\text { Mountain } \\\text { Peak }\end{array}$ & $\begin{array}{l}\text { Height } \\\text { (in feet) }\end{array}$ & $\begin{array}{l}\text { Appalachian } \\\text { Mountain } \\\text { Peak }\end{array}$ & $\begin{array}{l}\text { Height } \\\text { (in feet) }\end{array}$ \\\hline $\begin{array}{l}\text { Mount } \\\text { Elbert }\end{array}$ & 14,439 & $\begin{array}{l}\text { Mount } \\\text { Mitchell }\end{array}$ & 6,684 \\\hline $\begin{array}{l}\text { Mount } \\\text { Massive }\end{array}$ & 14,429 & Mount Craig & 6,647 \\\hline $\begin{array}{l}\text { Mount } \\\text { Harvard }\end{array}$ & 14,419 & $\begin{array}{l}\text { Clingman's } \\\text { Dome }\end{array}$ & 6,643 \\\hline $\begin{array}{l}\text { Blanca } \\\text { Peak }\end{array}$ & 14,350 & $\begin{array}{l}\text { Mount } \\\text { Guyot }\end{array}$ & 6,621 \\\hline $\begin{array}{l}\text { La Plata } \\\text { Peak }\end{array}$ & 14,343 & $\begin{array}{l}\text { Balsam } \\\text { Cone }\end{array}$ & 6,611 \\\hline\end{tabular} What is the height, in meters, of Blanca Peak? (Use 1 meter $=3.28$ feet)

A) 437.5 B) 4,375 C) 47,045 D) 47,068

B

The table give the heights, in feet, of 5 peaks in the Rocky Mountains and 5 peaks in the Appalachian Mountains. \begin{tabular}{|l|l|l|l|l|} \hline $\begin{array}{l}\text { Rocky } \\\text { Mountain } \\\text { Peak }\end{array}$ & $\begin{array}{l}\text { Height } \\\text { (in feet) }\end{array}$ & $\begin{array}{l}\text { Appalachian } \\\text { Mountain } \\\text { Peak }\end{array}$ & $\begin{array}{l}\text { Height } \\\text { (in feet) }\end{array}$ \\\hline $\begin{array}{l}\text { Mount } \\\text { Elbert }\end{array}$ & 14,439 & $\begin{array}{l}\text { Mount } \\\text { Mitchell }\end{array}$ & 6,684 \\\hline $\begin{array}{l}\text { Mount } \\\text { Massive }\end{array}$ & 14,429 & Mount Craig & 6,647 \\\hline $\begin{array}{l}\text { Mount } \\\text { Harvard }\end{array}$ & 14,419 & $\begin{array}{l}\text { Clingman's } \\\text { Dome }\end{array}$ & 6,643 \\\hline $\begin{array}{l}\text { Blanca } \\\text { Peak }\end{array}$ & 14,350 & $\begin{array}{l}\text { Mount } \\\text { Guyot }\end{array}$ & 6,621 \\\hline $\begin{array}{l}\text { La Plata } \\\text { Peak }\end{array}$ & 14,343 & $\begin{array}{l}\text { Balsam } \\\text { Cone }\end{array}$ & 6,611 \\\hline\end{tabular} For the given Appalachian Mountain peaks, the height of the highest peak is approximately what percent greater than the height of the lowest peak?

A) $1.1 \%$ B) $9.9 \%$ C) $73.0 \%$ D) $101.1 \%$

A

Data set $A: 2,4,6,6,8,12$ Data set B: $2,4,6,6,8,12,26$ Two data sets are shown. Which statement best compares the medians of the data sets?

A) The median of data set A is greater than the median of data set $B$ B) The median of data set A is less than the median of data set B C) The medians of data sets A and B are equal D) There is not enough information to compare the medians

C

$$0.79 x+1.0 y=100$$ The mass of a solution of isopropanol and water is 100 grams. The given equation represents this situation, where $x$ is the volume of isopropanol, in cubic centimeters, and $y$ is the volume of water, in cubic centimeters. If the volume of isopropanol is 70 cubic centimeters, what is the approximate volume of water, in cubic centimeters?

A) 45 B) 55 C) 70 D) 79

A

There are 435 voting members of the US House of Representatives. If $b$ voting members are in favor of a certain bill, which expression represents the percentage of the voting members in favor of the bill?

A. $100\left(\frac{b}{435}\right)$ B. $100\left(\frac{435}{b}\right)$ C. $435\left(\frac{b}{100}\right)$ D. $435(100 b)$

A

$$10(x+120)=120$$ Which of the following equations has the same solution as the given equation?

A) $x+120=12$ B) $x+120=130$ C) $x+12=12$ D) $x+12=120$

A

The given function $C$ models the annual soybean use in China, in millions of metric tons, between 1995 and 2014, where $x$ is the number of years after 1995. $$C(x)=4.3 x+19$$ According to the model, what is the best interpretation of 4.3 in this context?

