$\def\iii#1#2#3{\begin{array}{c}\text{#1}\\\text{#2}\\\text{#3}\end{array}}$
$\def\frac{\dfrac}$
$\def\tiii#1#2#3{\mbox{#1}&\mbox{#2}&\mbox{#3}}$
1. (Test3/Q $10 /$ Calculator)
$$\begin{array}{|l|c|}
\hline \text{Planet} & \text{Acceleration due to gravity }\left(\frac{\mathrm{m}}{\mathrm{sec}^{2}}\right) \\
\hline \hline \text{Mercury }& 3.6 \\
\hline \text{Venus }& 8.9 \\
\hline \text{Earth }& 9.8 \\
\hline \text{Mars }& 3.8 \\
\hline \text{Jupiter} & 26.0 \\
\hline \text{Saturn }& 11.1 \\
\hline \text{Uranus }& 10.7 \\
\hline \text{Neptune }& 14.1 \\
\hline
\end{array}$$
The chart above shows approximations of the acceleration due to gravity in meters per
second squared $\left(\frac{\mathrm{m}}{\sec ^{2}}\right)$ for the eight planets in our solar system. The weight of an object on a given planet can be found by using the formula $W=m g$, where $W$ is the weight of the object measured in newtons, $m$ is the mass of the object measured in kilograms, and $g$ is the acceleration due to gravity on the planet measured in $\frac{\mathrm{m}}{\sec ^{2}}$.
What is the weight, in newtons, of an object on Mercury with a mass of 90 kilograms?
A) 25
B) 86
C) 101
D) 324
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2. (Test3/Q 11/Calculator)
$$\begin{array}{|l|c|}
\hline \text{Planet} & \text{Acceleration due to gravity }\left(\frac{\mathrm{m}}{\mathrm{sec}^{2}}\right) \\
\hline \hline \text{Mercury }& 3.6 \\
\hline \text{Venus }& 8.9 \\
\hline \text{Earth }& 9.8 \\
\hline \text{Mars }& 3.8 \\
\hline \text{Jupiter} & 26.0 \\
\hline \text{Saturn }& 11.1 \\
\hline \text{Uranus }& 10.7 \\
\hline \text{Neptune }& 14.1 \\
\hline
\end{array}$$
The chart abowe shows approximations of the acceleration due to gravity in meters per
second squared $\left(\frac{\mathrm{m}}{\sec ^{2}}\right)$ for the eight planets in our solar system. The weight of an object on a given planet can be found by using the formula $W=m g$, where $W$ is the weight of the object measured in newtons, $m$ is the mass of the object measured in kilograms, and $g$ is the acceleration due to gravity on the planet measured in $\frac{\mathrm{m}}{\mathrm{sec}^{2}}$.
An object on Earth has a weight of 150 newtons. On which planet would the same object have an approximate weight of 170 newtons?
A) Venus
B) Saturn
C) Uranus
D) Neptune
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3. (Test4/Q $16 /$ Calculator)
Mr. Martinson is building a concrete patio in his backyard and deciding where to buy the materials and rent the tools needed for the project. The table below shows the materials' cost and daily rental costs for three different stores.
$$\begin{array}{|c|c|c|c|}
\hline \iii{}{Store}{} & \iii{Materials'}{ Cost, $M$}{ (dollars)} & \iii{Rental cost of}{ wheelbarrow, W}{ (dollars per day) }&\iii{ Rental cost of }{concrete mixer,}{ $K$ (dollars per day) }\\
\hline A & 750 & 15 & 65 \\
\hline B & 600 & 25 & 80 \\
\hline C & 700 & 20 & 70 \\
\hline
\end{array}$$
The total cost, $y$, for buying the materials and renting the tools in terms of the number of days, $x$, is given by $y=M+(W+K) x$.
For what number of days, $x$, will the total cost of buying the materials and renting the tools from Store B be less than or equal to the total cost of buying the materials and renting the tools from Store A ?
A) $x \leq 6$
B) $x \geq 6$
C) $x \leq 7.3$
D) $x \geq 7.3$
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4. (Test4/Q 17/Calculator)
Mr. Martinson is building a concrete patio in his backyard and deciding where to buy the materials and rent the tools needed for the project. The table below shows the materials' cost and daily rental costs for three different stores.
$$\begin{array}{|c|c|c|c|}
\hline \iii{}{Store}{} & \iii{Materials'}{ Cost, $M$}{ (dollars)} & \iii{Rental cost of}{ wheelbarrow, W}{ (dollars per day) }&\iii{ Rental cost of }{concrete mixer,}{ $K$ (dollars per day) }\\
\hline A & 750 & 15 & 65 \\
\hline B & 600 & 25 & 80 \\
\hline C & 700 & 20 & 70 \\
\hline
\end{array}$$
The total cost, $y$, for buying the materials and renting the tools in terms of the number of days, $x$, is given by $y=M+(W+K) x$.
