Online courses directory (237)

Language and Notation of the Circle. Circles: Radius, Diameter and Circumference. Length of an arc that subtends a central angle. Finding central angle measure given arc length. Parts of a Circle. Area of a Circle. Area of a sector given a central angle. Inscribed and Central Angles. Perpendicular Radius Bisects Chord. Right Triangles Inscribed in Circles (Proof). Area of Inscribed Equilateral Triangle (some basic trig used). Language and Notation of the Circle. Circles: Radius, Diameter and Circumference. Length of an arc that subtends a central angle. Finding central angle measure given arc length. Parts of a Circle. Area of a Circle. Area of a sector given a central angle. Inscribed and Central Angles. Perpendicular Radius Bisects Chord. Right Triangles Inscribed in Circles (Proof). Area of Inscribed Equilateral Triangle (some basic trig used).

If you can take one figure and flip, shift and rotate (not resize) it to be identical to another figure, then the two figures are congruent. This topic explores this foundational idea in geometry. Congruent Triangles and SSS. SSS to Show a Radius is Perpendicular to a Chord that it Bisects. Other Triangle Congruence Postulates. Two column proof showing segments are perpendicular. Finding Congruent Triangles. Congruency postulates. More on why SSA is not a postulate. Perpendicular Radius Bisects Chord. Congruent Triangle Proof Example. Congruent Triangle Example 2. Congruent triangles 1. Congruent triangles 2. Congruent legs and base angles of Isosceles Triangles. Equilateral Triangle Sides and Angles Congruent. Equilateral and Isosceles Example Problems. Triangle types. Triangle angles 1. Another Isosceles Example Problem. Example involving an isosceles triangle and parallel lines. Figuring out all the angles for congruent triangles example. Basic Triangle Proofs Module Example. Basic Triangle Proofs Module Example 2. Basic triangle proofs. Fill-in-the-blank triangle proofs example 1. Fill-in-the-blank triangle proofs example 2. Fill-in-the-blank triangle proofs. Wrong statements in triangle proofs example 1. Wrong statements in triangle proofs. Problem involving angle derived from square and circle. Congruent Triangles and SSS. SSS to Show a Radius is Perpendicular to a Chord that it Bisects. Other Triangle Congruence Postulates. Two column proof showing segments are perpendicular. Finding Congruent Triangles. Congruency postulates. More on why SSA is not a postulate. Perpendicular Radius Bisects Chord. Congruent Triangle Proof Example. Congruent Triangle Example 2. Congruent triangles 1. Congruent triangles 2. Congruent legs and base angles of Isosceles Triangles. Equilateral Triangle Sides and Angles Congruent. Equilateral and Isosceles Example Problems. Triangle types. Triangle angles 1. Another Isosceles Example Problem. Example involving an isosceles triangle and parallel lines. Figuring out all the angles for congruent triangles example. Basic Triangle Proofs Module Example. Basic Triangle Proofs Module Example 2. Basic triangle proofs. Fill-in-the-blank triangle proofs example 1. Fill-in-the-blank triangle proofs example 2. Fill-in-the-blank triangle proofs. Wrong statements in triangle proofs example 1. Wrong statements in triangle proofs. Problem involving angle derived from square and circle.

Understanding the purpose, notation, and building blocks of geometry. Euclid as the Father of Geometry. Language and Notation of Basic Geometry. Lines, Line Segments, and Rays. Identifying Rays. Identifying Parallel and Perpendicular Lines.

Conditional statements and deductive reasoning. Conditional statements exercise examples. Logical argument and deductive reasoning exercise example. Conditional statements and deductive reasoning. Conditional statements exercise examples. Logical argument and deductive reasoning exercise example.

