Skills to develop for the first test.

1. There are two important ideas which students need to learn and use in the first part of the course. They will reoccur repeatedly throughout the course. They are

a. the product of two numbers is zero if and only if at least one of them is zero and
b. the square of a number is never negative.
The other skills and concepts you need to do well on the first test are:
2. Define absolute value and use in calculations.
3. Apply hierarchy of operations to solve mathematical problems requiring multiple operations.
4. Perform operations on algebraic fractions.
5. Solve linear equations.
6. Solve several `types' of problems: work, uniform rate, interest, mixture.
7. Solve equations with radicals and fractional exponents.
8. Solve quadratic equations by factoring or by use of the quadratic formula.
9. Solve quadratic equations by completing the square
10. Solve equations involving algebraic fractions.
11. Solve formulas for a designated unknown.
12. Solve applied problems involving linear or quadratic equations.
13. Please note that you are responsible for ideas associated with POWs 1-9. The solutions are available at the website. Click on the POW itself.
14. Solving inequalities by the test interval technique.

1. Solving inequalities by the test interval technique.
2. Use the test interval technique to sketch the garph of a polynomial given its factored form.
3. Find symbolic representation of the composition of two functions, especially when one or both are defined in pieces.
4. Find an equation for a line: a. given two points on the line and b. given one point and the slope.
5. Find an equation for a circle given the center and the radius.
6. Find a line, which is perpendicular to a segment and bisects the segment. Determine when two lines are perpendicular.
7. Given and equation for it, find

a. the center and radius of a circle, and
b. the vertex of a parabola.
8. Use the factor theorem to find the factored form of a polynomial from its standard form.
9. Define the concept of one variable being a function of another.
10. Evaluate linear and quadratic functions.
11. Graph linear and quadratic functions on the rectangular coordinate system.
12. Solve applied problems using linear and quadratic functions.
13. Find the distance between two points.
14. Determine the evenness, oddness, (or neither) of a function.
15. Use a table to understand a function.
16. Determine the range and domain of a function from the graph or the symbolic form.
17. Inverse functions. What does the exponent -1 mean when applied to a function name?
18. Translation among the three models of functions: symbolic (equation model); graph (pictorial model); table (tabular model).
19. Translation between the polynomial form of a quadratic and the standard form. Construct the polynomial form given the vertex and another function value.
20. Using the Intermediate Value Theorem to guarantee a number of x-intercepts of a polynomial.
21. Long division of polynomials.
22. Using linear models to describe real situations.

1. Determine the evenness, oddness, (or neither) of a function.
2. Horizontal and Vertical Asymptotes
3. Use the Factor Theorem to find a zero of a polynomial function.
4. Follow up the use of the Factor Theorem by using long division of the polynomial by the determined factor to `reduce' the degree of the polynomial.
5. Sketch the graph of a rational function.
6. Build mathematical models based on percentages.
7. Sketch the graphs of exponential and logarithmic functions.
8. Solve equations with unknown exponents.
9. Use the change of base formula.
10. Use logarithmic and exponential functions to model situations, like compound interest and exponential decay.

1. Find the regression line for a small set of data points.
2. Understand and use the Binomial Theorem.
3. Construct Pascal's Triangle.
4. Count the number of outcomes for certain elementary experiments.
5. Use counting techniques to compute probabilities of certain elementary events.

The following are prefinal practice tests, each with ten problems from various sections covered during the course.
Practice Test 1.
Practice Test 2.
Practice Test 3.
Practice Test 4.
Practice Test 5.
Practice Test 6.