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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 Functions
1.2       Domain of a Function and Interval Notation
1.3       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 Polynomials
2.2       Finding a Polynomial Given the Roots
2.3       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 Functions
3.2       Graphing Rational Functions
3.3       Graphing Rational Functions Part II
3.4       Slant Asymptotes
3.5       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 Logarithms
4.5       Exponential/Logarithmic Inverse Property  

4.6       Natural Exponentials & Logarithms

4.7       Solving Exponential Equations
4.8       Solving Logarithmic Equations
4.9       Fitting Log Functions to Data

Unit 5  Vectors

5.1       Introduction to Vectors
5.2       Vectors in Two Dimensions
5.3       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 Complex
7.2       Adding and Subtracting Complex Numbers 
7.3       Multiplying Complex Numbers 

7.4       Complex Conjugate & Dividing
7.5       The Complex Plane
7.6       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 Functions
8.2        Radian Measure 
8.3        Standard Position & Reference Angles
8.4        Special Triangles and Exact Ratios
8.5        Graphing the Sine and Cosine Functions
8.6        Graphing the Tangent and Cotangent Functions
8.7        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 Trigonometry
9.2        Cofunction, Periodicity and Negative Angle Identities
9.3        Addition and Subtraction Identities
9.4        Double and Half-Angle Identitiees
9.5        Product to Sum Identities 
9.6        Solving Trigonometric Equations Algebraically
9.7        Solving Trigonometric Equations with Identities

 

Unit 10 Conic Sections

10.1        Introduction to Conic Sections     
10.2        Parabolas 
10.3        Parabolas Part II
10.4        Circles
10.5        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 Coordinates
11.2        Converting Rectangular to Polar Coordinates
11.3        Converting Polar to Rectangular Coordinates
11.4        Polar Equations and Graphs
11.5        Eccentricity of Conic Sections 
11.6        Polar Equations of Conic Sections
11.7        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 & Series
12.3       Arithmetic Sequences
12.4       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 Calculus
13.2       Limits and Continuity
13.3       Limits Involving Infinity
13.4       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