A broad set of tutorials covering perimeter area and volume with and without algebra. Perimeter and Area Basics. Area and Perimeter. Perimeter of a Polygon. Perimeter of a shape. Perimeter 1. Finding dimensions given perimeter. Area 1. Finding dimensions given area. Perimeter and Area Basics. Triangle Area Proofs. Area of triangles. Interesting Perimeter and Area Problems. Area of Diagonal Generated Triangles of Rectangle are Equal. Area of an equilateral triangle. Area of shaded region made from equilateral triangles. Shaded areas. Challenging Perimeter Problem. Triangle inqequality theorem. Triangle inequality theorem. Koch Snowflake Fractal. Area of an equilateral triangle. Area of Koch Snowflake (part 1) - Advanced. Area of Koch Snowflake (part 2) - Advanced. Heron's Formula. Heron's formula. Part 1 of Proof of Heron's Formula. Part 2 of the Proof of Heron's Formula. Circles: Radius, Diameter and Circumference. Parts of a Circle. Radius diameter and circumference. Area of a Circle. Area of a circle. Quadrilateral Overview. Quadrilateral Properties. Area of a Parallelogram. Area of parallelograms. Area of a trapezoid. Area of a kite. Area of trapezoids, rhombi, and kites. Perimeter of a Polygon. Perimeter and Area of a Non-Standard Polygon. How we measure volume. Measuring volume with unit cubes. Volume with unit cubes. Measuring volume as area times length. Volume of a rectangular prism or box examples. Volume 1. Volume word problem example. Volume word problems. Solid Geometry Volume. Cylinder Volume and Surface Area. Volume of a Sphere. Solid geometry. Perimeter and Area Basics. Area and Perimeter. Perimeter of a Polygon. Perimeter of a shape. Perimeter 1. Finding dimensions given perimeter. Area 1. Finding dimensions given area. Perimeter and Area Basics. Triangle Area Proofs. Area of triangles. Interesting Perimeter and Area Problems. Area of Diagonal Generated Triangles of Rectangle are Equal. Area of an equilateral triangle. Area of shaded region made from equilateral triangles. Shaded areas. Challenging Perimeter Problem. Triangle inqequality theorem. Triangle inequality theorem. Koch Snowflake Fractal. Area of an equilateral triangle. Area of Koch Snowflake (part 1) - Advanced. Area of Koch Snowflake (part 2) - Advanced. Heron's Formula. Heron's formula. Part 1 of Proof of Heron's Formula. Part 2 of the Proof of Heron's Formula. Circles: Radius, Diameter and Circumference. Parts of a Circle. Radius diameter and circumference. Area of a Circle. Area of a circle. Quadrilateral Overview. Quadrilateral Properties. Area of a Parallelogram. Area of parallelograms. Area of a trapezoid. Area of a kite. Area of trapezoids, rhombi, and kites. Perimeter of a Polygon. Perimeter and Area of a Non-Standard Polygon. How we measure volume. Measuring volume with unit cubes. Volume with unit cubes. Measuring volume as area times length. Volume of a rectangular prism or box examples. Volume 1. Volume word problem example. Volume word problems. Solid Geometry Volume. Cylinder Volume and Surface Area. Volume of a Sphere. Solid geometry.

This topic introduces the basic conceptual tools that underpin our journey through Euclidean geometry. These include the ideas of points, lines, line segments, rays, and planes. Euclid as the Father of Geometry. Language and Notation of Basic Geometry. Lines, Line Segments, and Rays. Recognizing rays lines and line segments. Specifying planes in three dimensions. Points, lines, and planes. Language and Notation of the Circle. The Golden Ratio. Identifying Rays. Measuring segments. Measuring segments. Congruent segments. Congruent segments. Segment addition. Segment addition. Algebraic midpoint of a segment exercise. Midpoint of a segment. Euclid as the Father of Geometry. Language and Notation of Basic Geometry. Lines, Line Segments, and Rays. Recognizing rays lines and line segments. Specifying planes in three dimensions. Points, lines, and planes. Language and Notation of the Circle. The Golden Ratio. Identifying Rays. Measuring segments. Measuring segments. Congruent segments. Congruent segments. Segment addition. Segment addition. Algebraic midpoint of a segment exercise. Midpoint of a segment.

Identifying types of quadrilaterals, finding measurements, and applying and proving postulates. Quadrilateral Overview. Quadrilateral Properties. Area of a Parallelogram. Area of a Regular Hexagon. Sum of Interior Angles of a Polygon. Sum of the exterior angles of convex polygon. Proof - Opposite Angles of Parallelogram Congruent. Proof - Opposite Sides of Parallelogram Congruent. Proof - Diagonals of a Parallelogram Bisect Each Other. Rhombus Diagonals. Proof - Rhombus Diagonals are Perpendicular Bisectors. Proof - Rhombus Area Half Product of Diagonal Length. Area of a Parallelogram. Area of a Regular Hexagon. Problem involving angle derived from square and circle. 2003 AIME II Problem 7. CA Geometry: Deducing Angle Measures.

