# Study Guide - Chapters 9 & 10

## Math 098

- Find the midpoint between two points. Look at 9 - 13 in section 9.1*.
- Find the distance between two points. Look at 1 - 7 in section 9.1*.
- Tell how the graph of each function differs from the graph of y=x^2. For example, y=x^2-3 is
down three units, y=(x-3)^2 is right three units, and y=1/2 x^2 opens half as quickly. Three
parts.
- Find the vertex of a parabola by completing the square. Look at 19 - 23 in section 9.2*.
- Write the equation of the circle satistfying the given conditions. Look at 1 - 9 in section 9.3*.
- Write the equation of the ellipse satisfying the given conditions. Look at 11 - 15 in section 9.3.
- Write the equation of the hyperbola satisfying the given conditions. Look at 7 - 11 in section
9.4*.
- Identify the type of conic section defined by each equation. Look at 21 - 31 in section 9.4.
Possible choices are line, parabola, circle, ellipse, and hyperboa. Five parts.
- Write the inverse of the function using functional notation. Look at 23 - 29 in section 10.1*.
- Solve exponential and logarithmic equations without the use of a calculator (in other words,
give exact answers). There are six parts, corresponding to the six types of equations that were
given in class on Thursday, Nov 30.
- Rewrite as the sum, difference, and/or multiples of simple logarithms. Look at problems 1 - 15
in section 10.4. Two parts.
- Rewrite as a single logarithm. Look at problems 17 - 25 in section 10.4. Two parts.
- Solve exponential and logarithmic equations with the use of a calculator to four decimal places.
There are six parts, corresponding to the six types of equations that were given in class on
Tuesday, April 30. There are two additional problems. Look at problems 23 - 39 and 41 - 49
in section 10.5* for those.
- Work a pH problem. Look at problems 29 - 32 in section 10.6.
- Sketch the graph of a parabola, circle, ellipse, hyperbola, exponential function, and logarithmic
function (not necessarily in that order).

Starred problems are directly from the odd problems in the section indicated.