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Everest Math | Semper Altius Squared
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Algebra I
Unit 01: Linear Equations
1.1 Simple Equations
1.2 Two-Step Equations
1.3 Variables on Both Sides
1.4 Absolute Value Equations
1.5 Literal Equations
Unit 02: Linear Inequalities
2.1 Writing Linear Inequalities
2.2 Graphing Linear Inequalities
2.3 Inequalities with Multiplication and Division
2.4 Multi-Step Inequalities
2.5 Compound Inequalities
2.6 Absolute Value Inequalities
Algebra II
Unit 0
0.1 - Solve Absolute Value Equations and Inequalities
0.2 - Functions
0.3 - Graphing Absolute Value Functions
Unit 1 - Systems of Equations and Inequalities
1.1 Solve Linear Systems by Graphing
1.4 Solving Systems of Equations in Three Variables
3.1: Solve Linear Systems by Graphing
3.2 Substitution and Elimination
3.3 Graphing Systems of Linear Inequalities
3.5 Basic Matrix Operations
3.6 Matrix Multiplication
3.7 Discriminants and Cramer's Rule
3.8 Use Inverse Matrices to Solve Linear Systems
Unit 2 - Quadratic Functions and Factoring
2.01 - Graph Quadratic Functions in Standard Form
2.02 Graph Quadratic Functions in Vertex or Intercept Form
2.03 Solve Simple Quadratics using Factoring
2.04 - Solve Quadratics with a not equal 1 by Factoring
2.05 - Solve Quadratic Equations by Finding Square Roots
2.06 - Perform Operations with Complex Numbers
2.07 - Complete the Square
2.08 - Use the Quadratic Formula and the Discriminant
2.09 - Graph and Solve Quadratic Inequalities
2.10 - Write Quadratic Functions and Models
Unit 3 - Polynomials
5.1 - Properties of Exponents
5.2 - Graph Polynomial Functions
5.3 - Polynomial Arithmetic
5.4 - Factor and Solve Polynomials
5.5 - The Remainder and Factor Theoreams
5.6 - Finding Rational Zeros
5.7 - FTA
5.8 - Analyze Polynomial Graphs
5.9 - Write Functions and Models
Unit 4 - Rational Functions
4.1 - Inverse Variation
4.2 - Graph Simple Rational Functions
4.3 Notes - Graphing Rational Functions and End Behavior
4.4 - Simplifying Rational Expressions
4.5 - Adding and Subtracting Rational Expressions
4.6 - Solving Rational Equations
Unit 5 - Trigonometry
5.1 - Use Trig with Right Angles
5.2 - Obtuse Angles and Radians
5.3 - Trig Functions of any Angle
5.4 - Inverse Trig Functions
5.5 - Law of Sines
5.6 - Law of Cosines
Unit 6 - Rational Exponents and Radical Functions
6.1 - nth Roots and Rational Exponents
6.2 - Properties of Rational Exponents
6.3 - Perform Functions Operations and Composition
6.4 - Use Inverse Functions
6.5 - Graphing Radical Functions
6.6 - Solve Radical Equations
Unit 7 - Exponential and Logarithmic Functions
7.1 - Graph Exponential Growth Functions
7.2 - Graph Exponential Decay Functions
7.3 - Use Functions Involving e
7.4 - Evaluate and Graph Logarithms
7.5 - Properties of Logarithms
7.6 - Solve Exponential and Logarithmic Equations
7.7 - Write Exponential Functions
Unit 8 - Counting and Probability
8.1 - Counting Principle and Permutations
8.2 - Combinations and Binomial Theorem
8.3 - Define and Use Probability
8.4 - Disjoint and Overlapping Events
8.5 - Independent and Dependent Events
8.6 - Binomial Probabilities
Unit 9 - Conic Sections
9.1 - Apply the Distance and Midpoint Formulas
9.2 - Graph and Write Equations of Parabolas
9.3 - Graph and Write Equations of Circles
9.4 - Graph and Write Equations of Ellipses
9.5 - Graph and Write Equations of Hyperbolas
9.6 - Conics not Centered at the Origin
9.7 - Solve Quadratic Systems
AP Calculus AB
Unit 1 - Limits
1.1 - Finding Limits
1.2 - Limits of Composite Functions
1.3 - Continuity
1.4 - Infinite Limits
Unit 2 - Derivative
2.1 Intro to Differentiation
2.2 Basic Derivative Rules
2.3 Product and Quotient Rules
2.4 Chain Rule
2.5 Derivative of Natural Log and e^x
2.6 Implicit Differentiation
2.7 Related Rates