Not all things with four sides have to be squares or rectangles! We will now broaden our understanding of quadrilaterals!. Quadrilateral Overview. Quadrilateral Properties. Proof - Opposite Sides of Parallelogram Congruent. Proof - Diagonals of a Parallelogram Bisect Each Other. Proof - Opposite Angles of Parallelogram Congruent. Proof - Rhombus Diagonals are Perpendicular Bisectors. Proof - Rhombus Area Half Product of Diagonal Length. Area of a Parallelogram. Whether a Special Quadrilateral Can Exist. Rhombus Diagonals. Quadrilateral Overview. Quadrilateral Properties. Proof - Opposite Sides of Parallelogram Congruent. Proof - Diagonals of a Parallelogram Bisect Each Other. Proof - Opposite Angles of Parallelogram Congruent. Proof - Rhombus Diagonals are Perpendicular Bisectors. Proof - Rhombus Area Half Product of Diagonal Length. Area of a Parallelogram. Whether a Special Quadrilateral Can Exist. Rhombus Diagonals.

Triangles are not always right (although they are never wrong), but when they are it opens up an exciting world of possibilities. Not only are right triangles cool in their own right (pun intended), they are the basis of very important ideas in analytic geometry (the distance between two points in space) and trigonometry. Pythagorean Theorem. The Pythagorean theorem intro. Pythagorean Theorem 1. Pythagorean Theorem 2. Pythagorean Theorem 3. Pythagorean theorem. Introduction to the Pythagorean Theorem. Pythagorean Theorem II. Garfield's proof of the Pythagorean Theorem. Bhaskara's proof of Pythagorean Theorem. Pythagorean Theorem Proof Using Similarity. Another Pythagorean Theorem Proof. 30-60-90 Triangle Side Ratios Proof. 45-45-90 Triangle Side Ratios. 30-60-90 Triangle Example Problem. Special right triangles. Area of a Regular Hexagon. 45-45-90 Triangles. Intro to 30-60-90 Triangles. 30-60-90 Triangles II. Pythagorean Theorem. The Pythagorean theorem intro. Pythagorean Theorem 1. Pythagorean Theorem 2. Pythagorean Theorem 3. Pythagorean theorem. Introduction to the Pythagorean Theorem. Pythagorean Theorem II. Garfield's proof of the Pythagorean Theorem. Bhaskara's proof of Pythagorean Theorem. Pythagorean Theorem Proof Using Similarity. Another Pythagorean Theorem Proof. 30-60-90 Triangle Side Ratios Proof. 45-45-90 Triangle Side Ratios. 30-60-90 Triangle Example Problem. Special right triangles. Area of a Regular Hexagon. 45-45-90 Triangles. Intro to 30-60-90 Triangles. 30-60-90 Triangles II.

Similar Triangle Basics. Similarity Postulates. Similar triangles 1. Similar Triangle Example Problems. Similar triangles 2. Similarity Example Problems. Solving similar triangles 1. Similarity example where same side plays different roles. Challenging Similarity Problem. Finding Area Using Similarity and Congruence. Similar triangles. Similar triangles (part 2). Similar Triangle Basics. Similarity Postulates. Similar triangles 1. Similar Triangle Example Problems. Similar triangles 2. Similarity Example Problems. Solving similar triangles 1. Similarity example where same side plays different roles. Challenging Similarity Problem. Finding Area Using Similarity and Congruence. Similar triangles. Similar triangles (part 2).

You probably like triangles. You think they are useful. They show up a lot. What you'll see in this topic is that they are far more magical and mystical than you ever imagined!. Circumcenter of a Triangle. Circumcenter of a Right Triangle. Three Points Defining a Circle. Area Circumradius Formula Proof. 2003 AIME II Problem 7. Point Line Distance and Angle Bisectors. Incenter and incircles of a triangle. Inradius Perimeter and Area. Angle Bisector Theorem Proof. Angle Bisector Theorem Examples. Angle bisector theorem. Triangle Medians and Centroids. Triangle Medians and Centroids (2D Proof). Medians divide into smaller triangles of equal area. Exploring Medial Triangles. Proving that the Centroid is 2-3rds along the Median. Median Centroid Right Triangle Example. Proof - Triangle Altitudes are Concurrent (Orthocenter). Common Orthocenter and Centroid. Review of Triangle Properties. Euler Line. Euler's Line Proof. Constructing a perpendicular bisector using a compass and straightedge. Constructing a perpendicular line using a compass and straightedge. Constructing an angle bisector using a compass and straightedge. Compass Constructions. Circumcenter of a Triangle. Circumcenter of a Right Triangle. Three Points Defining a Circle. Area Circumradius Formula Proof. 2003 AIME II Problem 7. Point Line Distance and Angle Bisectors. Incenter and incircles of a triangle. Inradius Perimeter and Area. Angle Bisector Theorem Proof. Angle Bisector Theorem Examples. Angle bisector theorem. Triangle Medians and Centroids. Triangle Medians and Centroids (2D Proof). Medians divide into smaller triangles of equal area. Exploring Medial Triangles. Proving that the Centroid is 2-3rds along the Median. Median Centroid Right Triangle Example. Proof - Triangle Altitudes are Concurrent (Orthocenter). Common Orthocenter and Centroid. Review of Triangle Properties. Euler Line. Euler's Line Proof. Constructing a perpendicular bisector using a compass and straightedge. Constructing a perpendicular line using a compass and straightedge. Constructing an angle bisector using a compass and straightedge. Compass Constructions.

