# SAT Prep

## Educators

Problem 16

The sales manager of a company awarded a total of
$\$ 3000$in bonuses to the most productive salespeople. The bonuses were awarded in amounts of$\$250$ or
$\$ 750$. If at least one$\$250$ bonus and at least one $\$ 750$bonus were awarded, what is one possible number of$\$250$ bonuses awarded?

Check back soon!

Math Test - Calculator - Problem 1

A musician has a new song available for
$\$ 0.09$each time the song is downloaded and$\$0.002$
each time the song is streamed. Which of the
following expressions represents the amount, in dollars, that the musician earns if the song is
downloaded $d$ times and streamed $s$ times?
$\begin{array}{ll}{\text { A) }} & {0.002 d+0.09 s} \\ {\text { B) }} & {0.002 d-0.09 s} \\ {\text { C) }} & {0.09 d+0.002 s} \\ {\text { D) }} & {0.09 d-0.002 s}\end{array}$

Colin C.

Math Test - Calculator - Problem 2

A quality control manager at a factory selects
7 lightbulbs at random for inspection out of every
400 lightbulbs produced. At this rate, how many
lightbulbs will be inspected if the factory produces
$20,000$ lightbulbs?
$$\begin{array}{l}{\text { A) } 300} \\ {\text { B) } 350} \\ {\text { C) } 400} \\ {\text { D) } 450}\end{array}$$

Colin C.

Math Test - Calculator - Problem 3

$$\ell=24+3.5 m$$
One end of a spring is attached to a ceiling. When an object of mass $m$ kilograms is attached to the other end of the spring, the spring stretches to a length of $\ell$ centimeters as shown in the equation above. What is $m$ when $\ell$ is 73$?$
$$\begin{array}{l}{\text { A) } 14} \\ {\text { B) } 27.7} \\ {\text { C) } 73} \\ {\text { D) } 279.5}\end{array}$$

Colin C.

Math Test - Calculator - Problem 4

How much money will the performer earn when 20 people attend a performance?
$$\begin{array}{l}{\text { A) } \ 960} \\ {\text { B) } \ 480} \\ {\text { C) } \ 300} \\ {\text { D) } \ 240}\end{array}$$

Colin C.

Math Test - Calculator - Problem 5

The performer uses 43$\%$ of the money earned to pay
the costs involved in putting on each performance.
The rest of the money earned is the performer's
profit. What is the profit the performer makes at a
performance where 8 people attend?
$$\begin{array}{l}{\text { A) } \ 51.60} \\ {\text { B) } \ 57.00} \\ {\text { C) } \ 68.40} \\ {\text { D) } \ 77.00}\end{array}$$

Colin C.

Math Test - Calculator - Problem 6

When 4 times the number $x$ is added to $12,$ the result is $8 .$ What number results when 2 times $x$ is added to 7$?$
$$\begin{array}{l}{\text { A) }-1} \\ {\text { B) } 5} \\ {\text { C) } 8} \\ {\text { D) } 9}\end{array}$$

Colin C.

Math Test - Calculator - Problem 7

$$y=x^{2}-6 x+8$$
The equation above represents a parabola in the $x y$ -plane. Which of the following equivalent forms of the equation displays the $x$ -intercepts of the parabola as constants or coefficients?
$$\begin{array}{l}{\text { A) } y-8=x^{2}-6 x} \\ {\text { B) } y+1=(x-3)^{2}} \\ {\text { C) } y=x(x-6)+8} \\ {\text { D) } y=(x-2)(x-4)}\end{array}$$

Colin C.

Math Test - Calculator - Problem 8

In a video game, each player starts the game with $k$ points and loses 2 points each time a task is not completed. If a player who gains no additional points and fails to complete 100 tasks has a score of 200 points, what is the value of $k ?$
$$\begin{array}{ccc}{\text { A) }} & {0} \\ {\text { 3) }} & {150} \\ {\text { C) }} & {250} \\ {\text { D) }} & {400}\end{array}$$

Colin C.