If the relationship between the total cost, $y$, of buying the materials and renting the tools at Store $\mathrm{C}$ and the number of days, $x$, for which the tools are rented is graphed in the $x y$-plane, what does the slope of the line represent?
A) The total cost of the project
B) The total cost of the materials
C) The total daily cost of the project
D) The total daily rental costs of the tools
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5. (Test4/Q 32/Calculator)
| The normal systolic blood pressure $P$, in millimeters of mercury, for an adult male $x$ years old can be modeled by the equation $P=\frac{x+220}{2}$. According to the model, for every increase of 1 year in age, by how many millimeters of mercury will the normal systolic blood pressure for an adult male increase?
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6. (Test4/Q 35/Calculator)
| $$q=\frac{1}{2} n v^{2}$$
The dynamic pressure $q$ generated by a fluid moving with velocity $v$ can be found using the formula above, where $n$ is the constant density of the fluid. An aeronautical engineer uses the formula to find the dynamic pressure of a fluid moving with velocity $v$ and the same fluid moving with velocity 1.5v. What is the ratio of the dynamic pressure of the faster fluid to the dynamic pressure of the slower fluid?
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7. (Test5/Q $8 /$ No Calculator)
In air, the speed of sound $S$, in meters per second, is a linear function of the air temperature $T$, in degrees Celsius, and is given by $S(T)=0.6 T+331.4$. Which of the following statements is the best interpretation of the number $331.4$ in this context?
A) The speed of sound, in meters per second, at $0^{\circ} \mathrm{C}$
B) The speed of sound, in meters per second, at $0.6^{\circ} \mathrm{C}$
C) The increase in the speed of sound, in meters per second, that corresponds to an increase of $1^{\circ} \mathrm{C}$
D) The increase in the speed of sound, in meters per second, that corresponds to an increase of $0.6^{\circ} \mathrm{C}$
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8. (Test5/Q $13 /$ No Calculator)
At a restaurant, $n$ cups of tea are made by adding $t$ tea bags to hot water. If $t=n+2$, how many additional tea bags are needed to make each additional cup of tea?
A) None
B) One
C) Two
D) Three
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9. (Test5/Q 10/Calculator)
The density $d$ of an object is found by dividing the mass $m$ of the object by its volume $V$. Which of the following equations gives the mass $m$ in terms of $d$ and $V$ ?
A) $m=d V$
B) $m=\frac{d}{V}$
C) $m=\frac{V}{d}$
D) $m=V+d$
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10. (Test5/Q 21/Calculator)
$$\frac{a-b}{a}=c$$
In the equation above, if $a$ is negative and $b$ is positive, which of the following must be true?
A) $c>1$
B) $c=1$
C) $c=-1$
D) $c < -1$
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11. (Test5/Q 30/Calculator)
$$y=x^{2}-a$$
In the equation above, $a$ is a positive constant and the graph of the equation in the $x y$-plane is a parabola. Which of the following is an equivalent form of the equation?
A) $y=(x+a)(x-a)$
B) $y=(x+\sqrt{a})(x-\sqrt{a})$
C) $y=\left(x+\frac{a}{2}\right)\left(x-\frac{a}{2}\right)$
D) $y=(x+a)^{2}$
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12. (Test6/Q 1/No Calculator)
Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor charges a one-time service fee for processing the purchase of the tickets. The equation $T=15 n+12$ represents the total amount $T$, in dollars, Salim will pay for $n$ tickets. What does 12 represent in the equation?
A) The price of one ticket, in dollars
B) The amount of the service fee, in dollars
C) The total amount, in dollars, Salim will pay for one ticket
D) The total amount, in dollars, Salim will pay for any number of tickets
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13. (Test6/Q $7 /$ No Calculator)
A bricklayer uses the formula $n=7 \ell h$ to estimate the number of bricks, $n$, needed to build a wall that is $\ell$ feet long and $h$ feet high. Which of the following correctly expresses $\ell$ in terms of $n$ and $h$ ?
A) $\ell=\frac{7}{n h}$
B) $\ell=\frac{h}{7 n}$
C) $\ell=\frac{n}{7 h}$
D) $\ell=\frac{n}{7+h}$
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14. (Test6/Q $17 /$ Calculator)
Note: Figure not drawn to scale.
When designing a stairway, an architect can use the riser-tread formula $2 h+d=25$, where $h$ is the riser height, in inches, and $d$ is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway-
The number of steps in a stairway is the number of its risers. For example, there are 5 steps in the stairway in the figure above. The total rise of a stairway is the sum of the riser heights as shown in the figure.
Which of the following expresses the riser height in terms of the tread depth?
A) $h=\frac{1}{2}(25+d)$
B) $h=\frac{1}{2}(25-d)$
C) $h=-\frac{1}{2}(25+d)$
D) $h=-\frac{1}{2}(25-d)$
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15. (Test6/Q 18/Calculator)
Note: Figure not drawn to scale.
