Algebra 2 and Trigonometry

Transcription

1 Algebra 2 and Trigonometry Text: Amsco Algebra II and Trigonometry Text/Workbook Topic Textbook 1. The Integers Alg II/Trig A. Adding and Subtracting Polynomials 1.3 B. Multiplying Polynomials 1.5 C. Factoring Completely 1.6 i. GCF and ii. Difference of 2 perfect squares iii. Factor by grouping iv. Trinomials where a=1 and v. Trinomials where a does not equal 1 E. Solving quadratic equations Rational Expressions Alg II/Trig A. Simplifying rational equations / identify when undefined/ opposite factors 2.2 B. Multiplying Rational Expressions and C. Dividing Rationals Expressions 2.3 D. Adding/Subtracting with Same Denominators 2.4 E. Adding/Subtracting with Different Denominators 2.4 F. Solving Rational Equations 2.7 G. Ratio and proportions (solving rational equations) 2.5 H. Complex Rational Expressions 2.6 (Include Topic 1. The Integers) 3. Absolute Value and Inequalities Alg II/Trig A. Solve Absolute Value Equations 1.4 B. Solve and Graph Absolute Value inequalities 1.4 and 3.1 C. Quadratic Inequalities 1.8 D. Solving Rational Inequalities Roots and Radicals Alg II/Trig A. Square, Cube and nth root of a number 3.2 B. Simplifying radicals (omit fractional radicand questions) 3.3 C. Adding and Subtracting Radicals (common and unlike radicands) 3.4 D. Multiply Radicals (include single distributive and double distributive-foil) 3.5 E. Divide Radicals 3.3 and 3.6 i. Perfect square fractions

2 ii. Denominator divides into numerator * do not include any problem that needs rationalizing F. Rationalizing the denominator 3.3, 3.6, 3.7 G. Solving Radical Equations 3.8 (Include Topic 3. Absolute Value and Inequalities) 5. Relations and Functions Alg II/Trig A. Relation and Functions 4.1, 4.2 B. Function Notation C. Linear Functions and Direct Variation 4.3 D. Absolute Value Function 4.4 F. Composition of Functions 4.7 G. Inverse Functions 4.8 I. Inverse Variation 4.10 End Marking Period 1 6. Quadratic Functions and Complex Numbers Alg II/Trig A. The Complex Numbers 5.4 B. Operations with Complex Numbers (add, subtract, multiply, divide) 5.5 C. Completing the Square 5.1 D. Quadratic Formula - real roots 5.2 E. Quadratic Formula - imaginary roots 5.6 F. The Nature of the Roots of any Quadratics (discriminant) 5.3 G. Sum and product of the Roots 5.7 H. Quadratic Linear Systems and Solving Quadratics Inequalities 5.9 I. Parabolas--Vertex Form 5.1 J. Circles 4.9 K. Solving Higher Degree Polynomial Equations 5.8 E. Polynomial Functions ( Solving Quadratic Functions) Exponential Functions Alg II/Trig A. Laws of Exponents 7.1 B. Zero and Negative Exponents 7.2 C. Fractional Exponents 7.3 D. Exponential Functions and their Graphs (include y = e x ) 7.4 E. Solving Equations involving Exponents 7.5 F. Solving Exponential Equations 7.6

3 G. Applications of Exponential Functions 7.7 End Midterm Examination 8. Logarithmic Functions Alg II/Trig A. Inverse of an Exponential Function 8.1 B. Logarithmic Form of an Exponential Equation 8.2 C. Logarithmic Relationships (Rules of Logarithms) 8.3 D. Common Logarithms 8.4 E. Natural Logarithms 8.5 F. Exponential Equations (Include Word Problems) 8.6 G. Logarithmic Equations (Include workbook problems 8.6) 8.7 H. Applications of Exponentials and Logarithmic Functions (8.6 and 8.7) WB End Marking Period 2 9. Sequences and Series Alg II/Trig A. Sequences 6.1 B. Arithmetic Sequences 6.2 C. Sigma Notation 6.3 D. Geometric Sequences 6.5 E. Arithmetic Series, Geometric Series and Infinite Series 6.4, 6.6, Trigonometric Functions Alg II/Trig A. Right Triangle 9.1 B. Terminal/Co-Terminal Angles, DMS (DMS: Supplement) 9.2 C. The Unit Circle; Sine, Cosine, Tangent 9.3 D. Special Angles in Right Triangle 9.6 E. Reference Angles 9.8 F. Reference Angles and Calculator More Trigonometric Functions Alg II/Trig A. Radian Measure 10.1 B. Trigonometric Function Values and Radian Measure 10.2 C. The Reciprocal Trigonometric Functions (include evaluating) 9.5 D. Cofunctions 10.6

4 (include Topic 9. Trigonometric Functions) 12. Graphs of Trigonometric Functions Alg II/Trig A. Amplitude, Period and Phase Shift, Frequency 11.3 B. Domain and Range of Trigonometric Functions 10.4 C. Graph of the Sine function 11.1 D. Graph of the Cosine function 11.2 E. Writing the equation of a Sine or Cosine Graph 11.4 F. Graph of the Tangent function 11.5 G. Graphs of the Recipocals Trigonometric Functions 11.6 H. Inverse Trigonometric Functions (domain, range and evaluating) 10.5 I. Graphs of Inverse Trigonometric Functions 11.7 J. Sketching Trigonometric Graphs including transformations (Honors:without calculator) 11.8 *Honors: Include Real World Applications of Trigonometric Graphs 13. Trigonometric Applications Alg II/Trig A. Law of Cosines 14.2, 14.3 B. Law of Sines 14.5 C. The Ambiguous Case 14.6 D. Solving Triangles (include Forces & Vectors) 14.7 E. Area of a Triangle 14.4 (Include Topic 11. Graphs of Trigonometric Functions) End Marking Period Trigonometric Identities Alg II/Trig A. Basic Trigonometric Identities and Pythagorean Identities 10.3, 12.1 B. Proving Trigonometric Identities 12.2 C. Sine/Cosine of the Sum/Difference of Two Angles 12.3, 12.4, 12.5 D. Tangent of the Sum/Difference of Two Angles 12.6 E. Function Values of Double Angles 12.7 F. Function Values of Half Angles Trigonometric Equations Alg II/Trig A. First Degree Trigonometric Equations 13.1 B. Using Factoring to Solve Second Degree Trigonometric Equations 13.2 C. Using the Quadratic Formula to Solve Second Degree Trigonometric Equations 13.3 D. Using Substitution to Solve Trigonometric Equations Involving More Than One Function 13.4, 13.5 (Include Topic 13. Trigonometric Identities)

5 16. Statistics Alg II/Trig A. Measures of Central Tendency and Measures of Central Tendency for Grouped Data 15.2, 15.3 B. Measures of Dispersion and Variance and Standard Deviation 15.4, 15.5 C. Normal Distribution/Bell Curve 15.6 D. Correlation Coefficient & Linear Regression 15.8 E. Non-Linear Regression 15.9 F. Interpolation and Extrapolation (Include Topic 15. Sequences and Series) 17. Probability and the Binomial Theorem Alg II/Trig A. The Counting Principle 16.1 B. Permutations and Combinations 16.2 C. Probability 16.3 D. Probability with Two Outcomes (exactly) 16.4 E. Binomial Probability and the Normal Curve (at least) 16.5 F. The Binomial Theorem 16.6 End Marking Period 4 Algebra 2/Trigonometry Regents Exam in June