A) Each year between 1995 and 2014, China used 4.3 million metric tons of soybeans B) Each year between 1995 and 2014, China's annual use of soybeans increased by 4.3 million metric tons C) China used 4.3 million metric tons of soybeans in 1995 D) China used a total of 4.3 million metric tons of soybeans between 1995 and 2014

B

$$ \begin{gathered} C(x)=50,000+0.75 x \\ R(x)=4.75 x \end{gathered}$$ The given function $C$ models the total cost (sum of fixed cost and variable cost), in dollars, of growing and harvesting $x$ bales of hay on a certain farm. The given function $R$ models the revenue, in dollars, earned from selling $x$ bales of hay. According to the function $R$, how many bales of hay would have to be sold to earn a revenue of $\$1,425$?

A) 100 B) 300 C) 500 D) 1,000

B

$$ \begin{gathered} C(x)=50,000+0.75 x \\ R(x)=4.75 x \end{gathered}$$ The given function $C$ models the total cost (sum of fixed cost and variable cost), in dollars, of growing and harvesting $x$ bales of hay on a certain farm. The given function $R$ models the revenue, in dollars, earned from selling $x$ bales of hay. Which of the following inequalities models the number of bales of hay that must be sold to earn a profit of $\$ 10,000$ or more? (profit $=$ revenue - cost)

A) $10,000 \leq 4 x-50,000$ B) $10,000 \geq 4 x-50,000$ C) $10,000 \leq 4 x+50,000$ D) $10,000 \geq 4 x+50,000$

A

Which expression is equivalent to $\left(x^2+4\right)^2+(x-2)(x+2) ?$

A) $x^4+x^2+20$ B) $x^4+5 x^2+16$ C) $x^4+9 x^2$ D) $x^4+9 x^2+12$

D

$$ \begin{aligned} & y=4 x+1 \\ & y=4 x+3 \end{aligned}$$ How many solutions does the given system of equations have?

A) Zero B) Exactly one C) Exactly two D) Infinitely many

A

$$ h(x)=3 x+3 $$ Which inequality represents all values of $x$ for which the graph of $y=h(x)$ in the $x y$-plane is above the $x$-axis?

A) $x<3$ B) $x<-1$ C) $x>-1$ D) $x>3$

C

Which quadratic equation has no real solutions?

A) $3 x^2-3=0$ B) $3 x^2+3 x=0$ C) $3 x^2+3 x+3=0$ D) $3 x^2-6 x+3=0$

C

In 1976, there were approximately 1,000 gray wolves in northern Minnesota. The number of gray wolves in northern Minnesota in 2008 was 190% greater than in 1976. Approximately how many gray wolves were in northern Minnesota in 2008?

A. 1,190 B. 1,900 C. 2,900 D. 19,000

C

When the quadratic function $f$ is graphed in the $x y$-plane, where $y=f(x)$, its vertex is $(-2,5)$. One of the $x$-intercepts of this graph is $\left(-\frac{7}{3}, 0\right)$. What is the other $x$-intercept of the graph?

A. $\left(-\frac{13}{3}, 0\right)$ B. $\left(-\frac{5}{3}, 0\right)$ C. $\left(\frac{1}{3}, 0\right)$ D. $\left(\frac{7}{3}, 0\right)$

B

For an exponential function $g$, the value of $g(x)$ decreases by $20 \%$ for each 1-unit increase in the value of $x$. If $g(2)=16$, which equation could define $g$ ?

A) $g(x)=16(0.8)^{x-2}$ B) $g(x)=16(0.8)^{x+2}$ C) $g(x)=16(0.2)^{x-2}$ D) $g(x)=16(0.2)^{x+2}$

A

Micha and Rana each selected a random sample of students at their school and asked how many soft drink servings each student had consumed the previous week. Micha estimated that the mean number of soft drink servings was 7.1, with an associated margin of error of 1.2. Rana estimated that the mean number of soft drink servings was 8.3, with an associated margin of error of 0.8. Assuming the margins of error were calculated in the same way, which of the following best explains why Rana obtained a smaller margin of error than Micha?

A. Rana's sample contained more students than Micha's sample contained. B. Rana's sample contained more students who drank soft drinks than Micha's sample contained. C. Rana's sample contained more students who drank exactly seven soft drink servings than Micha's sample contained. D. Rana's sample contained more students who drank exactly eight soft drink servings than Micha's sample contained.

A

A circle in the $x y$-plane has its center at $(-3,4)$ and the point $(-2,1)$ lies on the circle. Which equation represents this circle?

A) $(x-3)^2+(y+4)^2=\sqrt{10}$ B) $(x+3)^2+(y-4)^2=\sqrt{10}$ C) $(x-3)^2+(y+4)^2=10$ D) $(x+3)^2+(y-4)^2=10$

D

\begin{tabular}{|c|c|} \hline$x$ & $h(x)$ \\\hline 2 & 0 \\\hline 4 & 0 \\\hline 6 & 8 \\\hline \end{tabular} For the quadratic function $h$, the table gives three values of $x$ and their corresponding values of $h(x)$. At what value of $x$ does $h$ reach its minimum?

A) -1 B) 0 C) 3 D) 4

C