# SAT Prep

## Educators

### Problem 16

Number of Adults Contracting Colds
$$\begin{array}{|c|c|c|c|}\hline & {~ C o l d ~} & {\text { No cold }} & {\text { Total }} \\ \hline \text { Vitamin C } & {21} & {129} & {150} \\ \hline \text { Sugarpill } & {33} & {117} & {150} \\ \hline \text { Total } & {54} & {246} & {300} \\ \hline\end{array}$$
The table shows the results of a research study that
investigated the therapeutic value of vitamin $C$ in
preventing colds. A random sample of 300 adults
received either a vitamin C pill or a sugar pill each
day during a 2 -week period, and the adults reported
whether they contracted a cold during that time
period. What proportion of adults who received a
sugar pill reported contracting a cold?
$$\begin{array}{l}{\text { A) } \frac{11}{18}} \\ {\text { B) } \frac{11}{50}} \\ {\text { C) } \frac{9}{50}} \\ {\text { D) } \frac{11}{100}}\end{array}$$

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One pound of grapes costs $\$ 2 .$At this rate, how many dollars will$c$pounds of grapes cost? A) 2$c$B)$2+c$C)$\frac{2}{c}$D)$\frac{c}{2}$Lily A. Numerade Educator ### Math Test - Calculator - Problem 2 Tracy collects, sells, and trades figurines, and she tracks the number of figurines in her collection on the graph below. On what interval did the number of figurines decrease the fastest? A) Between 1 and 2 months B) Between 2 and 3 months C) Between 3 and 4 months D) Between 4 and 5 months Lily A. Numerade Educator ### Math Test - Calculator - Problem 3 In a random sample of 200 cars of a particular model, 3 have a manufacturing defect. At this rate, how many of$10,000$cars of the same model will have a manufacturing defect? A) 150 B) 200 C) 250 D) 300 Lily A. Numerade Educator ### Math Test - Calculator - Problem 4 The scatterplot above shows data collected on the lengths and widths of Iris setosa petals. A line of best fit for the data is also shown. Based on the line of best fit, if the width of an Iris setosa petal is 19 millimeters, what is the predicted length, in millimeters, of the petal? A) 21.10 B) 31.73 C) 52.83 D) 55.27 Lily A. Numerade Educator ### Math Test - Calculator - Problem 5 In the figure above, lines$\ell$and$m$are parallel,$y=20,$and$z=60 .$What is the value of$x ?$A) 120 B) 100 C) 90 D) 80 Lily A. Numerade Educator ### Math Test - Calculator - Problem 6 Two types of tickets were sold for a concert held at an amphitheater. Tickets to sit on a bench during the concert cost$\$75$ each, and tickets to sit on the lawn
during the concert cost $\$ 40$each. Organizers of the concert announced that 350 tickets had been sold and that$\$19,250$ had been raised through ticket sales
alone. Which of the following systems of equations
could be used to find the number of tickets for bench
seats, $B$ , and the number of tickets for lawn seats, $L$
that were sold for the concert?
$$\begin{array}{l}{\text { A) }(75 B)(40 L)=1,950} \\ \quad {B+L=350} \\ {\text { B) } 40 B+75 L=19,250} \\ \quad {B+L=350} \\ {\text { C) } 75 B+40 L=350} \\ \quad {B+L=19,250} \\ {\text { D) } 75 B+40 L=19,250} \\ \quad {B+L=350} \end{array}$$

Lily A.

### Math Test - Calculator - Problem 7

In the $x y$ -plane, the graph of which of the following
equations is a line with a slope of 3$?$
$$\begin{array}{l}{\text { A) } y=\frac{1}{3} x} \\ {\text { B) } y=x-3} \\ {\text { C) } y=3 x+2} \\ {\text { D) } y=6 x+3}\end{array}$$

Lily A.

### Math Test - Calculator - Problem 8

$$x+1=\frac{2}{x+1}$$
In the equation above, which of the following is a
possible value of $x+1 ?$
$$\begin{array}{l}{\text { A) } 1-\sqrt{2}} \\ {\text { B) } \sqrt{2}} \\ {\text { C) } 2} \\ {\text { D) } 4}\end{array}$$

Lily A.

