Curriculum

Geometry Package

  1. Points, Lines, and Planes

  2. Segments and their Measures

  3. Angles and their Measures

  4. Notions of Perimeter

  5. Logic

  6. Methods of Proof

  7. Parallelism

  8. Parallel Lines Cut by a Transversal

  9. Parallel lines in the coordinate plane

  10. Perpendicular lines in the coordinate plane

  11. Triangle Congruence Through SAS, SSS

  12. Triangle Congruence Through ASA,AAS

  13. Different types of triangles

  14. Triangle congruence in general

  15. Inequalities and Triangles

  16. General Polygons

  17. Different Classifications of Quadrilaterals(angles too)

  18. Areas of triangles and quadrilaterals

  19. Perimeter of triangles and quadrilaterals(or other polygons)

  20. Word Problems involving perimeter/area of triangles and quadrilaterals

  21. Solving triangles

  22. Problems involving congruence in general

  23. Translations

  24. Reflections

  25. Rotations

  26. Ratio and Proportion

  27. Similar Triangles

  28. Similar Polygons

  29. Showing Polygons are similar

  30. Word problems involving similar polygons

  31. The Pythagoreon Theorem

  32. Trigonometric Ratios

  33. Trigonometric Identities

  34. Solving right triangles using trigonometric identities

  35. Word Problems involving trigonometry

  36. The Unit Circle

  37. Defining the cosine and sine functions

  38. Tangents to Circles

  39. Arcs and Chords to Circles

  40. Inscribed angles

  41. Area of circles and sectors

  42. Word problems involving circles

  43. Equations of Circles in the coordinate plane

  44. Volume formulations

  45. Word problems involving volume formulations

  46. General notions of area

  47. The Distance Formula

  48. The Midpoint Formula

Precalculus Package  

  1. Operations with Functions

  2. Compositions of Functions

  3. Inverse Functions

  4. Inverse Functions with tables/graphs

  5. Review of Trigonometry from Geometry

  6. Special Trigonometric Values

  7. The Unit Circle and Geometry

  8. Trigonometric Identities

  9. Inverse Trig Functions

  10. Law of Sines and Law of Cosines

  11. Defining sine and cosine function

  12. Modeling with sinusoidal waves

  13. Angle sum identities

  14. Complex Numbers

  15. Operations with Complex Numbers

  16. The Complex Plane

  17. Solving Quadratic Equations with Complex Numbers

  18. Rational Functions

  19. End Behavior

  20. Intercepts and asymptotes of rational functions、

  21. Polynomial Long Division

  22. Graphs of Rational Functions

  23. Holes in graphs of rational functions

  24. Multiplying/Dividing rational expressions

  25. Adding/Subtracting Rational expressions

  26. Vectors

  27. Vector Addition and Scalar Multiplication

  28. Magnitude and Direction of Vectors

  29. Dot Product and Cross Product

  30. Vector Word Problems

  31. Matrices

  32. Limit Introduction

Prealgebra Package

  1. Addition/Subtraction of Negative Numbers

  2. Multiplication/Division with negative numbers

  3. Order of Operations

  4. Absolute Value

  5. Fractions

  6. Percents

  7. Conversion between Fractions, percents, and decimals

  8. Adding Rational Numbers

  9. Proportional Relationships

  10. Word Problems with Proportional Relationships

  11. Simplification via Combining Like Terms

  12. Simplification via distribution using the distributive property

  13. Simplification via factoring using the distributive property

  14. Equations Concepts

  15. Solving Basic Equations

  16. Solving Basic Inequalities

  17. Inequality Concepts

  18. Graphing Inequalities

  19. Area and Circumference of Circles

  20. Areas and Circumference of Other Shapes

  21. Missing Angle Problems

  22. Classification of Angles

  23. Volume and Surface Area Problems

  24. Basic Probability

Algebra 1 Subject List

  1. Writing Models

  2. Evaluating Algebraic Expressions

  3. Solving Linear Equations

  4. Exploring Concepts of solving equations

  5. Solving Quadratic Equations using any method

  6. Solving Quadratic Equations using completing the square

  7. Solving Quadratic Equations using the method of factoring

  8. Solving Quadratic Equations using the method of the quadratic formula

  9. Solving Linear Equations in conjunction with word problems

  10. Solving Quadratic Equations in conjunction with word problems

  11. Solving Inequalities with one variable

  12. Graphing Solutions to Inequalities(Coordinate Plane)

  13. Graphing Solutions to Inequalities(number line)

  14. Graphing in general(coordinate plane)

  15. Graphing Linear Functions(coordinate plane)

  16. Graphing Quadratic Functions(coordinate plane)

  17. Simplifying Algebraic Expressions Involving Addition/Subtraction

