Chapter ?: Circles, Parabolas, Ellipses and Hyperbalas i. If the equation of a parabola is written in standard form and p is negative and the directrix is a horizontal line, then what can we conclude about its graph? 2. What is the etfect on the graph of a parabola if its equation in standard form has increasing values of p? 3. What special case of the ellipse do we have when the major and minor axis are of the same length? For this case, what would be true about the foci of that ellipse? 4. Where must the center of hyperbola be relative to its foci? Chapter 8: Systems of Equations 1. Explain whether a system of two nonlinear equations can have exactly two solutions. What about exactly three? If not, explain why not. If so, give an example of such a system, in graph form, and explain why your choice gives two or three answers. 2. You are unsure if you correctly decomposed the partial fraction correctly. Explain how you could double-check your answer. 3. Can we add any two matrices together? If so, explain why; if not, explain why not and give an example of two matrices that cannot be added together. 4. lCan any two matrices of the same size be multiplied? If so, explain why, and if not, explain why not and give an example of two matrices of the same size that cannot be multiplied together. 5. lCan a matrix whose entry is O on the diagonal be solved? Explain why or why not. What would you do to remedy the situation? Chapter 9: Sequences and Series 1. Describe three ways that a sequence can be defined. 2. What happens to the terms an of a sequence when there is a negative factor in the formula that is raised to a power that includes n? 8. What are the main differences between using a recursive formula and using an explicit formula to describe an arithmetic sequence? 4. What is the difference between an arithmetic sequence and a geometric sequence? 5. What is the Binomial Theorem and what is its use? When is it an advantage to use the Binomial Theorem