### Math Test - Calculator - Problem 9

What is the value of $k,$ in centimeters?
$$\begin{array}{l}{\text { A) } 2.52} \\ {\text { B) } 7.67} \\ {\text { C) } 7.79} \\ {\text { D) } 10.11}\end{array}$$

Lily A.

### Math Test - Calculator - Problem 10

Water pours into the glass slowly and at a constant
rate. Which of the following graphs best illustrates
the height of the water level in the glass as it fills?

Lily A.

### Math Test - Calculator - Problem 11

Jenny has a pitcher that contains 1 gallon of water.
How many times could Jenny completely fill the glass
with 1 gallon of water? $(1$ gallon $=128$ fluid ounces $)$
$$\begin{array}{l}{\text { A) } 16} \\ {\text { B) } 8} \\ {\text { C) } 4} \\ {\text { D) } 3}\end{array}$$

Lily A.

### Math Test - Calculator - Problem 12

Roberto is an insurance agent who sells two types of
policies: a $\$ 50,000$policy and a$\$100,000$ policy. Last
month, his goal was to sell at least 57 insurance
policies. While he did not meet his goal, the total
value of the policies he sold was over $\$ 3,000,000$. Which of the following systems of inequalities describes$x$, the possible number of$\$50,000$ policies,
and $y$ , the possible number of $\$ 100,000$policies, that Roberto sold last month? $$\begin{array}{l}{\text { A) } x+y<57} \\ \quad {50,000 x+100,000 y<3,000,000} \\ {\text { B) } x+y>57} \\ \quad {50,000 x+100,000 y>3,000,000} \\ {\text { C) } x+y<57} \\ \quad {50,000 x+100,000 y>3,000,000} \\ {\text { D) } x+y>57} \\ \quad {50,000 x+100,000 y<3,000,000}\end{array}$$ Lily A. Numerade Educator ### Math Test - Calculator - Problem 13 If$a^{-\frac{1}{2}}=x,$where$a>0,$what is$a$in terms of$x ?$$$\begin{array}{l}{\text { A) } \sqrt{x}} \\ {\text { B) }-\sqrt{x}} \\ {\text { C) } \frac{1}{x^{2}}} \\ {\text { D) }-\frac{1}{x^{2}}}\end{array}$$ Lily A. Numerade Educator ### Math Test - Calculator - Problem 14 Which of the following is a value of$x$for which the expression$\frac{-3}{x^{2}+3 x-10}is undefined? $$\begin{array}{l}{\text { A) }-3} \\ {\text { B) }-2} \\ {\text { C) } 0} \\ {\text { D) } 2}\end{array}$$ Lily A. Numerade Educator ### Math Test - Calculator - Problem 15 A granite block in the shape of a right rectangular prism has dimensions 30 centimeters by 40 centimeters by 50 centimeters. The block has a density of 2.8 grams per cubic centimeter. What is the mass of the block, in grams? (Density is mass per unit volume.) \begin{aligned} \text { A) } & 336 \\ \text { B) } & 3,360 \\ \text { C) } & 16,800 \\ \text { D) } & 168,000 \end{aligned} Lily A. Numerade Educator ### Math Test - Calculator - Problem 17 Ages of 20 Students Enrolled in a College Class $$\begin{array}{|c|c|}\hline \text { Age } & {\text { Frequency }} \\ \hline 18 & {6} \\ \hline 19 & {5} \\ \hline 20 & {4} \\ \hline 21 & {2} \\ \hline 22 & {1} \\ \hline 23 & {1} \\ \hline 30 & {1} \\ \hline\end{array}$$ The table above shows the distribution of ages of the 20 students enrolled in a college class. Which of the following gives the correct order of the mean, median, and mode of the ages? A) mode<$median$<$mean B) mode$<$mean$<$median C) median$<$mode$<$mean D) mean$<$mode$<$median Lily A. Numerade Educator ### Math Test - Calculator - Problem 18 The figure below shows the relationship between the percent of leaf litter mass remaining after decomposing for 3 years and the mean annual temperature, in degrees Celsius$\left(^{\circ} \mathrm{C}\right),$in 18 forests in Canada. A line of best fit is also shown. A particular forest in Canada, whose data is not included in the figure, had a mean annual temperature of$-2^{\circ} \mathrm{C}$. Based on the line of best fit, which of the following is closest to the predicted percent of leaf litter mass remaining in this particular forest after decomposing for 3 years? $$\begin{array}{l}{\text { A) } 50 \%} \\ {\text { B) } 63 \%} \\ {\text { C) } 70 \%} \\ {\text { D) } 82 \%}\end{array}$$ Lily A. Numerade Educator ### Math Test - Calculator - Problem 19 The range of the polynomial function$f$is the set of real numbers less than or equal to$4 .$If the zeros of$f$are$-3$and$1,$which of the following could be the graph of$y=f(x)$in the$x y$-plane? Lily A. Numerade Educator ### Math Test - Calculator - Problem 20 The average annual energy cost for a certain home is$\$4,334 .$ The homeowner plans to spend $\$ 25,000$to install a geothermal heating system. The homeowner estimates that the average annual energy cost will then be$\$2,712 .$ Which of the following inequalities
can be solved to find $t,$ the number of years after
installation at which the total amount of energy cost
savings will exceed the installation cost?
$$\begin{array}{l}{\text { A) } 25,000>(4,334-2,712) t} \\ {\text { B) } 25,000<(4,334-2,712) t} \\ {\text { C) } 25,000-4,334>2,712 t} \\ {\text { D) } 25,000>\frac{4,332}{2,712} t}\end{array}$$