Let's think more visually about things like shifts, rotations, scaling and symmetry. Axis of symmetry. Translations of polygons. Determining a translation for a shape. Rotation of polygons example. Axis of symmetry. Translations of polygons. Determining a translation for a shape. Rotation of polygons example.

Sal does the 80 problems from the released questions from the California Standards Test for Geometry. Basic understanding of Algebra I necessary. Interesting Perimeter and Area Problems. Challenging Perimeter Problem. CA Geometry: deductive reasoning. CA Geometry: Proof by Contradiction. CA Geometry: More Proofs. CA Geometry: Similar Triangles 1. CA Geometry: Similar Triangles 2. CA Geometry: More on congruent and similar triangles. CA Geometry: Triangles and Parallelograms. CA Geometry: Area, Pythagorean Theorem. CA Geometry: Area, Circumference, Volume. CA Geometry: Pythagorean Theorem, Area. CA Geometry: Exterior Angles. CA Geometry: Deducing Angle Measures. CA Geometry: Pythagorean Theorem, Compass Constructions. CA Geometry: Compass Construction. CA Geometry: Basic Trigonometry. CA Geometry: More Trig. CA Geometry: Circle Area Chords Tangent. CA Geometry: Secants and Translations. Interesting Perimeter and Area Problems. Challenging Perimeter Problem. CA Geometry: deductive reasoning. CA Geometry: Proof by Contradiction. CA Geometry: More Proofs. CA Geometry: Similar Triangles 1. CA Geometry: Similar Triangles 2. CA Geometry: More on congruent and similar triangles. CA Geometry: Triangles and Parallelograms. CA Geometry: Area, Pythagorean Theorem. CA Geometry: Area, Circumference, Volume. CA Geometry: Pythagorean Theorem, Area. CA Geometry: Exterior Angles. CA Geometry: Deducing Angle Measures. CA Geometry: Pythagorean Theorem, Compass Constructions. CA Geometry: Compass Construction. CA Geometry: Basic Trigonometry. CA Geometry: More Trig. CA Geometry: Circle Area Chords Tangent. CA Geometry: Secants and Translations.

GMAT Math: 1. GMAT Math: 2. GMAT Math: 3. GMAT Math: 4. GMAT Math: 5. GMAT: Math 6. GMAT: Math 7. GMAT: Math 8. GMAT: Math 9. GMAT: Math 10. GMAT: Math 11. GMAT: Math 12. GMAT: Math 13. GMAT: Math 14. GMAT: Math 15. GMAT: Math 16. GMAT: Math 17. GMAT: Math 18. GMAT: Math 19. GMAT Math 20. GMAT Math 21. GMAT Math 22. GMAT Math 23. GMAT Math 24. GMAT Math 25. GMAT Math 26. GMAT Math 27. GMAT Math 28. GMAT Math 29. GMAT Math 30. GMAT Math 31. GMAT Math 32. GMAT Math 33. GMAT Math 34. GMAT Math 35. GMAT Math 36. GMAT Math 37. GMAT Math 38. GMAT Math 39. GMAT Math 40. GMAT Math 41. GMAT Math 42. GMAT Math 43. GMAT Math 44. GMAT Math 45. GMAT Math 46. GMAT Math 47. GMAT Math 48. GMAT Math 49. GMAT Math 50. GMAT Math 51. GMAT Math 52. GMAT Math 53. GMAT Math 54.

