ALGEBRA II HONORS

Final Exam Study Guide 2011

Chapter 4:  Polynomial and Rational Functions

q     Identify the zeros of a function and their multiplicity.

q     Given a graph of a polynomial, use the zeros and their multiplicity as well as the ends and y-intercept to determine a possible equation in factored form.

q     Find the domain, intercepts, holes, symmetry, and asymptotes (vertical, horizontal, and oblique) of a rational function.  Be able to take a graph of a rational function and determine various possible equations in factored form.

q     Solve polynomial and rational inequalities (also appeared in domain of log).

q     Application word problems for polynomial and rational inequalities.

q     Chapter 4 Review: p. 349−351 # 29a, 31, 35, 39, 43, 45, 51, 63

     Word Problems:  p. 347-348 # 53, 55

Chapter 5:  The Zeros of a Polynomial Function

q     Find all zeros (real and complex) of a polynomial function.  This involves being able to utilize synthetic division, Descartes’ Rule of Sign, listing the possible rational zeros, conjugate pairs theorem, being able to form a factor from given information and use long division to find other factor, ..etc.

q     Add, subtract, multiply and divide complex numbers.

q     Construct a polynomial function in standard form when given the degree, the leading coefficient or y-intercept, and all of the real zeros and some or all of the imaginary zeros.

q     Chapter 5 Review: p. 388-389 # 3, 17−23 odd, 43-49 odd, 53, 55, 65, 69

Chapter 6:  Exponential and Logarithmic Functions

q     Find the inverse of a function.

q     Change exponential expressions to logarithmic expressions and vice versa.

q     Solve exponential equations and logarithmic equations.

q     Use the change of base formula to approximate values or to solve an equation.

q     Use the properties of logarithms to expand or condense a logarithmic equation, to solve logarithmic equations and to use given info to determine other values.

q     Application problems: Continuous/Compound Interest, Newton’s Law of Cooling, Logistic Models, Growth and Decay, Earthquake,  writing exponential models, sound (decibels), finding models by running calculator regressions, …etc.

q      Chapter 6 Review:  p. 470-473 # 3, 5, 17, 23, 25, 31, 43, 47,

51, 53, 55, 57, 73, 77, 78, 83

Chapter 7:  Trigonometric Functions (Selected Topics from 7.1−7.3)

q     Convert from degrees to radians and vice versa.

q     Determine the trig value of acute angles with and without calculator.

q     Identify the trig values of the special angles:  30°, 60°, 45°

q     Apply properties of cofunctions, even/odd, and the fundamental trig    identities.  Complete  a proof using fundamental identities (8.3),

q     Chapter 7 Review:  p. 563-565 # 1, 5, 31, 35&37 (ignore signs/Quadrants)

Chapter 9:  Applications of Trigonometric Functions (Only 9.1)

q     Solve right triangles using SOH CAH TOA

q     Application word problems:  angle of elevation, angle of depression, clinometer types of problems, surveying, finding height, ..etc.

q     Chapter 9 Review:  p. 668-669 # 1−4, 35, 37, 39

Chapter 13:  Sequences; Series; Induction

q     Identify if a sequence or series is arithmetic, geometric, or neither.

q     Write the explicit and recursive rules for geometric/arithmetic sequences and identify a particular term.

q     Use a given explicit or recursive rule to identify terms.

q     Find the sum of an arithmetic, geometric, or infinite geometric series.

q     Application word problems.

q     Prove a statement is true for all counting numbers using mathematical induction.  (Note:  This topic may be covered at the end of the year)

q     Determine a particular term of a binomial expansion.

q     Expand a binomial.

q     Ch 13 Review: p. 940-942 # 1, 7, 17, 27, 33, 37, 41, 43, 51, 55, 57, 61

Chapter 14:  Counting and Probability

q     Solve counting problems using Counting Principle, permutations, and combinations.

q     Drawing Venn Diagrams.

q     Compute probabilities.

q     Chapter 14 Review:  p.  977-978 # 1, 5, 9, 11, 15, 23, 25, 27, 33, 37,

39, 41, 48, 49

STATS UNIT

q     Find the mean, median, mode of a data set.

q     Construct a stem and leaf plot, histogram, circle graph, and box and whisker plot.

q     Use a given a stem and leaf plot, histogram, circle graph, or a box and whisker plot, to answer questions.

q     Determine which visual representation would be best.

q     Give an example of a data set that meets a specified goal. (i.e. one whisker)

q     Identify the quartiles, range, and inter-quartile range of a data set.

SUGGESTIONS ON HOW TO PREPARE:

J     Begin SOON!  Begin SOON!  Find a study buddy and make a study plan.  Don’t wait until the weekend before the exam!

J     Review your own past tests and quizzes.  Cover up the solution and redo the problems.   This is the BEST WAY to prepare!

J     Complete some of the suggested problems from the review sections only as needed. 

J     Once you have completed some practice problems, identify the areas you need to relearn and come in for extra help.

WHAT TO BRING TO THE EXAM:

J     Pencils and your graphing calculator.  Borrowing one of my calculators may not be an option.

J     Your textbook if it has not already been collected.  Students are strongly encouraged to return books early!  Notes and prior tests are the best tools for preparing for the final exam.  If your book is lost or damaged then you need to bring in a check made payable to Dover Sherborn High School to replace your damaged/lost textbook ($121) or for binding repairs ($10). 

J     If you borrowed an additional book for a tutor, you are responsible for returning that as well.

OPPORTUNITIES FOR EXTRA HELP:  Extra help schedule posted on the calendar in classroom.  Be sure to double check the calendar!

J     Mrs. Bachand is often available Mondays, Wednesdays, and Thursdays after school; before school daily; and during A/B block DR. 

J     About two class periods prior to the exam will be devoted towards review.  Get ready for a cumulative fruitbowl game or more whiteboard fun!

FORMAT OF THE TEST: 

J     The test format is similar to the midyear exam.  Approximately 26 multiple-choice questions and about 12 show-all-of-your-algebraic work problems (and some extra credit too!).

Exam Date:  Tuesday 6/21 at 7:45.  Room TBD

Please see me with any questions.  Try not to be overwhelmed… easier said than done but if you break it up, exam prep should be manageable.   Come to the test with the right attitude!  Be sure to get a good night’s sleep and eat a healthy breakfast!  You can do it J

J GOOD LUCK J