CURRICULUM MAP. Course / Subject: Precalculus Grade: 11/12 Teacher: Kelly, Kirk, McCollick, Palkovics, Roderick Month: September (19 days)

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1 Month: September (19 days) - Change from radian to degree measure, & vice versa - Find angles that are coterminal with a given angle - Find reference angle for a given angle Angles & Their Measure (Section 5.1) ( B Measure & compare angles in degrees & radians.) - Chapter 5.1 Quiz Central Angles & Arcs (Section 5.2) ( F Use the properties of angles, arcs, chords, tangents, & secants to solve problems involving circles.) - Find the length of an arc given the measure of the central angle - Find the area of a sector Circular Functions (Section 5.3) ( F Use the properties of angles, arcs, chords, tangents, & secants to solve problems involving circles.) - Find the values of the six trigonometric functions of an angle in standard position given a point on its terminal side - Chapter Quiz Trigonometric Functions of Special Angles (Section 5.4) - Find exact values for the six trigonometric functions of special angles - Find decimal approximations for the

2 values of the six trigonometric functions of any angle Course / Subject: Precalculus Month: October (22 days) Grade: 11/12 Teacher: Kelly, Kirk, McCollick, - Solve right triangles using the trigonometric ratios Right Triangles (Section 5.5) ( B Identify, create, & solve practical problems involving right triangles using the trigonometric functions & the Pythagorean Theorem.) - Chapter Quiz The Law of Sines (Section 5.6) ( B Identify, create, & solve practical problems involving right triangles using the trigonometric functions & the Pythagorean Theorem.) - Solve triangles using the Law of Sines The Law of Cosines (Section 5.7) ( B Identify, create, & solve practical problems involving right triangles using the trigonometric functions & the Pythagorean Theorem.) - Solve triangles using the Law of Cosines Area of Triangles (Section 5.8) - Find the area of triangles - Chapter Quiz - Chapter 5 Exam

3 - Performance Assessment #2 Month: November (16 days) - Use the parent graphs of the trigonometric functions Graphs of the Trigonometric Functions (Section 6.1) ( A Use graphing calculators to display periodic & circular functions; describe properties of the graphs.) Amplitude, Period, Phase Shift, and Vertical Shift (Section 6.2) ( A Use graphing calculators to display periodic & circular functions; describe properties of the graphs.) - Find the amplitude, period, & phase shift for a trigonometric function - Write equations of trigonometric functions given the amplitude, period, & phase shift Graphing Trigonometric Functions (Section 6.3) ( A Use graphing calculators to display periodic & circular functions; describe properties of the graphs.) - Graph various trigonometric functions - Chapter 6 Exam Basic Trigonometric Identities (Section 7.1) - Identify & use reciprocal identities, quotient identities, & Pythagorean identities - Chapter 7.1 Quiz

4 Month: December (17 days) - Use the basic trigonometric identities to verify other identities - Find numerical values of trigonometric functions Verifying Trigonometric Identities (Section 7.2) - Chapter 7.2 Quiz Sum & Difference Identities (Section 7.3) - Use the sum & difference identities for sine, cosine, & tangent functions - Chapter 7.3 Quiz Half-Angle & Double-Angle Identities (Section 7.4) Solving Trigonometric Equations (Section 7.5) Polar Coordinates (Section 9.1) - Use the double-angle & half-angle identities for sine, cosine, & tangent functions - Solve trigonometric equations - Graph polar coordinates & simple polar equations - Chapter 7.4 Quiz - Chapter 7.5 Quiz - Chapter 7 Exam

5 Graphs of Polar Equations (Section 9.2) - Graph polar equations Month: January (19 days) Polar & Rectangular Coordinates (Section 9.3) - Convert from polar coordinates to rectangular coordinates, & vice versa Simplifying Complex Numbers (Section 9.5) - Add, subtract, multiply, & divide complex numbers in rectangular form Polar Form of Complex Numbers (Section 9.6) Relations & Functions (Section 1.1) ( O Determine the domain & range of a relation, given a graph or set of ordered pairs) Composition & Inverses of Functions (Section 1.2) - Change complex numbers from rectangular to polar form, & vice versa - Determine whether a given relation is a function - Identify the domain & range of any relation or function - Perform operations with functions - Find composite functions - Find inverse functions - Midterm (Trigonometry) - Chapter Quiz

