Friday's Chapter 15 Test Topics
Here’s a list of topics for Friday’s test. Can you believe it’s our last one?
Precalculus Chapter 15 Test Topics:
Identify the degree, number of real and complex zeros and the leading coefficient of a polynomial from its graph
Sketch the graph of a rational function.
Identify transformations of functions.
Simplify rational functions.
Determine the zeros, the sum of the zeros, the product of the zeros, the sum of the pairwise product of the zeros, and a possible equation from the graph of a cubic function.
Sketch the graph of a given polynomial.
Identify the zeros of the polynomial.
Factor the polynomial.
Prove that a quadratic has no real zeros.
Show that a value is a zero of a polynomial.
Find zeros of a polynomial.
Discuss the implications of nonreal zeros.
Determine an average rate of change.
Provide a formula for an average rate of change.
Determine an instantaneous rate of change.
13 questions on the non-calculator portion, 11 on the calculator portion. That’s it! I’ll be around after school on Thursday afternoon, and in early on Friday.
Mathematicians are like Frenchmen: whatever you say to them, they translate it into their own language, and forthwith it means something entirely different.
- Johann Wolfgang von Goethe
Here’s a problem to consider:
Driving problem: Hezzy Tate drives through an intersection. At time t = 2 sec she crosses the stripe at the beginning of the intersection. She slows down a bit, but does not stop, and then speeds up again. Hezzy is good at mathematics, and she figures that her displacement, , in feet, from the first stripe is given by
Use the results of the synthetic substitution and the quadratic formula to find the other two zeros of d(t).
How do the zeros of confirm the fact that Hezzy does not stop and go back across the stripe?
What is Hezzy’s average velocity from t = 3 to 3.01 sec?
Write the equation for the rational algebraic function equal to Hezzy’s average velocity from 3 sec to t sec.
By appropriate simplification of the fraction in Problem 16, calculate Hezzy’s instantaneous velocity at time t = 3 .