Unit 3 - Applications of Derivatives
3.1 - Extrema on an Interval
3.2 - Rolle's Theorem and the MVT
3.3 - Increasing, Decreasing, Concavity and Derivative Tests
3.4 - Particle Motion
3.5 - Linear Approximations
3.6 - Optimization
Unit 4 - Integration
4.1: Definite Integrals and Applications
4.2 Properties of Integration and MVT for Integration
4.3 Riemann Sums
4.4 Limits of Riemann Sums
4.5 FTC part 1 (existence of antiderivative)
4.6 FTC Part 2 (Definite Integral Computation)
4.7 Integration by Substitution
4.8 Antiderivatives
Unit 5 - Transcendentals
5.1: Derivatives and Integrals of Exponential and Logarithmic Functions
5.2: Inverse Functions and Derivatives
5.3: Derivatives of Inverse Trig Functions
5.4: Integrals Involving Inverse Trig Functions
Unit 6 - Introduction to Differential Equations
6.1 - Separation of Variables
6.2: Slope Fields
Unit 7 - Solids of Revolution
7.1: Area between Curves
7.2: Solids of Revolution
7.3: Solids with Known Cross Sections
AP Calculus BC
Midterm
Unit 01: Limits
1.1 Finding Limits
1.2 Limits of Composite Functions
1.3 Continuity
1.4 Infinite Limits
Unit 02: Derivatives
2.1 Intro to Differentiation
2.2 Basic Derivative Rules
2.3 Product and Quotient Rule
2.4 Chain Rule
2.5 Derivative of Natural Log and e^x
2.6 Implicit Differentiation
2.7 Related Rates
Unit 03: Applications of Derivatives
3.1 Extrema on Interval
3.2 Rolle's and Mean Value Theorem
3.3 Concavity and Derivative Tests
3.4 Particle Motion
3.5 Linear Approximation
3.7 Optimization
3.8 Newton's Method
3.8 Newton's Method
Unit 04: Integration
4.1 Definite Integrals and Applications
4.2 Properties of Integration and MVT for Integration
4.3 Riemann Sums
4.4 Limits of Riemann Sums
4.5 FTC part 1 (existence of antiderivative)
4.6 FTC Part 2 (Definite Integral Computation)
4.7 Integration by Substitution
4.8 Integration by Parts
4.9 Antiderivatives
Unit 05: Transcendentals
5.1 Integration and Derivatives using Exponential and Logarithmic Functions
5.2 Inverse Functions
5.3 Derivative Trig Inverse
5.4 Inverse Trig Integration
Unit 06: Intro. Diff. Eq.
6.1 Separation of Variables
6.2 Slope Fields
6.3 Euler's Method
6.4 Logistic Functions
Unit 07: Integration Applications
7.1 Area between Curves
7.2 Solids of Revolution
7.3 Solids with Known Cross Sections
7.4 Arc Length
Unit 08: Advanced Integration Techniques
8.1 Limits and l'Hospital's Rule
8.2 Improper Integrals
8.3 Integration by Partial Fractions
Unit 09: Series
9.1 Constructing Taylor Polynomials
9.2 Infinite Geometric Series
9.3 Integral Convergence Test
9.4 Comparison Tests
9.5 Alternating Series and Absolute Convergence
9.6 Ratio and Root Tests
9.7 Power Series and Intervals of Convergence
9.8 Series Error Bounds
Unit 10: Parametric and Polar Equations
10.1: Parametric Equations
10.2 Parametric Equations and Derivatives
10.3 Parametric Two Dimensional Motion
10.4 Polar Equations
10.5 Particle on Polar Curve
Useful Links
Geometry
00: Algebra Review
0.1: Equations of Lines
0.2 Factoring
3.4-3.5 Equations of Lines
01: Basics of Geometry
1.1 Points, Lines, and Planes
1.2 Segments
1.3 Classifying Angles
1.4 Pairs of Angles
Handouts
Test Review
02: Reasoning & Logic
2.1 Inductive Reasoning
2.2 Logical Statements
2.3 Laws of Detachment and Syllogism
2.4 Properties and Postulates
2.5 Logical Systems
2.6 Introduction to Proofs
Chapter Review
Handouts
03: Lines and Angles
3.1 Lines Cut by Transversal
3.2 Parallel Lines & Transversals
3.3 Angles of Triangles
3.4 Exterior Angles
Chapter Review
Handouts
04: Triangle Congruence and Constructions
4.1: Compass and Straight Edge Constructions
4.2 SSS and CPCTC
4.3 SAS (not SSA)
4.4: Two Angles and One Side
4.5 Base Angles
4.6 Construction Proofs
Chapter 4 Review
Handouts
05 Relationships within Triangles
5.1 Circumcenter
5.2 Incenter
5.3 Centroid