Math Test - Calculator - Problem 9

A worker uses a forklift to move boxes that weigh either 40 pounds or 65 pounds each. Let $x$ be the number of 40 -pound boxes and $y$ be the number of 65 -pound boxes. The forklift can carry up to either 45 boxes or a weight of $2,400$ pounds. Which of the following systems of inequalities represents this relationship?
$$A)\left\{\begin{array}{l}{40 x+65 y \leq 2,400} \\ {x+y \leq 45}\end{array}\right.$$
$$B)\left\{\begin{array}{l}{\frac{x}{40}+\frac{y}{65} \leq 2,400} \\ {x+y \leq 45}\end{array}\right.$$
$$C)\left\{\begin{array}{l}{40 x+65 y \leq 45} \\ {x+y \leq 2,400}\end{array}\right.$$
$$D)\left\{\begin{array}{l}{x+y \leq 2,400} \\ {40 x+65 y \leq 2,400}\end{array}\right.$$

Colin C.

Math Test - Calculator - Problem 10

A function $f$ satisfies $f(2)=3$ and $f(3)=5 . \mathrm{A}$ function $g$ satisfies $g(3)=2$ and $g(5)=6 .$ What is the value of $f(g(3)) ?$
\begin{array}{l}{\text { A) } 2} \\ {\text { B) } 3} \\ {\text { C) } 5} \\ {\text { D) } }\end{array}

Colin C.

Math Test - Calculator - Problem 11

Tony is planning to read a novel. The table above shows information about the novel, Tony's reading speed, and the amount of time he plans to spend reading the novel each day. If Tony reads at the rates given in the table, which of the following is closest to the number of days it would take Tony to read the entire novel?
$$\begin{array}{l}{\text { A) } 6} \\ {\text { B) } 8} \\ {\text { C) } 23} \\ {\text { D) } 324}\end{array}$$

Colin C.

Math Test - Calculator - Problem 12

On January $1,2000,$ there were $175,000$ tons of trash in a landfill that had a capacity of $325,000$ tons. Each year since then, the amount of trash in the landfill increased by $7,500$ tons. If $y$ represents the time, in years, after January $1,2000,$ which of the following inequalities describes the set of years where the landfill is at or above capacity?
$$\begin{array}{l}{\text { A) } 325,000-7,500 \leq y} \\ {\text { B) } 325,000 \leq 7,500 y} \\ {\text { C) } 150,000 \geq 7,500 y} \\ {\text { D) } 175,000+7,500 y \geq 325,000}\end{array}$$

Colin C.

Math Test - Calculator - Problem 13

A researcher conducted a survey to determine whether people in a certain large town prefer watching sports on television to attending the sporting event. The researcher asked 117 people who visited a local restaurant on a Saturday, and 7 people refused to respond. Which of the following factors makes it least likely that a reliable conclusion can be drawn about the sports-watching preferences of all people in the town?
$$\begin{array}{l}{\text { A) Sample size }} \\ {\text { B) Population size }} \\ {\text { C) The number of people who refused to respond }} \\ {\text { D) Where the survey was given }}\end{array}$$

Colin C.

Math Test - Calculator - Problem 14

According to the line of best fit in the scatterplot above, which of the following best approximates the year in which the number of miles traveled by air passengers in Country X was estimated to be 550 billion?
$$\begin{array}{l}{\text { A) } 1997} \\ {\text { B) } 2000} \\ {\text { C) } 2003} \\ {\text { D) } 2008}\end{array}$$

Colin C.

Math Test - Calculator - Problem 15

The table above summarizes the results of 200 law
school graduates who took the bar exam. If one of
the surveyed graduates who passed the bar exam is
chosen at random for an interview, what is the
probability that the person chosen did not take the review course?
$$\begin{array}{l}{\text { A) } \frac{18}{25}} \\ {\text { B) } \frac{7}{25}} \\ {\text { C) } \frac{25}{200}} \\ {\text { D) } \frac{7}{200}}\end{array}$$

Colin C.

Math Test - Calculator - Problem 16

The distance traveled by Earth in one orbit around the Sun is about $580,000,000$ miles. Earth makes one complete orbit around the Sun in one year. Of the following, which is closest to the average speed of Earth, in miles per hour, as it orbits the Sun?
$$\begin{array}{l}{\text { A) } 66,000} \\ {\text { B) } 93,000} \\ {\text { C) } 210,000} \\ {\text { D) } 420,000}\end{array}$$

Colin C.

