1. (Test1/Q 6/No Calculator)
$$
h=3 a+28.6
$$
A pediatrician uses the model above to estimate the height $h$ of a boy, in inches, in terms of the boy's age $a$, in years, between the ages of 2 and 5 . Based on the model, what is the estimated increase, in inches, of a boy's height each year?
A) 3
B) $5.7$
C) $9.5$
D) $14.3$
|
|
2. (Test $2 / Q 35 /$ Calculator)
| $$
a=18 t+15
$$
Jane made an initial deposit to a savings account. Each week thereafter she deposited a fixed amount to the account. The equation above models the amount $a$, in dollars, that Jane has deposited after $t$ weekly deposits. According to the model, how many dollars was Jane's initial deposit? (Disregard the $\$$ sign when gridding your answer.)
|
3. (Test2/Q 37/Calculator)
| A botanist is cultivating a rare species of plant in a controlled environment and currently has 3000 of these plants. The population of this species that the botanist expects to grow next year, $N_{\text {next year }}$, can be estimated from the number of plants this year, $N_{\text {this year }}$, by the equation below.
$$
N_{\text {next year }}=N_{\text {this year }}+0.2\left(N_{\text {this year }}\right)\left(1-\frac{N_{\text {this year }}}{K}\right)
$$
The constant $K$ in this formula is the number of plants the environment is able to support.
According to the formula, what will be the number of plants two years from now if $K=4000$ ? (Round your answer to the nearest whole number.)
|
4. (Test $2 / \mathrm{Q} 38 /$ Calculator)
| A botanist is cultivating a rare species of plant in a controlled environment and currently has 3000 of these plants. The population of this species that the botanist expects to grow next year, $N_{\text {next year }}$, can be estimated from the number of plants this year, $N_{\text {this year }}$, by the equation below.
$$
N_{\text {next year }}=N_{\text {this year }}+0.2\left(N_{\text {this year }}\right)\left(1-\frac{N_{\text {this year }}}{K}\right)
$$
The constant $K$ in this formula is the number of plants the environment is able to support.
The botanist would like to increase the number of plants that the environment can support so that the population of the species will increase more rapidly. If the botanist's goal is that the number of plants will increase from 3000 this year to 3360 next year, how many plants must the modified environment support?
|
5. (Test5/Q 7/Calculator)
The Downtown Business Association (DBA) in a certain city plans to increase its membership by a total of $n$ businesses per year. There were $b$ businesses in the DBA at the beginning of this year. Which function best models the total number of businesses, $y$, the DBA plans to have as members $x$ years from now?
A) $y=n x+b$
B) $y=n x-b$
C) $y=b(n)^{x}$
D) $y=n(b)^{x}$
|
|
6. (Test7/Q $17 /$ Calculator)
$$
y=19.99+1.50 x
$$
The equation above models the total cost $y$, in dollars, that a company charges a customer to rent a truck for one day and drive the truck $x$ miles. The total cost consists of a flat fee plus a charge per mile driven. When the equation is graphed in the
$x y$-plane, what does the $y$-intercept of the graph represent in terms of the model?
A) A flat fee of $\$ 19.99$
B) A charge per mile of $\$ 1.50$
C) A charge per mile of $\$ 19.99$
D) Total daily charges of $\$ 21,49$
|
|
7. (Test $7 / Q 24 /$ Calculator)
$$
h(t)=-16 t^{2}+110 t+72
$$
The function above models the height $h$, in feet, of an object above ground $t$ seconds after being launched straight up in the air. What does the number 72 represent in the function?
A) The initial height, in feet, of the object
B) The maximum height, in feet, of the object
C) The initial speed, in feet per second, of the object
D) The maximum speed, in feet per second, of the object
|
|
8. (Test8/Q 13/No Calculator)
Oil and gas production in a certain area dropped from 4 million barrels in 2000 to $1.9$ million barrels in 2013. Assuming that the oil and gas production decreased at a constant rate, which of the following linear functions $f$ best models the production, in millions of barrels, $t$ years after the year 2000 ?
A) $f(t)=\frac{21}{130} t+4$
B) $f(t)=\frac{19}{130} t+4$
C) $f(t)=-\frac{21}{130} t+4$
D) $f(t)=-\frac{19}{130} t+4$
|
|
9. (Test $8 / Q 25 /$ Calculator)
$$\text{Population of Greenleaf, Idaho}\\
\begin{array}{|c|c|}
\hline \text{Year }& \text{Population} \\
\hline 2000 & 862 \\
\hline 2010 & 846 \\
\hline
\end{array}$$
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?
