# Final exam

This exam is worth 120 points.  Questions 1 – 10 are each worth 4 points; do not show your work.  Questions 11 – 20 are each worth 6 points; show your work to earn full credit.  Questions 21 and 22 are each worth 10 points; show your work to earn full credit.

Leave answers in exact form unless otherwise directed to approximate the results.  Write all fractions in lowest form.  Round decimals to hundredths unless otherwise directed to round. Write answers using positive exponents except when using scientific notation.  Simplify all radicals and rationalize the denominators.   Applied problems must have the variables identified (Let x =), an equation, and the units (degree, inches, \$, etc.) for full credit.

Write your answers on the answer sheet provided with this exam.  Do not post this exam in the assignment folder.  Post only your Answer Sheet in the assignment folder.

SHORT ANSWER.  Do not show how your work. The following questions are each worth 4 points.

Fill in the blank.

• What is the exact value of the expression: ?

• Find the exact value of .

Select the letter of the one alternative that best completes the statement or answers the question.
For multiple choice questions, check that the answers are all letters (A, B, C, D, or E) and not a value.

• Find the sum of the geometric sequence.

1. A) 5456   B)   1360   C)   272   D)   10,280   E)   none of these

4.)   Find the exact ||v + w|| if v = 5i – 7j and w = 3i + 2j.

1. A)         B)      C)     D)     E) none of these

5.)   Identify this conic: .

1. A) parabola   B)  circle   C)   ellipse   D)   hyperbola   E) none of these

6.)   Write out the first five terms of the sequence.

1. A)    B)    C)     D)
2. E) none of these

7.)   Solve the right triangle using the information given: a = 6 and β = 20°.  Find b, c, and α.  Round answers to tenths.

A)  b = 2.2   B)  b = 3.2  C)  b = 2.2   D)   b = 3.2

c = 7.4         c = 7.4        c = 6.4          c = 6.4

α = 70°        α = 70°        α = 70°         α = 70°

1. E) none of these

8.)   Solve the system:

1. A) x = 9, y = -9  B)  x = 5, y = -5   C)  x = 2, y = 5    D)  x = -5, y = 5     E)  none of these

9.)   A local civic theater has 22 seats in the first row and 21 rows in all.  Each successive row contains 3 additional seats.  How many seats are in the civic theater?

1. A) 1092 seats B)  1070 seats   C)  790 seats    D)  1010 seats    E) none of these

10.)  Using the polar grid function of the Desmos Graphing Calculator or any other graphing calculator, copy and paste the graph of the polar equation:  .  Do not post a hand-drawn graph.
(2 points)

Also include any one point on the graph of the equation that is NOT the origin and is NOT on the x or y axis. Label the point. (2 points)

SHORT ANSWER.  Show your work. The following questions are each worth 6 points.

11.)    Using the Desmos Graphing Calculator or any other graphing calculator, copy and paste the graph of  on the interval (-2π, 2π).  Near the graph, identify the amplitude, period, phase shift, and vertical shift.  Do not post a hand-drawn graph.

12.)    a.  Write the equation in standard form of the conic   .
Post the equation above the graph in part b. (3 points)

1. Using the Desmos Graphing Calculator or any other graphing calculator, copy and paste the

graph of equation in part a.   Use appropriate domain and range to include the entire graph of                the conic.  Do not post a hand-drawn graph.  (3 points)

13.)    Find the sum of this sequence:  1 + 3 + 5 + … + 883.

14.)    Find the center and foci (exact values) of  .

15.)    An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving.  A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

16.)    Compute the future value of the annuity with payments of \$200, the interest rate is 2.0%, and the term is 35 years.  Assume the payment is made monthly, the interest rate given is the annual rate, and the interest is compounded monthly.  (Just show equation with given values and final calculation.)

17.)    Prove: .

18.)   If  and , then find the exact value of sin θ.

19.)   Find the approximate value of the angle between  and .

20.)   The angle of elevation of the sun is 35.1° at the instant the shadow cast by a monument is 789 feet long.  Use this information to calculate the height of the monument.

LONG ANSWER.  Show your work. The following questions are each worth 10 points.

21.)  Prove: .

22.)  Solve the system of equations by using Gauss-Jordan elimination.

(reduced row echelon form, not triangular form)