  18. Simplifying Algebraic Expressions Involving the Distributive Property

  19. Definitions associated with the set of real numbers

  20. The commutative/associative laws of the real numbers

  21. The distributive law and the real numbers

  22. Translating words to math and vice versa

  23. Solving Systems of Equations Algebraically via substitution

  24. Solving Systems of Equations Algebraically via elimination

  25. Solving Systems of Equations Graphically

  26. Solving Systems of Inequalities Algebraically

  27. Solving Systems of Inequalities Graphically

  28. Solving Systems of Equations Using Any Method

  29. Factoring Quadratic Expressions

  30. General Factoring

  31. Factoring General Trinomials

  32. Function Definitions

  33. Evaluation of Functions

  34. More general concepts with functions

  35. Determining information about linear functions based on graphs

  36. Determining information about quadratic functions based on graphs

  37. Definition of Exponents

  38. Simplifying Algebraic Expressions involving positive exponents

  39. Simplifying Algebraic Expressions involving integer exponents

  40. Definition of Radicals

  41. Simplifying Simple Expressions involving Radicals

  42. The Number Line

  43. The Coordinate Plane

  44. Absolute Value Definition

  45. Solving Equations with Absolute Value

  46. Proportions and Ratios

  47. Percents

  48. Practice Isolating Variables in Expressions(variables and numbers)

  49. Practice Isolating Variables in Expressions(only variables)

  50. Order of Operations(PEMDAS)

Calculus Subject List

  1. Review prior to starting Calculus

  2. Limits

  3. Evaluating Limits

  4. Limits at Infinity

  5. Continuity

  6. Limit Definition of Derivative

  7. Approximating Derivatives with Difference Quotient

  8. Continuity and Differentiability

  9. Derivatives of Basic Functions

  10. Derivatives of power functions

  11. Derivatives of products of functions

  12. Derivatives of quotients of functions

  13. Derivatives of compositions for functions

  14. Derivatives of trig functions

  15. Derivatives of inverse functions

  16. Derivatives of hyperbolic functions

  17. Derivatives of Exponential Functions

  18. Derivatives of sums of functions

  19. Increasing/Decreasing connection to derivatives

  20. First derivative sign charts

  21. Concavity connection to derivatives

  22. Inflection Points

  23. Second derivative sign chart

  24. Graphing functions using this information

Algebra 2 Subject List

  1. Complex Numbers

  2. Solving Quadratic equations involving Complex Numbers

  3. Graphs of Quadratic Functions and Complex Numbers

  4. Exponential Functions

  5. Graphing Exponential Functions

  6. Modeling with Exponential Functions

  7. Logarithms

  8. Logarithmic Functions

  9. Properties of Logarithms

  10. Graphing Logarithmic Functions

  11. Modeling with Logarithmic Functions

  12. Solving Exponential Equations using Logarithms

  13. Solving Exponential Equations without necessarily using logarithms

  14. Word problems involving solving exponential equations

  15. Word Problems involving solving logarithmic equations

  16. Solving Equations involving Fractional Exponents

  17. Functions Involving Fractional Exponents

  18. Graphing Functions Involving Fractional Exponents

  19. Simplifying expressions involving fractional exponents

  20. Determing Domain and Range from the graph of a function

  21. Determing Domain and Range from the formula of a function

  22. Determining the Domain and Range from how a function is defined

  23. General Polynomial Functions

  24. Graphing Polynomial Functions

  25. Determing information about polynomial function from its graph

  26. Solving higher order polynomial equations using factoring

  27. Solving higher order polynomial equations using synthetic division

  28. Solving higher order polynomial equations using the rational root theorem

  29. Rational Functions

  30. Determing information about the graph of a rational function from its formula

  31. Determining information about the formula of a rational function from its graph

  32. Oblique Asymptotes/Polynomial Division

  33. Word problems involving rational functions/Solving rational equations

  34. Simplifying Rational Expressions

  35. Absolute Value Inequalities

  36. Conic Sections and Hyperbola

  37. Basics of Probability

  38. Basics of Statistics

  39. Matrices

  40. Addition and Scalar Multiplication of Matrices

  41. Matrix Multiplication

  42. Sequences

  43. Arithmetic Sequences

  44. Summation Notation

  45. Geometric sums

  46. Geometric sequences

  47. Sums involving arithmetic sequences

  48. Infinite Sums

  49. Graphing Miscellaneous Functions