A) $P(t)=862-1.6 t$
B) $P(t)=862-16 t$
C) $P(t)=862+16(t-2,000)$
D) $P(t)=862-1.6(t-2,000)$
|
|
10. (Test6/Q 15/Calculator)
$$\begin{array}{|c|c|c|c|c|c|}
\hline x & 1 & 2 & 3 & 4 & 5 \\
\hline y & \frac{11}{4} & \frac{25}{4} & \frac{39}{4} & \frac{53}{4} & \frac{67}{4} \\
\hline
\end{array}$$
Which of the following equations relates $y$ to $x$ for the values in the table above?
A) $y=\frac{1}{2} \cdot\left(\frac{5}{2}\right)^{x}$
B) $y=2 \cdot\left(\frac{3}{4}\right)^{x}$
C) $y=\frac{3}{4} x+2$
D) $y=\frac{7}{2} x-\frac{3}{4}$
|
|
11. (Test7/Q 25/Calculator)
$$\begin{array}{l}
\text{Energy per Gram of Typical Macronutrients }\\
\begin{array}{|l|c|c|}
\hline \text{Macronutrient} & \text{Food calories }& \text{ Kilojoules }\\
\hline \text{Protein} & 4.0 & 16.7 \\
\hline \text{Fat }& 9.0 & 37.7 \\
\hline \text{Carbohydrate }& 4.0 & 16.7 \\
\hline
\end{array}
\end{array}$$
The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food.
If $x$ food calories is equivalent to $k$ kilojoules, of the following, which best represents the relationship between $x$ and $k$ ?
A) $k=0.24 x$
B) $k=4.2 x$
C) $x=4.2 k$
D) $x k=4.2$
|
|
12. (Test7/Q $26 /$ Calculator)
$$\text{Energy per Gram of Typical Macronutrients}$$
$$\begin{array}{|l|c|c|}
\hline \text{Macronutrient} & \text{Food calories} & \text{Kilojoules }\\
\hline \text{Protein} & 4.0 & 16.7 \\
\hline \text{Fat} & 9.0 & 37.7 \\
\hline \text{Carbohydrate} & 4.0 & 16.7 \\
\hline
\end{array}$$
The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food.
If the 180 food calories in a granola bar come entirely from $p$ grams of protein, $f$ grams of fat, and $c$ grams of carbohydrate, which of the following expresses $f$ in terms of $p$ and $c$ ?
A) $f=20+\frac{4}{9}(p+c)$
B) $f=20-\frac{4}{9}(p+c)$
C) $f=20-\frac{4}{9}(p-c)$
D) $f=20+\frac{9}{4}(p+c)$
|
|
13. (Test $8 / Q 2 /$ No Calculator)
The graph above shows the distance traveled $d$, in feet, by a product on a conveyor belt $m$ minutes after the product is placed on the belt. Which of the following equations correctly relates $d$ and $m$ ?
A) $d=2 m$
B) $d=\frac{1}{2} m$
C) $d=m+2$
D) $d=2 m+2$
|
|
14. (Test8/Q 5/No Calculator)
The width of a rectangular dance floor is $w$ feet. The length of the floor is 6 feet longer than its width.
Which of the following expresses the perimeter, in feet, of the dance floor in terms of $w$ ?
A) $2 w+6$
B) $4 w+12$
C) $w^{2}+6$
D) $w^{2}+6 w$
|
|
15. (Test1/Q $17 /$ No Calculator)
| (Cest1/Q $17 /$
A summer camp counselor wants to find a length, $x$, in feet, across a lake as represented in the sketch above. The lengths represented by $A B, E B, B D$, and $C D$ on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively.