6 Linear Functions & Inequalities (Section 1.3) - Find zeros of linear functions - Graph linear equations & inequalities Month: February (18 days) - Find distance between two points - Find slope of line through two points - Write linear equations using slopeintercept form - Write linear equations using point-slope form - Write equations of parallel & - Chapter 1 Exam perpendicular lines Distance & Slope (Section 1.4) Forms of Linear Equations (Section 1.5) ( L Write the equation of a line when given the graph of a line, two points on a line, or the slope of the line & a point on the line.) Parallel & Perpendicular Lines (Section 1.6) Solving Systems of Equations (Section 2.1) ( G Analyze & explain systems of equations, systems of inequalities, & matrices.) Introduction to Matrices (Section 2.2) ( G Analyze & explain systems of equations, systems of inequalities, & matrices.) ( I Use matrices to organize& manipulate data, including matrix addition, subtraction, multiplication, & scalar multiplication.) Determinant & Multiplicative Inverses of Matrices (Section 2.3) - Solve systems of equations algebraically & graphically - Add, subtract, & multiply matrices - Evaluate determinants - Find inverses of matrices - Solve systems of equations by using

7 Solving Systems of Equations by Using Matrices (Section 2.4) ( G Analyze & explain systems of equations, systems of inequalities, & matrices.) inverses of matrices - Solve systems of equations by using matrices - Chapter 2 Exam Month: March (20 days) Polynomial Functions (Section 4.1) Quadratic Equations & Inequalities (Section 4.2) - Determine roots of polynomial equations - Apply the Fundamental Theorem of Algebra - Solve quadratic equations - Use the discriminant to describe the roots of quadratic equations - Graph quadratic equations & inequalities - Chapter Quiz The Remainder & Factor Theorems (Section 4.3) - Find the factors of polynomials using the Remainder & Factor Theorems The Rational Root Theorem (Section 4.4) Locating the Zeros of a Function (Section 4.5) - Identify all possible rational roots of a polynomial equation by using the Rational Root Theorem - Approximate the real zeros of a polynomial function - Chapter 4 Exam

8 -Graph polynomial functions Month: April (20 days) PSSA - PSSA Review - PSSA Tests

9 Month: May (19 days) Rational Exponents (Section 11.1) Exponential Functions (Section 11.2) The number e (Section 11.3) Logarithmic Functions (Section 11.4) ( S Analyze properties & relationships of functions (linear, polynomial,rational, trigonometric, exponential, logarithmic)) Common Logarithms (Section 11.5) ( S) Logarithmic & Exponential Functions (Section 11.6) ( S) Natural Logarithms (Section 11.7) The Circle - Use the properties of exponents - Evaluate & simplify expressions containing rational exponents - Evaluate expressions with irrational exponents - Graph exponential functions - Use the exponential function y=e x - Evaluate expressions & solve equations involving logarithms - Find common logarithms & antilogarithms of numbers - Solve exponential & logarithmic equations & inequalities - Find natural logarithms of numbers - Solve equations using natural logarithms - Use the standard & general forms of the - Chapter 11 Exam

10 (Section 10.1) ( E Use equations to represent curves (lines, circles, ellipses, parabolas, hyperbolas.) The Parabola (Section 10.2) ( E.) equation of a circle & graph circles - Use the standard & general forms of the equation of a parabola & graph parabolas Month: June (11 days) The Ellipse (Section 10.3) ( E.) - Use the standard & general forms of the equation of an ellipse & graph ellipses The Hyperbola (Section 10.4) ( E Use equations to represent curves (lines, circles, ellipses, parabolas, hyperbolas.) - Use the standard & general forms of the equation of a hyperbola & graph hyperbolas - Chapter 10 Exam Final Exam Review - Final Exam

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