Quarter 4 Benchmark Review

Quarter 4 Benchmark Review

​Treat this like a practice test.

Labelling

The unit circle is shown. Some angles are labeled. Drag tiles to label the remaining angles. $$\frac{3\pi}{4}$$

Drag labels to their correct position on the image

Multiple Choice

What is the radian measure of $$\angle A$$ ?

$$\theta=\frac{arc\ length}{radius}$$

• $$5\pi$$

• $$\frac{\pi}{5}$$

• $$\frac{5}{\pi}$$

• $$\frac{\pi}{10}$$

Match

Each of the given equations can be represented by one of the given graphs. Drag times to match each equation with its graph.

• $$y=3\cos\left(\frac{\pi}{2}x\right)+1$$

• $$y=2\sin\left(\frac{\pi}{3}x\right)-2$$

• $$y=-3\cos\left(\frac{\pi}{2}x\right)+1$$

• $$y=-2\sin\left(\frac{3\pi}{3}x\right)-2$$

Multiple Select

The graphs show two bank accounts over the course of 24 years. Use the graph to select all statements that are true.

• The bank accounts increase by the same amount each year.

• The value of the bank accounts are ever increasing.

• The value of the bank account is the same somewhere around x=16.

• The bank accounts values are the same somewhere between x=17 and x=19.

• After some time, the bank accounts stop increasing.

Multiple Choice

The exponential growth model $$y=Ae^{rt}$$ can be used to calculate the future population of a city. In this model, A is the current population, r is the rate of growth, and y is the future population for a specific time, t, in years.

A certain city's population has a growth rate of r=0.06. Approximately how long will it take the city's population to grow from 350,000 to 700,000?

• 11.5 years

• 32 years

• 0 years

• 5 years

Multiple Choice

$$\tan\theta=1$$ and $$\theta$$ is in Quadrant II. What is $$\theta$$ ?

• $$\frac{\pi}{4}$$

• $$\frac{3\pi}{4}$$

• $$\frac{5\pi}{4}$$

• $$\frac{7\pi}{4}$$

Dropdown

Use y=log(x) as a parent function. To graph y=log(x-4)+7, the parent function should be translated vertically ​

Select answer

(up or down) by ​ ​

Select answer

units. The vertical asymptote should be shifted horizontally to the ​

Select answer

(left or right) by ​

Select answer

units.

Multiple Choice

The graph of a logarithmic function in the form $$y=b+a\log\left(x\right)$$ is shown. Which of the following equations does this graph represent?

• $$y=2-5\log\left(x\right)$$

• $$y=2+5\log\left(x\right)$$

• $$y=5-2\log\left(x\right)$$

• $$y=-2+5\log\left(x\right)$$

Multiple Select

Liz is buying a new car. Her bank offers her a loan of $10,000 with a 5.25% annual interest rate compounded quarterly, or every 3 months. Which of the following equations could model the bank's offer? Select all that apply.

• $$A=10000\left(1.0175\right)^{4t}$$

• $$A=10000\left(1+\frac{0.0525}{4}\right)^{4t}$$

• $$A=10000\left(1.013125\right)^{4t}$$

• $$A=10000\left(1+\frac{0.0525}{3}\right)^{3t}$$

Multiple Select

Newton's Law of Cooling can be used to describe how the temperature of an object changes in relation to the surrounding temperature. For example, a cup of tea will eventually cool to almost room temperature. The function that models this behavior is the exponential function:

$$h\left(x\right)=t_r+t_d\cdot e^{kx}$$

$$t_r$$ is the room temperature , $$t_d$$ is the difference between the initial temperature and the room temperature, $$k$$ is the constant of proportionality, $$x$$ is time.

Select true statements based on the equations below.

$$h\left(x\right)=55+105e^{-0.03x}$$

$$k\left(x\right)=60+105e^{-0.03x}$$

• The room temperature for the model h(x) is 5 degrees colder than the model k(x).

• Both models represent exponential growth.

• Both models represent exponential decay

• The initial temperature of the two cups is the same.

Multiple Choice

The graph of a logarithmic function of a base 3 has a vertical stretch of 4 and a vertical asymptote at $$x=-6$$ . Which of the following equations does the graph represent?

• $$y=4\log_3\left(x-6\right)$$

• $$y=3\log_4\left(x+6\right)$$

• $$y=4\log_3\left(x+6\right)$$

• $$y=-6\log_3\left(x+3\right)$$

• $$y=-4\log_3\left(x+6\right)$$

Multiple Choice

Which of the following is the graph of $$f\left(x\right)=-3\left(2\right)^x+4$$