Segments $A C$ and $D E$ intersect at $B$, and $\angle A E B$ and $\angle C D B$ have the same measure. What is the value of $x$ ?
|
16. (Test2/Q 18/No Calculator)
| In the figure above, $\overline{A E} \| \overline{C D}$ and segment $A D$ intersects segment $C E$ at $B$. What is the length of segment $C E$ ?
|
17. (Test3/Q 20/No Calculator)
| B $20 /$ No
In triangle $A B C$, the measure of $\angle B$ is $90^{\circ}$,
$B C=16$, and $A C=20$. Triangle $D E F$ is similar to triangle $A B C$, where vertices $D, E$, and $F$ correspond to vertices $A, B$, and $C$, respectively, and each side of triangle $D E F$ is $\frac{1}{3}$ the length of the corresponding side of triangle $A B C$. What is the value of $\sin F$ ?
|
18. (Test4/Q 16/No Calculator)
| Jim has a triangular shelf system that attaches to his showerhead. The total height of the system is 18 inches, and there are three parallel shelves as shown above. What is the maximum height, in inches, of a shampoo bottle that can stand upright on the middle shelf?
|
19. (Test5/Q 32/Calculator)
| The painting The Starry Night by Vincent van Gogh is rectangular in shape with height 29 inches and width $36.25$ inches. If a reproduction was made where each dimension is $\frac{1}{3}$ the corresponding original dimension, what is the height of the reproduction, in inches?
|
20. (Test $6 / \mathrm{Q} 18 /$ No Calculator)
| In the figure above, $\overline{B D}$ is parallel to $\overline{A E}$. What is the length of $\overline{C E}$ ?
|
21. (Test7/Q $36 /$ Calculator)
| In the figure above, $\tan B=\frac{3}{4} .$ If $B C=15$ and $D A=4$, what is the length of $\overline{D E}$ ?
|
22. (Test1/Q $19 /$ No Calculator)
| In a right triangle, one angle measures $x^{\circ}$, where $\sin x^{\circ}=\frac{4}{5} .$ What is $\cos \left(90^{\circ}-x^{\circ}\right) ?$
|
23. (Test2/Q 19/No Calculator)
| In the $x y$-plane above, $O$ is the center of the circle, and the measure of $\angle A O B$ is $\frac{\pi}{a}$ radians. What is the value of $a$ ?
|
24. (Test4/Q $17 /$ No Calculator)
| In the triangle above, the sine of $x^{0}$ is $0.6$. What is the cosine of $y^{\circ}$ ?
|
25. (Test6/Q $16 /$ Calculator)
Triangles $A B C$ and $D E F$ are shown above. Which of the following is equal to the ratio $\frac{B C}{A B}$ ?
A) $\frac{D E}{D F}$
B) $\frac{D F}{D E}$
C) $\frac{D F}{E F}$
D) $\frac{E F}{D E}$
|
|
26. (Test8/Q 36/Calculator)
| In triangle RST above, point $W$ (not shown) lies on $\overline{R T}$. What is the value of $\cos (\angle R S W)-\sin (\angle W S T) ?$
|
27. (Test5/Q 3/Calculator)
To make a bakery's signature chocolate muffins, a baker needs $2.5$ ounces of chocolate for each muffin. How many pounds of chocolate are needed to make 48 signature chocolate muffins?
(1 pound $=16$ ounces)
A) $7.5$
B) 10
C) $50.5$
D) 120
|
|
28. (Test5/Q 9/Calculator)
In the 1908 Olympic Games, the Olympic marathon was lengthened from 40 kilometers to approximately 42 kilometers. Of the following, which is closest to the increase in the distance of the Olympic marathon, in miles? ( 1 mile is approximately $1.6$ kilometers.)
A) $1.00$
B) $1.25$
C) $1.50$
D) $1.75$
|
|
29. (Test7/Q 18/No Calculator)
| The number of radians in a 720 -degree angle can be written as $a \pi$, where $a$ is a constant. What is the value of $a$ ?
|
30. (Test7/Q 3/Calculator)
A certain package requires 3 centimeters of tape to be closed securely. What is the maximum number of packages of this type that can be secured with 6 meters of tape? ( 1 meter $=100 \mathrm{~cm}$ )
A) 100
B) 150
C) 200
D) 300
|
|
31. (Test $8 / Q 9 /$ Calculator)
The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces.
What is the value of $k$, in centimeters?
A) $2.52$
B) $7.67$
C) $7.79$
D) $10.11$
|
|
32. (Test8/Q 10/Calculator)
| The glass pictured above can hold a maximum volume 473 cubic centimeters, which is approximately 16 fluid ounces.
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?
|
33. (Test8/Q 11/Calculator)
The glass pictured above can hold a maximum volume 473 cubic centimeters, which is approximately 16 fluid ounces.
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)
|
Answer
Post a Comment