Core Precalculus Precalculus is a course that combines reviews of algebra, geometry, and functions into a preparatory course for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. The first semester includes linear, quadratic, exponential, logarithmic, radical, polynomial, and rational functions; systems of equations; and conic sections. The second semester covers trigonometric ratios and functions; inverse trigonometric functions; applications of trigonometry, including vectors and laws of cosine and sine; polar functions and notation; and arithmetic of complex numbers. Within each Precalculus lesson, students are supplied with a post-study Checkup activity that provides them the opportunity to hone their computational skills by working through a low-stakes problem set before moving on to formal assessment. Unit-level Precalculus assessments include a computer-scored test and a scaffolded, teacher-scored test. The content is based on the National Council of Teachers of Mathematics (NCTM) standards and is aligned with state standards. Length:Two Semesters UNIT 1: FUNCTIONS LESSON 1: WHAT IS A FUNCTION? Study: Relating to Functions(cid:10) Learn about functions, their graphs, and some special functions.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on functions.(cid:10) Duration: 0 hr 50 min Quiz: What Is a Function?(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 2: GRAPHING FUNCTIONS Study: Testing and Special Functions(cid:10) Core > Precalculus Copyright © 2013 Apex Learning Inc. Apex Learning® , the Apex Learning logo, ClassTools® , ClassTools Achieve® , ClassTools Virtual, Literacy Advantage, and Beyond Books® are either registered trademarks or trademarks of Apex Learning Inc. 1of 29 Learn the vertical line and horizontal line tests for evaluating a function. Evaluate a function for given values and explore special functions.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on graphing functions.(cid:10) Duration: 0 hr 50 min Quiz: Graphing Functions(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 3: LINEAR FUNCTIONS Study: Walking the Line(cid:10) Learn about slope and the three main forms of linear functions.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on linear functions.(cid:10) Duration: 0 hr 50 min Quiz: Linear Functions(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 4: ARITHMETIC SEQUENCES AND SERIES Study: It All Adds Up(cid:10) Learn about arithmetic sequences and series.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on arithmetic sequences and series.(cid:10) Duration: 0 hr 50 min Quiz: Arithmetic Sequences and Series(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points Core > Precalculus Copyright © 2013 Apex Learning Inc. Apex Learning® , the Apex Learning logo, ClassTools® , ClassTools Achieve® , ClassTools Virtual, Literacy Advantage, and Beyond Books® are either registered trademarks or trademarks of Apex Learning Inc. 2of 29 LESSON 5: LINEAR EQUATIONS AND INEQUALITIES Study: On Equal Footing(cid:10) Learn how to solve linear equations and inequalities.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on linear equations and inequalities.(cid:10) Duration: 0 hr 50 min Quiz: Linear Equations and Inequalities(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 6: LINEAR SYSTEMS Study: Finding the Point of Intersection(cid:10) Find the point of intersection of linear systems using algebra, graphing, and matrices.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on linear systems.(cid:10) Duration: 0 hr 50 min Quiz: Linear Systems(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 7: ARITHMETIC OF FUNCTIONS Study: Mixing and Matching(cid:10) Learn how to add, subtract, multiply, divide, and compose functions.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on the arithmetic of functions.(cid:10) Duration: 0 hr 50 min Quiz: Arithmetic of Functions(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Core > Precalculus Copyright © 2013 Apex Learning Inc. Apex Learning® , the Apex Learning logo, ClassTools® , ClassTools Achieve® , ClassTools Virtual, Literacy Advantage, and Beyond Books® are either registered trademarks or trademarks of Apex Learning Inc. 3of 29 Duration: 0 hr 40 min Scoring: 20 points LESSON 8: FUNCTIONS WRAP-UP Review: Functions(cid:10) Prepare for the unit test by reviewing key concepts and skills.(cid:10) Duration: 0 hr 50 min Review: Calculator Skills(cid:10) Review key calculator skills.(cid:10) Duration: 0 hr 25 min Practice: Functions(cid:10) Complete a set of practice problems.