5.5 Triangle Inequality
5.6 Hinge Theorem
Chapter 5 Review
Handouts
06: Similarity
6.1 Similar Figures
6.2 AA Postulate
6.3 SSS and SAS Similarity
6.4 Proportionality Theorems and Proofs
6.5 Similar Right Triangles
Chapter Review
Handouts
07: Transformations
7.1 Translations, Isometries, Vectors
7.2: Reflections
7.3: Rotations
7.4 Dilations
7.5 Composite Transformations
Handouts
08: Right Triangle Trigonometry
8.0 Simplify Radicals
8.1 Pythagorean Theorem
8.2 Pythagorean Converse
8.3 Special Right Triangles
8.4 Tangent Ratio
8.5 Sine and Cosine Ratio
8.6 Inverse Trig Ratios
Handouts
09: Polygons and Quadrilaterals
9.1 Properties of Parallelograms
9.2 Rhombus, Rectangle, Square
9.3 Kites and Trapezoids
Chapter Review
Notes and Assignments
10: Angles and Areas of Polygons
10.1 Interior and Exterior Sums
10.2 Area of Triangles and Parallelograms
10.3 Area of Rhombi and Kites
10.4 Area of Trapezoids
10.5: Inscribed Polygon, Central Angles, Radius, Apothem
10.6 Area of Regular Polygons
10.7 Area of Similar Figures
Chapter Review
11: Circumference and Area
11.1: Two Special Ratios
11.2 Arc Measures
11.3 Arc Length
11.4 Sector Area
11.5: Special Areas
Chapter Review
12: Circles, Angles, Chords
12.1: Tangents and Secants
12.2 Properties of Chords
12.3 Inscribed Angles and Polygons
12.4 Angles Inside and Outside of Circles
12.5: Other Lengths of Circles
Handouts
13: Three-Dimensional Figures
13.3 Surface Area of Prism and Cylinder
14: Analytic Geometry
1.3 Distance and Midpoint
11.6 Equations of Circles
Chapter Review
Midterm
Semester 2 Review
Syllabus
Precalculus
Syllabus, Yearly Plan, Lesson Plans
Unit 00: Review
0.1: Inequalities
0.2: Distance, Circle, Midpoint
0.3: Solving Inequalities
0.4: Lines in a Plane
0.5: Quadratics and Absolute Value
0.6: Complex Numbers
0.7: Quadratic and Absolute Value Inequalities
1.1 Solving Quadratics
Unit 01: Functions and Graphs
1.1 Functions
1.2: Domain and Range
1.3 Analyzing Functions
1.4 Function Compositions
1.5 Function Inverses
1.6 Function Transformations
1.7 Modeling and Regression
Handouts
Unit 02: Trigonometric Functions
2.1 Angles and Radian
2.2 Special Angles
2.3 Unit Circle
2.4 Sinusoids
2.5 Applications of Sinusoids and Trigonometry
2.6 Tangent Secant and Cosec
2.7 Inverse Trig Functions
Handouts
Test Review
Unit 03: Applications of Trigonometry
3.1 Vectors
3.2 Force and Work
3.3 Parametric Equations
3.4 Applications of Parametric
3.5 Polar Coordinates
3.6 Polar Equations
3.7 Law of Sines
3.8 Law of Cosines
Unit Review
Unit 04: Analytical Trigonometry
4.1 Trig Identities
4.2 Proving Trig. Identities
4.3 Angle Sum and Difference
4.4 Multiple of Angles
Handouts
Unit 05: Polynomials
5.1 Quadratics in standard and vertex forms
5.2 Power Functions
5.3 Graph Behavior
5.4 Rational Zeros and Synthetic Division
5.5: The FTA
5.6 Rational Functions
5.8: Sign Charts and Inequalities
Handouts
Test Review
Unit 06: Exponential and Logistics
6.1 Exponential Equations
6.2 Logarithms
6.3 Rules of Logarithms
6.4 Exponential and Log Functions
6.5 Applications of Exponential Functions
6.6 Euler's Number and Natural Log
6.7 Finance Mathematics
6.8 Logistic Functions
Chapter Review
Unit 07: Introduction to Calculus
7.1 Limits using Algebraic Methods
7.2 Instantaneous Rate of Change
7.3 Derivative Applications
7.4 Rules of Limits
7.5 The Definite Integral
7.6 Applications of Definite Integrals
7.7 Limits of Composite Functions
Unit 08: Discrete Mathematics
8.1 Permutations & Combinations (Review)
8.2 Binomial Theorem and Applications
8.3 Factorial Identities
8.4 Sequences
8.5 Series
8.6 Mathematical Induction
8.7 Conditional Probability
Unit 09: Conics
Technology Tutorials
Desmos Plot
GeoGebra Scatter Plot
Everest Math | Semper Altius Squared
6.4 Proportionality Theorems and Proofs
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