College Algebra Semester Exam Review - Baggett (Fall 2013) Your exam is Wednesday, December 18, 2012; at 8:30 am in room C-4 for A- Block. Please bring two sharpened pencils. The midterm will be no calculator. There will be about 90 multiple choice questions and 8 graphs to sketch. You may bring in one 3 by 5 index card with formulas and information. You should go through all old quizzes and old tests. Study by doing problems!!! Please be able to do the following: R1 : The Real Number System 1. Be able to read and use interval notation (i.e., (1,∞)& [2 , 8)) 2. Identify various kinds of real numbers. 3. Find the absolute value of a number. R2: Integer Exponents, Scientific Notation, and Order of Operations 1. Simplify expressions with integer exponents 2. Solve problems using scientific notation 3. Use the rules for order of operations R3: Addition, Subtraction and Multiplication of Polynomials 1. Identify terms coefficients and degree of a polynomial 2. Add, subtract, and multiply polynomials. R4: Factoring 1. 2. 3. 4. Factor polynomials by removing a common factor Factor by grouping Factor trinomials of the form 𝑥 2 + 𝑏𝑥 + 𝑐 Factor trinomials of the form 𝑎 𝑥 2 + 𝑏𝑥 + 𝑐 𝑤ℎ𝑒𝑟𝑒 𝑎 ≠ 1 QUIZ R.1-R.4 R5: The basics of Problem Solving 1. Solve linear equations 2. Solve quadratic equations R6: Rational Expressions 1. Determine the domain of a rational expression 2. Simplify rational expressions 3. Multiply, divide, add, and subtract rational expressions 4. Simplify complex rational expressions R7: Radical Notation and Rational Exponents 1. 2. 3. 4. Simplify radical expressions Rationalize denominators in rational expressions Covert between exponential and radical notation Simplify expressions with rational expressions TEST R Sections Also had HW quizzes: R.2a, R.2b, R.3, R.5, R.6a, R.6b, R.7 Section 1.1: Introduction to Graphing 1. 2. 3. 4. 5. 6. Finding x and y-intercepts Graphing lines Finding the distance between two points using the distance formula Using the midpoint formula Finding the equation of a circle Graphing circles Section 1.2: Functions and Graphs 1. 2. 3. 4. 5. 6. Determining whether a relation is a function Finding function values using a formula or a graph Graphing functions Determine whether a graph is a function Find the domain and range of a function Solving application problems using functions Section 1.3: Linear Functions, Slope and Applications 1. 2. 3. 4. 5. Determine the slope given two points on a line Solve applications problems involving slope Find the slope and y-intercept given an equation Graph a linear equation using the slope and the y-intercept Solve application problems Quiz 1.1-1.3 Section 1.4: Equations of lines and modeling 1. 2. 3. 4. Determining equations of lines Given two lines – determine whether the lines are parallel or perpendicular Model a set of data with a linear equation Fit a regression line through data – and use the equation to make predictions Section 1.5: Linear equations, functions, zeros, and applications 1. 2. 3. 4. Solving linear equations Solving application problems using linear models Finding zeros of linear equations Solve a formula for a given variable QUIZ word problems section 1.5 Section 1.6 Solving Linear Inequalities 1. Solve Linear Inequalities 2. Solve Compound Inequalities 3. Application Problems TEST Chapter 1 Also had HW quizzes: 1.1a, 1.1b, 1.1-1.2, 1.3b, 1.4a, 1.4b, 1.5, 1.5-6. END OF 1ST 9 WEEKS Section 2.1 Increasing, Decreasing, and Piecewise Functions; Applications 1. Identify where functions are increasing, decreasing, and constant 2. Identify where there are relative maxima and relative minima 3. Graph piecewise functions Section 2.2 The Algebra of Functions 1. Find the sum, difference, product, and quotient of two functions. 2. Determine the domain of combination of functions 3. Find the difference quotient Section 2.3 The Composition of Functions 1. Find the composition of two functions and its domain TEST 2.1-2.3 Section 2.4 Symmetry and Transformations 1. Determine the symmetry of a graph 2. Determine whether a function is even, odd, or neither Given a graph of a function, graph its transformation under translations, reflections, stretchings, and shrinking Test 2.4 Section 2.5 Variation and Applications 1. Find equations of direct variation, inverse variation, and joint variation 2. Solve applied problems involving variation Take-home Quiz 2.5 Also had HW quizzes: 2.1a, 2.1 b, 2.2a, 2.2b, 2.3a, 2.4a, 2.4b, 2.4c, 2.4d, 2.5 Section 3.1 The Complex Numbers 1. Perform Computations involving complex numbers Section 3.2 Quadratic Equations, Functions, Zeros, and Models 1. Find zeros of quadratic functions and solve quadratic equations using the principle of zero products, by using the principle of square roots, by completing the square, and by using the quadratic formula. 2. Solve applied quadratic equations. Test Sections 2.5, 3.1, 3.2 Also has some HW quizzes The exam will be multiple choice and some short answer. Know how to graph your basic functions. Review sheets or practice problems were given for all tests – these should be used to help you study for your midterm. Also, several worksheets were given throughout the semester. You should review these. Be sure to see me for correct answers for old tests, quizzes, and worksheets – before you leave for the weekend – this will make your studying time much more productive.