Free Practice Quiz Question List

12 Integrated Applications Online Quiz Questions

Use this free practice quiz with 20 questions to review 12 Integrated Applications, test your knowledge, and prepare for your next test or exam.

20 questions

True or false

1 point

True or false: A function assigns exactly one output to each input.

A
True
B
False

Choose one

1 point

A drone's path is modeled by $(y=-0.02(x-30)^2+18)$ . Which interpretation of this model is correct?

A
The maximum height is 30 meters at $(x=18)$ .
B
The minimum height is 18 meters at $(x=30)$ .
C
The maximum height is 18 meters at $(x=30)$ .
D
The minimum height is 30 meters at $(x=18)$ .

Written response

1 point

What is the exact period, in radians, of the function $(y=3\\cos(4x-1)+2)$ ?

Choose all

1 point

Select all situations that are appropriately modeled by an exponential function.

A
A savings account increases by 4% each year.
B
A tank is filled by 3 liters every minute.
C
A medication amount decreases by 12% per hour.
D
A taxi fare increases by a fixed amount for every kilometer.

Fill in the blank

1 point

In the linear model $(f(x)=mx+b)$ , $m$ represents the , and $b$ represents the .

Choose one

1 point

A battery starts with 120 units and retains 92% of its charge after each flight. Approximately how many units remain after 5 flights?

A
Approximately 52.3 units
B
Approximately 78.7 units
C
Approximately 79.1 units
D
Approximately 92.0 units

True or false

1 point

True or false: The argument of every real logarithm must be positive.

A
True
B
False

Written response

1 point

A point has coordinates $((20,16))$ . What is its angle of elevation from the origin, in degrees, rounded to the nearest tenth?

Choose all

1 point

Select all practices that help avoid common modeling errors.

A
Use degree mode when an angle is required in degrees.
B
Reverse an inequality when dividing by a negative number.
C
Treat a sequence as continuous because its formula resembles an exponential function.
D
Check that the model's domain is appropriate for the situation.

Fill in the blank

1 point

For a non-right triangle, the equation $c^2=a^2+b^2-2ab\cos C$ is the Law of , where $C$ is the between sides $a$ and $b$ .

Choose one

1 point

A battery is modeled by $B_n=120(0.92)^n$ . After how many whole-number flights does its charge first fall below 50 units?

A
10 flights
B
11 flights
C
12 flights
D
14 flights

Open ended

1 point

Explain the difference between a geometric sequence and an exponential function. Address both their domains and how they model change.

Choose one

1 point

What is the midpoint of the segment joining $((2,-1))$ and $((8,5))$ ?

A
$((3,2))$
B
$((5,3))$
C
$((5,2))$
D
$((10,4))$

Choose one

1 point

Which type of model is most appropriate when a quantity changes by approximately a constant amount per unit of input?

A
A quantity changes by a constant percentage.
B
A quantity changes by approximately a constant amount.
C
A quantity repeats in regular cycles.
D
A quantity has a maximum or minimum and a parabolic shape.

Choose one

1 point

Which statement correctly describes a function?

A
Each input must have at least two outputs.
B
Every output must have exactly one input.
C
Each input must have exactly one output.
D
The inputs and outputs must be equal.

True or false

1 point

True or false: A sequence is a discrete model because its domain is usually the positive integers, whereas a function may be defined over a continuous interval.

A
True
B
False

Choose one

1 point

A data set shows that each output is approximately 1.08 times the preceding output. Which model is most justified by this pattern?

A
A linear model, because the outputs have approximately constant differences.
B
An exponential model, because the outputs have approximately constant ratios.
C
A sinusoidal model, because every data set is periodic.
D
A quadratic model, because every data set has a vertex.

Choose one

1 point

A water level is modeled by $y=-4\sin(3t)+2$ , where $y$ is measured in metres. What is the range of possible water levels predicted by this model?

A
$[-4,4]$
B
$[0,4]$
C
$[-2,6]$
D
$[2,6]$

Written response

1 point

In a triangle, side $a=10$ units is opposite angle $A=30^\circ$ , and side $b$ is opposite angle $B=45^\circ$ . Using the Law of Sines, what is $b$ , to the nearest tenth of a unit?

Written response

1 point

A staircase design uses an arithmetic sequence of riser heights. The first height is $7$ cm, and each successive height increases by $4$ cm. What is the height of the twelfth riser, in centimetres?