When designing a stairway, an architect can use the riser-tread formula $2 h+d=25$, where $h$ is the riser height, in inches, and $d$ is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway-
The number of steps in a stairway is the number of its risers. For example, there are 5 steps in the stairway in the figure above. The total rise of a stairway is the sum of the riser heights as shown in the figure.
Some building codes require that, for indoor stairways, the tread depth must be at least 9 inches and the riser height must be at least 5 inches.
According to the riser-tread formula, which of the following inequalities represents the set of all possible values for the riser height that meets this code requirement?
A) $0 \leq h \leq 5$
B) $h \geq 5$
C) $5 \leq h \leq 8$
D) $8 \leq h \leq 16$
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16. (Test $6 / Q 19 /$ Calculator)
Note: Figure not drawn to scale.
When designing a stairway, an architect can use the riser-tread formula $2 h+d=25$, where $h$ is the riser height, in inches, and $d$ is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway.
The number of steps in a stairway is the number of its risers. For example, there are 5 steps in the stairway in the figure above. The total rise of a stairway is the sum of the riser heights as shown in the figure.
An architect wants to use the riser-tread formula to design a stairway with a total rise of 9 feet, a riser height between 7 and 8 inches, and an odd number of steps. With the architect's constraints, which of the following must be the tread depth, in inches, of the stairway? ( 1 foot $=12$ inches)
A) $7.2$
B) $9.5$
C) $10.6$
D) 15
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17. (Test $6 / \mathrm{Q} 29 /$ Calculator)
A motor powers a model car so that after starting from rest, the car travels $s$ inches in $t$ seconds, where $s=16 t \sqrt{t}$. Which of the following gives the average speed of the car, in inches per second, over the first $t$ seconds after it starts?
A) $4 \sqrt{t}$
B) $16 \sqrt{t}$
C) $\frac{16}{\sqrt{t}}$
D) $16 t$
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18. (Test7/Q 1/No Calculator)
$$x+y=75$$
The equation above relates the number of minutes, $x$, Maria spends running each day and the number of minutes, $y$, she spends biking each day.
In the equation, what does the number 75 represent?
A) The number of minutes spent running each day
B) The number of minutes spent biking each day
C) The total number of minutes spent running and biking each day
D) The number of minutes spent biking for each minute spent running
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19. (Test7/Q 19/Calculator)
Mosteller's formula: $A=\frac{\sqrt{h w}}{60}$
Current's formula: $A=\frac{4+w}{30}$
The formulas above are used in medicine to estimate the body surface area $A$, in square meters, of infants and children whose weight $w$ ranges between 3 and 30 kilograms and whose height $h$ is measured in centimeters.
Based on Current's formula, what is $w$ in terms of $A$ ?
A) $w=30 \mathrm{~A}-4$
B) $w=30 A+4$
C) $w=30(A-4)$
D) $w=30(A+4)$
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20. (Test $7 / \mathrm{Q} 20 /$ Calculator)
Mosteller's formula: $A=\frac{\sqrt{h w}}{60}$
Current's formula: $A=\frac{4+w}{30}$
The formulas above are used in medicine to estimate the body surface area $A$, in square meters, of infants and children whose weight w ranges between 3 and 30 kilograms and whose height $h$ is measured in centimeters.
If Mosteller's and Current's formulas give the same estimate for $A$, which of the following expressions is equivalent to $\sqrt{h w}$ ?
A) $\frac{4+w}{2}$
B) $\frac{4+w}{1,800}$
C) $2(4+w)$
D) $\frac{(4+w)^{2}}{2}$
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21. (Test8/Q $3 /$ No Calculator)
The formula below is often used by project managers to compute $E$, the estimated time to complete a job, where $O$ is the shortest completion time, $P$ is the longest completion time, and $M$ is the most likely completion time.
$$E=\frac{O+4 M+P}{6}$$
Which of the following correctly gives $P$ in terms of $E, O$, and $M$ ?
A) $P=6 E-O-4 M$
B) $P=-6 E+O+4 M$
C) $P=\frac{O+4 M+E}{6}$
D) $P=\frac{O+4 M-E}{6}$
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22. (Test $8 / \mathrm{Q} 12 /$ No Calculator)
If $\frac{2 a}{b}=\frac{1}{2}$, what is the value of $\frac{b}{a}$ ?
A) $\frac{1}{8}$
B) $\frac{1}{4}$
C) 2
D) 4
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23. (Test8/Q 19/No Calculator)
| A start-up company opened with 8 employees.
The company's growth plan assumes that 2 new employees will be hired each quarter (every
3 months) for the first 5 years. If an equation is written in the form $y=a x+b$ to represent the number of employees, $y$, employed by the company $x$ quarters after the company opened, what is the value of $b$ ?
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24. (Test $8 / Q 23 /$ Calculator)
$$M=1,800(1.02)^{t}$$
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?
A) $M=1,800(1.02)^{\frac{9}{4}}$
B) $M=1,800(1.02)^{4 / 4}$
C) $M=1,800(1.005)^{4 q}$
D) $M=1,800(1.082)^{9}$
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Answer
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