(cid:10) Duration: 0 hr 50 min Scoring: 50 points Discuss: What Questions Do You Have?(cid:10) Discuss ideas about this unit that are still unclear. Help to answer your classmates' questions.(cid:10) Duration: 0 hr 30 min Scoring: 20 points Test (CS): Functions(cid:10) Take a computer-scored test to assess what you have learned in this unit.(cid:10) Duration: 0 hr 50 min Scoring: 60 points Test (TS): Functions(cid:10) Take a teacher-scored test to assess what you have learned in this unit.(cid:10) Duration: 0 hr 50 min Scoring: 100 points LESSON 9: DIAGNOSTIC Diagnostic: Functions(cid:10) Take a diagnostic unit test that will generate a study plan based on your responses.(cid:10) Duration: 0 hr 40 min Scoring: 20 points UNIT 2: QUADRATIC FUNCTIONS LESSON 1: FORMS OF QUADRATIC FUNCTIONS Core > Precalculus Copyright © 2013 Apex Learning Inc. Apex Learning® , the Apex Learning logo, ClassTools® , ClassTools Achieve® , ClassTools Virtual, Literacy Advantage, and Beyond Books® are either registered trademarks or trademarks of Apex Learning Inc. 4of 29 Study: Express Yourself(cid:10) Express quadratic functions in a variety of forms.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on forms of quadratic functions.(cid:10) Duration: 0 hr 50 min Quiz: Forms of Quadratic Functions(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 2: GRAPHING QUADRATIC FUNCTIONS Study: Putting the Pieces Together(cid:10) Use key components such as vertex, axis of symmetry, and x- and y-intercepts to sketch the graphs of quadratic functions and solve quadratic inequalities.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on graphing quadratic functions.(cid:10) Duration: 0 hr 50 min Quiz: Graphing Quadratic Functions(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 3: TRANSFORMATIONS Study: Getting a Move On(cid:10) Learn how to reflect about the x- and y-axes. Learn about horizontal and vertical shifts and horizontal and vertical stretches.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on transformations.(cid:10) Duration: 0 hr 50 min Quiz: Transformations(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points Core > Precalculus Copyright © 2013 Apex Learning Inc. Apex Learning® , the Apex Learning logo, ClassTools® , ClassTools Achieve® , ClassTools Virtual, Literacy Advantage, and Beyond Books® are either registered trademarks or trademarks of Apex Learning Inc. 5of 29 LESSON 4: SOLVING QUADRATIC EQUATIONS Study: Answers to Your Questions(cid:10) Use factoring and the quadratic formula to solve an equation. Also relate solutions to zeros and work with complex numbers.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on solving quadratic equations.(cid:10) Duration: 0 hr 50 min Quiz: Solving Quadratic Equations(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 5: APPLICATIONS OF QUADRATIC FUNCTIONS Study: Solving Problems Using Quadratic Functions(cid:10) Set up and solve application problems involving quadratic functions.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on applications of quadratic functions.(cid:10) Duration: 0 hr 50 min Quiz: Applications of Quadratic Functions(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 6: QUADRATIC FUNCTIONS WRAP-UP Review: Quadratic Functions(cid:10) Prepare for the unit test by reviewing key concepts and skills.(cid:10) Duration: 0 hr 50 min Review: Calculator Skills(cid:10) Review key calculator skills.(cid:10) Duration: 0 hr 25 min Core > Precalculus Copyright © 2013 Apex Learning Inc. Apex Learning® , the Apex Learning logo, ClassTools® , ClassTools Achieve® , ClassTools Virtual, Literacy Advantage, and Beyond Books® are either registered trademarks or trademarks of Apex Learning Inc. 6of 29 Practice: Quadratic Functions(cid:10) Complete a set of practice problems.(cid:10) Duration: 0 hr 50 min Scoring: 50 points Discuss: What Questions Do You Have?(cid:10) Discuss ideas about this unit that are still unclear. Help to answer your classmates' questions.(cid:10) Duration: 0 hr 30 min Scoring: 20 points Test (CS): Quadratic Functions(cid:10) Take a computer-scored test to assess what you have learned in this unit.(cid:10) Duration: 0 hr 50 min Scoring: 60 points Test (TS): Quadratic Functions(cid:10) Take a teacher-scored test to assess what you have learned in this unit.(cid:10) Duration: 0 hr 50 min Scoring: 100 points LESSON 7: DIAGNOSTIC Diagnostic: Quadratic Functions(cid:10) Take a diagnostic unit test that will generate a study plan based on your responses.(cid:10) Duration: 0 hr 40 min Scoring: 20 points UNIT 3: POLYNOMIAL AND RATIONAL FUNCTIONS LESSON 1: POLYNOMIAL EXPRESSIONS Study: What Is a Polynomial?