Math 116 - Chapter 4 & 7 Study Guide

No Calculators are allowed on this exam.

  1. Find the inverse of the function.
  2. Rewrite the exponential expression in logarithmic form.
  3. Rewrite the logarithmic expression in exponential form.
  4. Find the greatest integer of a logarithmic expression. In English, that means to give the integer part (usually first digit) of a logarithm. For example, the log5.4 412 is somewhere between 3 and 4 because 5.43<412<5.44. The greatest integer of any value between 3 and 4 is 3, so the answer is 3. The greatest integer function is symbolized using the double bracket and is a "round down" function.
  5. Rewrite a logarithm using the change of base formula. Do not simplify or evaluate, just rewrite it.
  6. Write the expression as a sum, difference, and/or constant multiple of logarithms and simplify (if possible). Three parts.
  7. Write the expression as the logarithm of a single quantity. Three parts.
  8. Solve the equations. Give an exact answer. The problems have been designed so the answers can be found without a calculator. Pay attention to domain. Four parts.
  9. Simplify the expressions. Thirteen parts.
  10. Identify the conic section or degenerate case. Choices are no graph, point, line, parallel lines, intersecting lines, parabola, circle, ellipse, and hyperbola. Nine parts.
  11. Given a parametrically defined curve, complete a table of values and sketch the curve, indicating the direction of increasing t. Eliminate the parameter and solve for y. Be sure to include any restrictions that are necessary.
  12. Find the equation of the parabola with vertex at the origin.
  13. Find the equation of the ellipse with center at the origin.
  14. Find the equation of the hyperbola with center at the origin.
  15. Find the vertex, focus, and directrix of the parabola. Do not graph.
  16. Find the center, foci, and vertices of the ellipse. Do not graph.
  17. Find the center, foci, and vertices of the hyperbola. Also give the equations of the asymptotes. Do not graph.
  18. Identify the conic section and write the equation based on the graph. If a parabola, give the focal length; if an ellipse, give the center; if a hyperbola, give the center.
  19. Same instructions as #18.
  20. Same instructions as #18.
  21. Complete the square to put a conic into standard form. Identify the type of conic, coordinates of the center (vertex for a parabola), and the change in x and change in y (for a hyperbola or ellipse) or focal length (for a parabola).


Points per problem

# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Take
Pts 2 2 2 2 2 6 6 12 13 9 3 3 3 3 3 3 3 3 3 3 4 35 125