Questions from previous IIT JEEs. IIT JEE Trigonometry Problem 1. IIT JEE Perpendicular Planes (Part 1). IIT JEE Perpendicular Plane (part 2). IIT JEE Complex Root Probability (part 1). IIT JEE Complex Root Probability (part 2). IIT JEE Position Vectors. IIT JEE Integral Limit. IIT JEE Algebraic Manipulation. IIT JEE Function Maxima. IIT JEE Diameter Slope. IIT JEE Hairy Trig and Algebra (part 1). IIT JEE Hairy Trig and Algebra (Part 2). IIT JEE Hairy Trig and Algebra (Part 3). IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). IIT JEE Differentiability and Boundedness. IIT JEE Integral with Binomial Expansion. IIT JEE Symmetric and Skew-Symmetric Matrices. IIT JEE Trace and Determinant. IIT JEE Divisible Determinants. IIT JEE Circle Hyperbola Intersection. IIT JEE Circle Hyperbola Common Tangent Part 1. IIT JEE Circle Hyperbola Common Tangent Part 2. IIT JEE Circle Hyperbola Common Tangent Part 3. IIT JEE Circle Hyperbola Common Tangent Part 4. IIT JEE Circle Hyperbola Common Tangent Part 5. IIT JEE Trigonometric Constraints. IIT JEE Trigonometric Maximum. Vector Triple Product Expansion (very optional). IIT JEE Lagrange's Formula. Tangent Line Hyperbola Relationship (very optional). 2010 IIT JEE Paper 1 Problem 50 Hyperbola Eccentricity. Normal vector from plane equation. Point distance to plane. Distance Between Planes. Complex Determinant Example. Series Sum Example. Trigonometric System Example. Simple Differential Equation Example. IIT JEE Trigonometry Problem 1. IIT JEE Perpendicular Planes (Part 1). IIT JEE Perpendicular Plane (part 2). IIT JEE Complex Root Probability (part 1). IIT JEE Complex Root Probability (part 2). IIT JEE Position Vectors. IIT JEE Integral Limit. IIT JEE Algebraic Manipulation. IIT JEE Function Maxima. IIT JEE Diameter Slope. IIT JEE Hairy Trig and Algebra (part 1). IIT JEE Hairy Trig and Algebra (Part 2). IIT JEE Hairy Trig and Algebra (Part 3). IIT JEE Complex Numbers (part 1). IIT JEE Complex Numbers (part 2). IIT JEE Complex Numbers (part 3). IIT JEE Differentiability and Boundedness. IIT JEE Integral with Binomial Expansion. IIT JEE Symmetric and Skew-Symmetric Matrices. IIT JEE Trace and Determinant. IIT JEE Divisible Determinants. IIT JEE Circle Hyperbola Intersection. IIT JEE Circle Hyperbola Common Tangent Part 1. IIT JEE Circle Hyperbola Common Tangent Part 2. IIT JEE Circle Hyperbola Common Tangent Part 3. IIT JEE Circle Hyperbola Common Tangent Part 4. IIT JEE Circle Hyperbola Common Tangent Part 5. IIT JEE Trigonometric Constraints. IIT JEE Trigonometric Maximum. Vector Triple Product Expansion (very optional). IIT JEE Lagrange's Formula. Tangent Line Hyperbola Relationship (very optional). 2010 IIT JEE Paper 1 Problem 50 Hyperbola Eccentricity. Normal vector from plane equation. Point distance to plane. Distance Between Planes. Complex Determinant Example. Series Sum Example. Trigonometric System Example. Simple Differential Equation Example.

This course provides a brief review of introductory algebra topics. Topics to be covered include integer operations, order of operations, perimeter and area, fractions and decimals, scientific notation, ratios and rates, conversions, percents, algebraic expressions, linear equations, the Pythagorean theorem, and graphing.

Statistics is about extracting meaning from data. In this class, we will introduce techniques for visualizing relationships in data and systematic techniques for understanding the relationships using mathematics.

Improve your understanding of data and learn how to develop graphs and charts so you can use this information to make better decisions.

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.

Course Format

This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

• A complete set of Lecture Videos by Professor Gilbert Strang.
• Summary Notes for all videos along with suggested readings in Prof. Strang's textbook Linear Algebra.
• Problem Solving Videos on every topic taught by an experienced MIT Recitation Instructor.
• Problem Sets to do on your own with Solutions to check your answers against when you're done.
• A selection of Java® Demonstrations to illustrate key concepts.
• A full set of Exams with Solutions, including review material to help you prepare.