Simplify the sum state any restrictions on the variables

Algebra 2 Final Exam Name/Student Number:_________

Answer the questions below. Make sure to show your work and justify all of your answers

Simplify the trigonometric expression. Show your work.

1.

image28.jpg

2. In image2.jpg, image3.jpgis a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth. Show your work.

3. Please show your work to find the mean and standard deviation of the data. Round to the nearest tenth.

20, 16, 18, 14, 9, 20, 16

Sum of last column:

Standard Deviation:

4. What are the points of discontinuity? Are they all removable? Please show your work.

image4.png

5. A sound wave is modeled with the equation image5.png.

a. Find the period. Explain your method.

b. Find the amplitude. Explain your method.

c. What is the equation of the midline? What does it represent?

6. Paula spots a glider located at an angle of elevation of 42°. The distance between the glider and Paula is 3280 feet. To the nearest foot, what is the height of the glider h from the ground? Show your work.

image6.emf

Paula

Glider

42

o

3280fth

7. What is the product in simplest form? State any restrictions on the variable. Please show your work.

image7.emf

y

2

y3



y

2

y6

y

2

y

Verify the identity. Justify each step.

image1.jpg 8.

9. Verify the identity .

image26.jpg

10. Find the values of the 30th and 90th percentiles of the data. Please show your work.

129, 113, 200, 100, 105, 132, 100, 176, 146, 152

11. What is the quotient in simplified form? State any restrictions on the variable. Show Work.image8.emf

a2

a5



a1

a

2

8a15

12. Vance is designing a garden in the shape of an isosceles triangle. The base of the garden is 36 feet long. The function image9.png models the height of the triangular garden.

image10.emf

36feet

not drawn to scale

y



a. What is the height of the triangle when image11.png y = 18 tan 45 = 18 feet

b. What is the height of the triangle when image12.png y = 18 tan 55 = 25.7 feet

c. Vance is considering using either image13.png or image14.png for his garden. Compare the areas of the two possible gardens. Explain how you found the areas.

The area of the garden with the 18 foot height is smaller by almost 140 square feet than the garden with the height of 25.7 feet. I found the area by using the triangle area formula: Area is half of the base times the height.

13. Verify the identity. Justify each step.

image15.png

14. Compare the graphs of the inverse variations. Please provide at least 3 comparisons

/ image16.png and image17.png

15. Use a graphing calculator to solve the equation image18.jpgin the interval from image19.jpg. Round to the nearest hundredth.

image27.jpg16. The equation models the height h in centimeters after t seconds of a weight attached to the end of a spring that has been stretched and then released.

a. Solve the equation for t.

b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.

c. Find the times at which the weight is at a height of 1 cm, of 3 cm, and of 5 cm below the rest position for the second time. Round your answers to the nearest hundredth.

17.

Consider the graph of the cosine function shown below.

image20.emf



2



O



2

4

–2

–4

y

a. Find the period and amplitude of the cosine function.

b. At what values of image21.png for image22.png do the maximum value(s), minimum values(s), and zeros occur?

18.

Use the graph of the sine function image23.jpg shown below. image24.jpg a. How many cycles occur in the graph? b. Find the period of the graph. c. Find the amplitude of the graph.

19. Verify the Pythagorean Identity.

image25.png

20.

Howard is flying a kite and wants to find its angle of elevation. The string on the kite is 32 meters long and the kite is level with the top of a building that he knows is 28 meters high.

To the nearest tenth of a degree, find the angle of elevation. Show your work.