Year 12 Math's Specialist

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Year 12 Math's Specialist

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Maths Specialist

116 Lessons

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Year 12 Math's Specialist

1. Complex Numbers

22 Lessons

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1. Complex Solutions of the Quadratic Equation

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2. Representing Complex Numbers

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3. Cartesian Form

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4. Polar Form

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5. Complex Conjugate Pairs

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6. Cartesian Form Operations

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7. Polar Form Operations

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8. Exponential Form Operations

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9. From Complex Solutions to Quadratic Equation

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10. Locus of Points and Graphs

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11. Cartesian Equation from Locus of Points

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12. Vectors

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13. Circles

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14. Max/Min Circle Problems

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15. Perpendicular Bisector

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16. Line Between two Complex Numbers

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17. Distance Between Points

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18. Graphs of Vectors in Polar Form

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19. De Moivre's Theorem

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20. Trigonometric Identities Using De Moivre's Theorem

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21. Z Transformations

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22. Questions

2. Functions and Curve Sketching

16 Lessons

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1. Domain and Range of Functions

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2. Composite Functions

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3. Domain and Range of Composite Functions

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4. Inverse Functions

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5. Graphing Inverse Functions

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6. Absolute Value Functions

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7. Graphing Absolute Value Functions

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8. Solving Absolute Value Equations

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9. Solving Absolute Value Inequalities

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10. Function Transformations

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11. Polynomial Functions

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12. Factor and Remainder Theorem

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13. Rational Functions

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14. Graphing Rational Functions

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15. Graphing Reciprocal Functions

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16. Questions

3. Vectors in 3D

15 Lessons

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1. 2D Vectors

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2. 3D Vectors

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3. Dot (Scalar) Product

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4. Unit Vector, Scalar Projection, and Vector Projection

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5. Cross (Vector) Product

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6. Planes

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7. Lines

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8. Spheres

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9. Closest Approach and Collision

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10. Angle Between Lines and Planes

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11. Angle Between Two Planes

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12. Shortest Distance Between Point and Line

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13. Shortest Distance Between Point and Plane

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14. Intersections

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15. Questions

4. Vector Calculus

13 Lessons

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1. Vector Functions

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2. Calculus of Vector Functions

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3. Displacement, Velocity, and Acceleration

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4. Limits, Continuity, and Differentiability

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5. Curvilinear Motion

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6. Graphing Curvilinear Motion

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7. Equations for Curvilinear Motion

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8. Projectile Motion

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9. Shortest Distance and Collisions

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10. Maximum Height

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11. Speed

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12. Circular and Elliptical Motion

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13. Questions

5. Differential Equations and Rates of Change

13 Lessons

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1. First Principles Differentiation

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2. Rules for Differentiation

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3. Equations of Tangent Lines

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4. Implicit Differentiation

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5. Differentiation Involving Parametric Equations

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6. Simple Harmonic Motion

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7. Rectilinear Motion

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8. Related Rates

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9. Logarithmic Differentiation

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10. Separation of Variables

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11. Solving Logistic Equations

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12. Slope Fields

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13. Questions

6. Integration and Applications of Integration

17 Lessons

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1. Limit Theorems

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2. Differentiation of Trigonometric Functions

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3. Integration and Substitution

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4. Fundamental Theorem of Calculus

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5. Integration of Trigonometric Functions

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6. Inverse Functions

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7. Inverse Trigonometric Functions and Graphing

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8. Calculus of Inverse Trigonometric Functions

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9. Exponential Functions

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10. Logarithmic Functions

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11. Total Change

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12. Area Between Curves

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13. Volume of Solid of Revolution

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14. Integration by Parts

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15. Partial Fractions

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17. Questions

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16. Numerical Integration

7. Statistical Interence

11 Lessons

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1. Probability Density Function (PDF)

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2. Uniform Distributionubution

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3. Exponential Distribution

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4. Normal Distribution

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5. Population, Samples, and Properties of Samples

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6. Distribution of Sample Means

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7. Central Limit Theorem

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8. Confidence Intervals

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9. Confidence Intervals for Population Means

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10. Sample Size and Margin of Error

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11. Questions

8. Systems of Linear Equations

9 Lessons

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1. Three Planes Intersecting

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2. Augmented Matrix

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3. Gaussian Elimination Row Operations

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4. Row Echelon Form and Reduced Row Echelon Form

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5. Unique Solutions

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6. Infinite Solutions

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7. No Solutions

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8. Existence of Solutions and Plane Orientation

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9. Questions

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About the teacher

Juan

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