Calculus Exam 2 Review

Velamur Quiz 7

Velamur Quiz 8 *Note: Inflection points are not on Exam 2.

Velamur Quiz 9 *Note: Inflection points are not on Exam 2.


Trigonometry Test Review Solutions

a. \frac{\sqrt{2}}{2}

b. \frac{\sqrt{3}}{3}

c. -1

d. -2

e. -1

2. 45

3. \frac{-13}{12}

4. unknown angle is 43 degrees, unknown sides are 18 feet and 13 feet

5. 39

6. The fire is 182.3 miles from station A and 128.7 miles from station B.

more triangle trigonometry questions

  1. Calculate the area of a regular octagon inscribed in a unit circle.
  2. In quadrilateral ABCD, AB=3, BC=4, CD=5, and DA=6. The length of diagonal BD is 7. Calculate the length of the other diagonal.
  3. From the top of an observation post that is 90 meters high, a ranger sights a campsite at an angle of depression of 10°. Turning in a different direction, the ranger sees another campsite at an angle of depression of 13°. The angle between these two sight lines is 35°. How far apart are the campsites?

Trigonometry Test 2 is on Tuesday!

There are 14 questions, broken down as follows.

3 graphing rational functions

2 simplifying logs

3 log equations

2 exponential equations

1 inverse function

1 graphing exponential function

1 graphing log function

1 write the equation of an exponential function given certain conditions

Here are some good review questions.

  1. Solve for x: \log_5(2x)=\log_5(x+1)-1
  2. Solve for x and express your solution as a ratio of natural logs: 3^{\frac{-x}{2}}=4^{x+1}
  3. Sketch the graph of f(x)=-\ln(x-4)+2
  4. Sketch the graph of f(x)=e^{\frac{-x}{3}+1}
  5. Sketch the graph of f(x)=\frac{(x+2)^2(x+1)}{(x-4)^3(x-6)}
  6. f(x) has a horizontal asymptote at y=5. Where is the asymptote for f^{-1}(x)?
  7. f(x)=-5^x+1. Write the equation for f^{-1}(x).
  8. Solve for x and express your solution as a ratio of natural logs: 3^x+2=10.
  9. Re-write as an exponential equation: \log_{64}4=\frac{1}{3}.
  10. Sketch the graph of f(x)=\frac{6x^2+19x-7}{2x+7}

Also study quizzes 2, 3, and 4.

Critical vocabulary for midterm

Can you define all these terms? Doing so should be excellent practice for the exam, as well as a chance to review topics we’ve focused on over the past six weeks.

Rational function

Exponential function

Logarithmic function





Inverse function

Logarithmic scale

Exponential growth

Exponential decay

Exponential growth rate

Exponential decay rate

Continuously compounded interest