Algebra Mid Exam – 20 Questions. **Answer the questions below. Make sure to show your work and justify all of your answers**

Simplify the trigonometric expression**. Show your work.**

1.

**2.** In , is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth**. Show your work.**

*a* = 3, *c* = 19

**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**

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

**5. **A sound wave is modeled with the equation .

**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**.

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

**Verify the identity. Justify each step.**

8.

9. **Is there any bias in the survey question? Explain.**

What do think would help students pay more attention in class?

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.**

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

**a.** What is the height of the triangle when

**b.** What is the height of the triangle when

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

13. **Verify the identity. ****Justify each step.**

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

and

15. Use a graphing calculator to solve the equation in the interval from . Round to the nearest hundredth.

16. 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.

- 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.

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

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

18.

Use the graph of the sine function shown below.

**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.

**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**.