Lily A.

### Math Test - Calculator - Problem 21

Which of the following is the best interpretation of
the number 3.39 in the context of the problem?
A) The amount of plastic, in billions of pounds,
produced in the United States during the
year 1985
B) The number of years it took the United States to
produce 1 billion pounds of plastic
C) The average annual plastic production, in
billions of pounds, in the United States from
1985 to 2003
D) The average annual increase, in billions of
pounds, of plastic produced per year in the
United States from 1985 to 2003

Lily A.

### Math Test - Calculator - Problem 22

Which of the following is closest to the percent
increase in the billions of pounds of plastic produced
in the United States from 2000 to 2003$?$
$$\begin{array}{l}{\text { A) } 10 \%} \\ {\text { B) } 44 \%} \\ {\text { C) } 77 \%} \\ {\text { D) } 110 \%}\end{array}$$

Lily A.

### Math Test - Calculator - Problem 23

$$M=1,800(1.02)^{t}$$
The equation above models the number of
members, $M,$ of a gym $t$ years after the gym opens.
Of the following, which equation models the number
of members of the gym $q$ quarter years after the gym
opens?
$$\begin{array}{l}{\text { A) } M=1,800(1.02)^{\frac{q}{4}}} \\ {\text { B) } M=1,800(1.02)^{4 q}} \\ {\text { C) } M=1,800(1.005)^{4 q}} \\ {\text { D) } M=1,800(1.082)^{q}}\end{array}$$

Lily A.

### Math Test - Calculator - Problem 24

For the finale of a TV show, viewers could use either
social media or a text message to vote for their
favorite of two contestants. The contestant receiving
more than 50$\%$ of the vote won. An estimated 10$\%$ of
the viewers voted, and 30$\%$ of the votes were cast on
social media. Contestant 2 earned 70$\%$ of the votes
cast using social media and 40$\%$ of the votes cast
using a text message. Based on this information,
which of the following is an accurate conclusion?
A) If all viewers had voted, Contestant 2 would
have won.
B) Viewers voting by social media were likely to be
younger than viewers voting by text message.
C) If all viewers who voted had voted by social
media instead of by text message, Contestant 2
would have won.
D) Viewers voting by social media were more likely
to prefer Contestant 2 than were viewers voting
by text message.

Lily A.

### Math Test - Calculator - Problem 25

Population of Greenleaf, Idaho
$$\begin{array}{|c|c|}\hline \text { Year } & {\text { Population }} \\ \hline 2000 & {862} \\ \hline 2010 & {846} \\ \hline\end{array}$$
The table above shows the population of Greenleaf,
Idaho, for the years 2000 and $2010 .$ If the relationship
between population and year is linear, which of the
following functions $P$ models the population of
Greenleaf $t$ years after 2000$?$
$$\begin{array}{l}{\text { A) } P(t)=862-1.6 t} \\ {\text { B) } P(t)=862-16 t} \\ {\text { C) } P(t)=862+16(t-2,000)} \\ {\text { D) } P(t)=862-1.6(t-2,000)}\end{array}$$

Lily A.