(cid:10) Learn what makes a polynomial and how to test for one.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on polynomial expressions.(cid:10) Duration: 0 hr 50 min Quiz: Polynomial Expressions(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points Core > Precalculus Copyright © 2013 Apex Learning Inc. Apex Learning® , the Apex Learning logo, ClassTools® , ClassTools Achieve® , ClassTools Virtual, Literacy Advantage, and Beyond Books® are either registered trademarks or trademarks of Apex Learning Inc. 7of 29 LESSON 2: DIVIDING POLYNOMIALS Study: Synthetic Doesn't Mean Fake(cid:10) Learn the technique for dividing polynomials and testing for factors.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on dividing polynomials.(cid:10) Duration: 0 hr 50 min Quiz: Dividing Polynomials(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 3: SOLVING POLYNOMIAL EQUATIONS Study: These Roots Grow Deep(cid:10) Find all solutions to polynomial equations.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on solving polynomial equations.(cid:10) Duration: 0 hr 50 min Quiz: Solving Polynomial Equations(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 4: GRAPHING POLYNOMIAL FUNCTIONS Study: What Goes Up Sometimes Comes Down(cid:10) Explore the behavior of polynomial functions and find key points of the graph of the function.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on graphing polynomial functions.(cid:10) Duration: 0 hr 50 min Core > Precalculus Copyright © 2013 Apex Learning Inc. Apex Learning® , the Apex Learning logo, ClassTools® , ClassTools Achieve® , ClassTools Virtual, Literacy Advantage, and Beyond Books® are either registered trademarks or trademarks of Apex Learning Inc. 8of 29 Quiz: Graphing Polynomial Functions(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 5: RATIONAL FUNCTIONS Study: Top and Bottom(cid:10) Identify rational functions, find domain and range, look at asymptotes, and sketch complete graphs.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on rational functions.(cid:10) Duration: 0 hr 50 min Quiz: Rational Functions(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 6: POLYNOMIAL AND RATIONAL FUNCTIONS WRAP-UP Review: Polynomial and Rational Functions(cid:10) Prepare for the unit test by reviewing key concepts and skills.(cid:10) Duration: 0 hr 50 min Review: Calculator Skills(cid:10) Review key calculator skills.(cid:10) Duration: 0 hr 25 min Practice: Polynomial and Rational Functions(cid:10) Complete a set of practice problems.(cid:10) Duration: 0 hr 50 min Scoring: 50 points Discuss: What Questions Do You Have?(cid:10) Discuss ideas about this unit that are still unclear. Help to answer your classmates' questions.(cid:10) Duration: 0 hr 30 min Scoring: 20 points Test (CS): Polynomial and Rational Functions(cid:10) Take a computer-scored test to assess what you have learned in this Core > Precalculus Copyright © 2013 Apex Learning Inc. Apex Learning® , the Apex Learning logo, ClassTools® , ClassTools Achieve® , ClassTools Virtual, Literacy Advantage, and Beyond Books® are either registered trademarks or trademarks of Apex Learning Inc. 9of 29 unit.(cid:10) Duration: 0 hr 50 min Scoring: 60 points Test (TS): Polynomial and Rational Functions(cid:10) Take a teacher-scored test to assess what you have learned in this unit.(cid:10) Duration: 0 hr 50 min Scoring: 100 points LESSON 7: DIAGNOSTIC Diagnostic: Polynomial and Rational Functions(cid:10) Take a diagnostic unit test that will generate a study plan based on your responses.(cid:10) Duration: 0 hr 40 min Scoring: 20 points UNIT 4: EXPONENTIAL AND LOGARITHMIC FUNCTIONS LESSON 1: EXPONENTS AND RADICALS Study: Rational Exponents and Radical Expressions(cid:10) Learn the rules of exponents and how to express radicals.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on exponents and radicals.(cid:10) Duration: 0 hr 50 min Quiz: Exponents and Radicals(cid:10) Take a quiz to assess your understanding of the material.(cid:10) Duration: 0 hr 40 min Scoring: 20 points LESSON 2: EXPONENTIAL FUNCTIONS Study: Exponential Functions and Their Graphs(cid:10) Explore the basic exponential graphs.(cid:10) Duration: 0 hr 50 min Checkup: Lessons Learned(cid:10) Complete a set of practice problems on exponential functions.(cid:10) Core > Precalculus Copyright © 2013 Apex Learning Inc. Apex Learning® , the Apex Learning logo, ClassTools® , ClassTools Achieve® , ClassTools Virtual, Literacy Advantage, and Beyond Books® are either registered trademarks or trademarks of Apex Learning Inc. 10of 29