# UnLock Pre-Calculus

## UnLock Pre-Calculus Scope & Sequence

Take a look at our scope and the sequence in which the lessons are placed. Our lessons break math into bite size chunks and build one concept upon another in a logical fashion that enhances learning and reduces math anxiety.

 Unit 1  Review of Functions & Quadratics 1.1       Introduction to Functions1.2       Domain of a Function and Interval Notation1.3       Range of a Function and Interval Notation 1.4       Composition of Functions 1.5       Inverse of Functions 1.6       Introduction to Quadratic Functions  1.7       Graphing Quadratic Functions in Vertex Form 1.8       Solving Quadratic Equations with Square Roots 1.9       Solving Quadratics by Completing the Square 1.10     Converting to Vertex Form by Completing the Square 1.11     Graphing Quadratic Inequalities Unit 2   Polynomial Functions 2.1       Introduction to Polynomials2.2       Finding a Polynomial Given the Roots2.3       Dividing Polynomials Using Long Division 2.4       Dividing Polynomials Using Synthetic Division 2.5       Remainder Theorem/Factor Theorem 2.6       Location principle & Multiplicity of Zeros 2.7       Rational Root Theorem 2.8       Complex Conjugate Root Theorem 2.9       Fundamental Theorem of Algebra & Descartes Rule of             signs 2.10     Graphing Polynomials Unit 3  Rational Functions 3.1       Introduction to Rational Functions3.2       Graphing Rational Functions3.3       Graphing Rational Functions Part II3.4       Slant Asymptotes3.5       Parabolic Asymptotes 3.6       Multiplying and Dividing Rational Expressions 3.7       Solving Rational Equations Unit 4  Exponential & Logarithmic Functions 4.1       Introduction to Exponential & Logarithmic Functions 4.2       Graphing Exponential Functions 4.3       Logarithmic Functions and Change of Base Formula 4.4       Properties of Logarithms4.5       Exponential/Logarithmic Inverse Property   4.6       Natural Exponentials & Logarithms 4.7       Solving Exponential Equations4.8       Solving Logarithmic Equations4.9       Fitting Log Functions to Data Unit 5  Vectors 5.1       Introduction to Vectors5.2       Vectors in Two Dimensions5.3       Adding & Subtracting Vectors 5.4       Multiplying Vectors by a Scalar 5.5       Vector Components 5.6       Vector Notation  5.7       Operations in Vector Noation 5.8       Dot Product Unit 6   Matrices 6.1       Introduction to Matrices  6.2       Basic Matrix Operations  6.3       Matrix Multiplication  6.4       Determinant of 2x2 Matrices 6.5       Determinant of 3x3 Matrices 6.6       Inverse of Matrices 6.7       Elementary Row Operations & Augmented Matrices  6.8       Using Matrices to Solve 2x2 Systems  6.9       Using Matrices to Solve 3x3 Systems Unit 7   Complex Numbers 7.1       Introduction to Complex7.2       Adding and Subtracting Complex Numbers 7.3       Multiplying Complex Numbers  7.4       Complex Conjugate & Dividing 7.5       The Complex Plane7.6       Modulus of Complex Numbers 7.7       Distance in the Complex Plane    7.8       Midpoint in the Complex Plane Unit 8   Trigonometric Functions 8.1        Introduction to Trigonometric Functions8.2        Radian Measure 8.3        Standard Position & Reference Angles 8.4        Special Triangles and Exact Ratios8.5        Graphing the Sine and Cosine Functions8.6        Graphing the Tangent and Cotangent Functions8.7        Graphing the Secant and Cosecant Functions 8.8        Applications of Trigonometric Functions 8.9        Modelling Trigonometric Functions 8.10      Inverse Trigonometric Functions Unit 9   Analytic Trigonometry 9.1        Introduction to Analytic Trigonometry9.2        Cofunction, Periodicity and Negative Angle Identities9.3        Addition and Subtraction Identities9.4        Double and Half-Angle Identitiees9.5        Product to Sum Identities 9.6        Solving Trigonometric Equations Algebraically9.7        Solving Trigonometric Equations with Identities Unit 10 Conic Sections 10.1        Introduction to Conic Sections     10.2        Parabolas 10.3        Parabolas Part II10.4        Circles10.5        Circles Part II 10.6        Ellipses  10.7        Ellipses Part II 10.8        Hyperbolas  10.9        Hyperbolas Part II 10.10      Solving Non Linear Systems 10.11      Parametric Equations  10.12      Parametric Equations of Conic Sections Unit 11   Polar Coordinates 11.1        Introduction to Polar Coordinates11.2        Converting Rectangular to Polar Coordinates11.3        Converting Polar to Rectangular Coordinates11.4        Polar Equations and Graphs11.5        Eccentricity of Conic Sections 11.6        Polar Equations of Conic Sections11.7        Complex Numbers in Polar Notation 11.8        Multiplication and Division with Polar Notation 11.9        DeMoivre's Theorem Unit 12  Series & Patterns 12.1       Introduction to Sequences and Series 12.2       Sequences & Series12.3       Arithmetic Sequences12.4       Arithmetic Series  12.5       Geometric Sequences 12.6       Finite Geometric Series  12.7       Infinite Geometric Series 12.8       Permutations and Combinations 12.9       Pascal's Triangle 12.10     Binomial Theorem Unit 13  Introductions to Calculus 13.1       Introduction to Calculus13.2       Limits and Continuity13.3       Limits Involving Infinity13.4       Slope of a Tangent Line 13.5       The Power Rule 13.6       The Product and Quotient Rules 13.7       The Chain Rule 13.8       Applications of Derivatives 13.9       Antiderivatives 13.10     Integrals and the Area Under a Curve