Math Test - Calculator - Problem 17

The atomic weight of an unknown element, in atomic mass units (amu), is approximately 20$\%$ less than that of calcium. The atomic weight of calcium is 40 amu. Which of the following best approximates the atomic weight, in amu, of the unknown element?
$$\begin{array}{l}{\text { A) } 8} \\ {\text { B) } 20} \\ {\text { C) } 32} \\ {\text { D) } 48}\end{array}$$

Colin C.

Math Test - Calculator - Problem 18

A survey was taken of the value of homes in a county,
and it was found that the mean home value was
$\$ 165,000$and the median home value was$\$125,000$ .
Which of the following situations could explain the
difference between the mean and median home
values in the county?
\begin{array}{l}{\text { A) The homes have values that are close to each }} \\ {\text { other. }} \\ {\text { B) There are a few homes that are valued much less }} \\ {\text { than the rest. }} \\ {\text { C) There are a few homes that are valued much }} \\ {\text { more than the rest. }} \\ {\text { D) Many of the homes have values between }} \\ {\$125,000 \text { and } \$ 165,000 .}\end{array}

Colin C.

Math Test - Calculator - Problem 19

What is the median number of siblings for all the
students surveyed?
$$\begin{array}{l}{\text { A) } 0} \\ {\text { B) } 1} \\ {\text { C) } 2} \\ {\text { D) } 3}\end{array}$$

Colin C.

Math Test - Calculator - Problem 20

Based on the survey data, which of the following
most accurately compares the expected total number
of students with 4 siblings at the two schools?
$$\begin{array}{l}{\text { A) The total number of students with } 4 \text { siblings is }} \\ {\text { expected to be equal at the two schools. }} \\ {\text { B) The total number of students with } 4 \text { siblings at }} \\ {\text { Lincoln School is expected to be } 30 \text { more than at }} \\ {\text { Washington School. }}\end{array}$$
$$\begin{array}{l}{\text { C) The total number of students with } 4 \text { siblings at }} \\ {\text { Washington School is expected to be } 30 \text { more }} \\ {\text { than at Lincoln School. }} \\ {\text { D) The total number of students with } 4 \text { siblings at }} \\ {\text { Washington School is expected to be } 900 \text { more }} \\ {\text { than at Lincoln School. }}\end{array}$$

Colin C.

Math Test - Calculator - Problem 21

A project manager estimates that a project will take $x$ hours to complete, where $x>100 .$ The goal is for the estimate to be within 10 hours of the time it will actually take to complete the project. If the manager meets the goal and it takes $y$ hours to complete the project, which of the following inequalities represents the relationship between the estimated time and the actual completion time?
$$\begin{array}{l}{\text { A) } x+y < 10} \\ {\text { B) } y > x+10} \\ {\text { C) } y < x-10} \\ {\text { D) }-10 < y-x < 10}\end{array}$$

Colin C.

Math Test - Calculator - Problem 22

Which of the following expresses the square of the
distance from the radio antenna in terms of the
intensity of the radio signal and the power of the
signal?
$$\begin{array}{l}{\text { A) } r^{2}=\frac{I P}{4 \pi}} \\ {\text { B) } r^{2}=\frac{P}{4 \pi I}} \\ {\text { C) } r^{2}=\frac{4 \pi I}{P}} \\ {\text { D) } r^{2}=\frac{I}{4 \pi P}}\end{array}$$

Colin C.

Math Test - Calculator - Problem 23

For the same signal emitted by a radio antenna,
Observer A measures its intensity to be 16 times the
intensity measured by Observer B. The distance of
Observer A from the radio antenna is what fraction
of the distance of Observer B from the radio
antenna?
$$\begin{array}{l}{\text { A) } \frac{1}{4}} \\ {\text { B) } \frac{1}{16}} \\ {\text { C) } \frac{1}{64}} \\ {\text { D) } \frac{1}{256}}\end{array}$$

Colin C.
$$x^{2}+y^{2}+4 x-2 y=-1$$
The equation of a circle in the $x y$ -plane is shown above. What is the radius of the circle?
$$\begin{array}{l}{\text { A) } 2} \\ {\text { B) } 3} \\ {\text { C) } 4} \\ {\text { D) } 9}\end{array}$$