Free Practice Quiz Question List

14/14 14. Algebraic Modeling and Applications Online Quiz Questions

Use this free practice quiz with 20 questions to review 14/14 14. Algebraic Modeling and Applications, test your knowledge, and prepare for your next test or exam.

20 questions

Choose one

1 point

A service charges a fixed enrollment fee plus the same monthly amount for each month of membership. Which type of model best represents the total cost as a function of the number of months?

A
A quadratic function
B
A linear function
C
An exponential function
D
A reciprocal-rate equation

Choose all

1 point

Which two relationships are essential when modeling a mixture made from two solutions with different concentrations? Select all correct choices.

A
The quantities of the two solutions must add to the total mixture quantity.
B
The percentages can be added without multiplying by the quantities.
C
The active-substance contributions must add to the active substance in the final mixture.
D
Only the more concentrated solution needs to appear in the equation.

True or false

1 point

True or false: If two machines work on the same job at the same time, their individual completion rates should be added to obtain the combined rate.

A
True
B
False

Written response

1 point

A van is 30 miles ahead of a car. The van travels at 60 miles per hour, and the car travels at 75 miles per hour. How long will the car take to catch the van? Enter the time in hours as a number.

Open ended

1 point

An investor has $12,000 to place in two accounts. One earns 4% annually and the other earns 9% annually. The investor wants to earn $900 in one year. Determine how much should be placed in each account, and justify the result with a system of equations or an equivalent calculation.

Choose one

1 point

Which formula models an initial principal $P$ earning annual rate $r$ , compounded $n$ times per year for $t$ years?

A
$A=P+Prt$
B
$A=Pe^{rt}$ for continuous compounding only
C
$A=P\left(1+\frac{r}{n}\right)^{nt}$
D
$A=P(1+rt)$ for any compounding schedule

Choose all

1 point

When interpreting a solution from an algebraic model, which three checks are appropriate? Select all correct choices.

A
Check that the value lies in the realistic domain.
B
Check that the units match what the question asks for.
C
Accept every algebraic root automatically.
D
Substitute the result into the original relationships.

True or false

1 point

True or false: If solving a geometry equation gives both $w=8$ and $w=-8$ for a rectangle’s width, both values are physically meaningful dimensions.

A
True
B
False

Written response

1 point

What mathematical term names the turning point used to find the maximum or minimum of a quadratic function?

Fill in the blank

1 point

A rectangle has width $w$ feet, and its length is 3 feet greater than its width. The length is feet.

Choose one

1 point

An object starts at position $s_0$ and moves with constant velocity $v$ . Which position function represents its location after $t$ units of time?

A
$s(t)=s_0-vt$
B
$s(t)=s_0+vt$
C
$s(t)=vt^2+s_0$
D
$s(t)=s_0+v$

Choose one

1 point

An investment of $2,000 earns 4.5% simple interest for 3 years. Which expression gives the final amount, and what is that amount?

A
$A=2000(1+4.5\cdot3)=29{,}000$
B
$A=2000(1+0.045\cdot3)=2{,}270$
C
$A=2000(0.045)(3)=270$
D
$A=2000(1+0.045)^3\approx2{,}282.73$

Choose one

1 point

A rectangle has perimeter 54 feet, and its length is 3 feet greater than its width. Which dimensions satisfy both conditions?

A
The width is 9 feet and the length is 18 feet.
B
The width is 12 feet and the length is 15 feet.
C
The width is 13.5 feet and the length is 13.5 feet.
D
The width is 15 feet and the length is 12 feet.

Choose one

1 point

A technician mixes $x$ liters of a 20% solution with $20-x$ liters of a 50% solution to make 20 liters of a 32% solution. Which equation models the amount of active ingredient?

A
$0.20x+0.50(20-x)=0.32(20)$
B
$0.20x+0.50x=0.32(20)$
C
$0.20(20-x)+0.50(20-x)=0.32x$
D
$0.20x+0.50(20)=0.32(20-x)$

Choose one

1 point

One machine completes a job in 6 hours and another completes the same job in 10 hours. How long do they take working together?

A
8 hours
B
4.5 hours
C
2.5 hours
D
3.75 hours

Choose one

1 point

A theater sells 120 tickets at $20 each. For every $2 increase in price, 10 fewer tickets are sold. Under this model, which price and number of tickets sold maximize revenue?

A
Price $20; 120 tickets sold
B
Price $22; 110 tickets sold
C
Price $24; 100 tickets sold
D
Price $32; 60 tickets sold

True or false

1 point

True or false: In an algebraic model, every solution of the equation should be accepted, even if it violates a domain restriction from the original situation.

A
True
B
False

Written response

1 point

An investment of $2,000 earns 4.5% simple interest for 3 years. Enter the final amount in dollars as a whole number.

Written response

1 point

A ball is thrown upward from a platform 20 feet above the ground with initial velocity 48 feet per second, modeled by $s(t)=-16t^2+48t+20$ . Enter the positive time when it reaches the ground, rounded to the nearest hundredth of a second.

Fill in the blank

1 point

Two cyclists start 180 miles apart and ride directly toward each other. One travels at 55 miles per hour, and the other travels at 65 miles per hour. Their meeting time in hours is , and the distance traveled by the faster cyclist is miles.