Algebra II Honors

Midyear Exam 2010-2011 Study Guide

Chapter R: Review

¨     Classifying Numbers (Rational, Real, ..etc) (R.1)

¨     Evaluating an expression using order of operations (PEMDAS)  (R.1)

¨     Recognizing the following algebraic properties:  associative, commutative, identity, inverse, and distributive.  (R.1)

¨     Determining Domain when given an equation  (R.2 also in CH3)

¨     Applying basic geometric formulas (R.3)

¨     Simplifying an expression using Laws of Exponents and Rational Exponents (R.4&R.9)

¨     Classifying polynomials of one variable based on the number of terms and the degree (R.5)

¨     Adding, Subtracting, Multiplying, and Dividing (long) Polynomials  (R.5)

¨     Factoring Polynomials (multiple techniques such as grouping, ..etc; the sum/difference of cubes formula will be provided if needed)  (R.6)

¨     Simplifying (factoring and reducing), Adding/Subtracting (involves getting common denominator), Multiplying/Dividing Rational Expressions (R.7)

¨     Simplifying Radical Expressions (i.e. smush into one radical then pull out buddies if square root, triples if cube root…etc)  (R.8)

¨     Expressing as a single quotient. (R.9)

¨     Factoring an expression that involves rational powers.  (R.9)

¯     Chapter R Review,  p. 80-82:  # 7, 11, 23, 29, 33, 39, 43, 51, 53, 59, 67, 71, 75, 79

Chapter 1: Equations and Inequalities

¨     Solving Linear Equations (1.1)

¨     Setting up and Solving Applied Problems (mixture, working together, rate…etc.) (1.2)

¨     Solving Quadratic Equations and Equations Quadratic in Form (u-sub) by factoring, completing the square, and quadratic formula (1.3, 1.4)

¨     Using the discriminant to determine the number of real solutions (1.3)

¨     Solving Radical Equations (1.4)

¨     Solving Inequalities (1.5)

¨     Solving Equations and Inequalities that Involve Absolute Value (1.6)

¯     Chapter 1 Review, p. 141-143 # 3, 5, 13, 23, 41, 45, 53, 57, 61, 65, 69, 73

Chapter 2: Graphs

¨     Utilize the Distance and Midpoint Formulas (2.1)

¨     Graphing Linear Functions either via intercepts or slope-intercept method (2.2)

¨     Determining symmetry via graph or equation (2.2)

¨     Finding equations of lines given point and slope, or two points or a graph, or the graph, or facts about being parallel/perpendicular to other lines …etc. (2.3/2.4)

¨     Finding the equation for a circle given information or analyzing the equation of the circle (given in general or in standard) to identify the center and radius. (2.4)

¨     Finding the Line of Best Fit using Graphing Calculator and making predictions (2.5)

¨     Analyzing the goodness of a line of best fit using correlation coefficient (2.5)

¨     Variation Problems and Word Problems: Direct, Inverse, Joint, and Combined (2.6)

¯     Chapter 2 Review, p. 200-201 # 3, 5, 9, 11, 14, 15, 17, 19, 25, 27, 29, 31, 34, 41

Chapter 3: Functions and Their Graphs

¨     Determining if a relation is a function given graph or input/output boxes (3.1)

¨     Properties of Functions: Max, Min, Increasing, Decreasing, Even, Odd, Neither, Domain, Range (from graph only), Intercepts…etc. (3.2)

¨     Find the Average Rate of Change of a Function (includes the difference quotient, between two specific x values, and between x=# and some x) (3.2)

¨     Characteristics of the Library of Functions (3.3)

¨     Graph and/or Construct the Equation of Piecewise-defined Functions (3.3)

¨     Finding the intercepts of a Piecewise function without graphing (3.3)

¨     Graph a function or describe the graph using transformation techniques (3.4)

¨     Adding, Subtracting, Multiplying, Dividing Functions (3.5)

¨     Composing Functions and Decomposing Functions (3.5)

¨     Describe the domain of a composition of Functions (3.5)

¨     Constructing Functions-Word Problems (3.6)

¯     Chapter 3 Review, p. 276-277 # 5, 6, 9, 15, 19, 23, 27, 31, 39, 45, 51, 57

Chapter 4:  Polynomial and Rational Functions (Only section 4.1)

¨     Identifying characteristics of quadratics such as open up or down, maximum or minimum, axis of symmetry, vertex, and intercepts.

¨     Using a quadratic to model such as revenue, projectile motion, fencing problems

¨     Determining the quadratic of best fit using graphing calculator

¨     Graphing a quadratic via transformation techniques.

¯     Chapter 4 Review, p. 349-350 # 1, 5, 17, 19, 57, 62bcd

Chapter 12: Systems of Equations and Inequalities

¨     Solving systems of two and three variables by the following methods:  Substitution, Elimination, Graphing (either by hand or on your graphing calculator), Cramer’s Rule and Inverse Matrix Method.

¨     Creating and solving a system given a word problem.  (12.1/12.2)

¨     Determining quadratic that fits three points. (12.2)

¨     Matrix Algebra (Both with and without the aid of your graphing calculator): adding, subtracting, scalar multiplication, and multiplication.  Solve for an unknown in a matrix equation.  (12.5)

¨     Using matrices to organize data and complete necessary operations. (12.5)

¨     Graphing a System of Inequalities.  (12.8)

¨     Writing the inequalities when given the graph. (12.8)

¨     Linear Programming Word Problems (12.9)

¯     Chapter 12 Rev, p. 893-896 # 1, 19, 21-25 odd, 37, 43, 45, 51, 79, 87, 97, 101, 113

Suggestions on how to prepare for the exam:

Ø      Begin preparing soon!  Begin preparing soon!  Begin preparing soon!

Ø      Find a study buddy and make a schedule of dates to work together.  Don’t try to tackle too much in a day…spread it out.

Ø      Review and re-do past quizzes and tests.  Cover up the solution and work through the question again.  Identify any areas that you may need to go back and revisit.  This is the best way to prepare for this midyear exam as the exam!  Pay special attention to the problems that involve multiple concepts!!!  You will be given additional copies of questions that are exact questions or similar to past assessment questions to complete. 

Ø      Review and re-do practice quizzes and tests (including Fruitbowl/whiteboard slides)

Ø      Work on problems from the review sections.  As you work through the problems, identify the areas that you need to spend more time on.  If you get stuck on any problems that you attempt, refer to your book/class notes or meet with your study buddy and see are able to clarify any areas of confusion.  If you are still experiencing difficulty, please come for extra help as soon as possible. 

Ø      Any concepts that you are still feeling shaky on, ask for help, another lesson on the concept, re-teaching worksheets, more practice problems...whatever you need, ask!

Ø      On the eve of the exam, get a good night sleep.  This is very important!

Ø      On the morning of the exam, be sure to have a balanced breakfast.

Ø      Immediately prior to the start of the exam, take a deep breath!  You CAN do it!

Opportunities for Extra Help:  

Extra help is usually available after school on Mondays, Wednesdays, and Thursdays.  Please check the calendar on the classroom bulletin board to check for any exceptions.  While extra help is not typically available on Tuesdays, there will be extra help on Tuesday 1-18.  There will also probably be two class session for Fruitbowl/whiteboard review.

Format of the test:  

The test will contain around 150 points.  There will be approximately 26 multiple choice questions worth 3 points each and the rest of the questions (around 17) will be show all your work problems. 

Your Algebra II Exam will likely be the second exam (10:30−12:30) on Wednesday 1/19. 

Room Assignments:  122/123

Be sure to bring:

Graphing calculator

A writing utensil