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3. Gaussian Elimination Row Operations

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Year 12 Math's Specialist
8. Systems of Linear Equations
3. Gaussian Elimination Row Operations

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Year 12 Math's Specialist

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1. Complex Numbers

1. Complex Solutions of the Quadratic Equation

2. Representing Complex Numbers

3. Cartesian Form

5. Complex Conjugate Pairs

6. Cartesian Form Operations

7. Polar Form Operations

8. Exponential Form Operations

9. From Complex Solutions to Quadratic Equation

10. Locus of Points and Graphs

11. Cartesian Equation from Locus of Points

14. Max/Min Circle Problems

15. Perpendicular Bisector

16. Line Between two Complex Numbers

17. Distance Between Points

18. Graphs of Vectors in Polar Form

19. De Moivre's Theorem

20. Trigonometric Identities Using De Moivre's Theorem

21. Z Transformations

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2. Functions and Curve Sketching

1. Domain and Range of Functions

2. Composite Functions

3. Domain and Range of Composite Functions

4. Inverse Functions

5. Graphing Inverse Functions

6. Absolute Value Functions

7. Graphing Absolute Value Functions

8. Solving Absolute Value Equations

9. Solving Absolute Value Inequalities

10. Function Transformations

11. Polynomial Functions

12. Factor and Remainder Theorem

13. Rational Functions

14. Graphing Rational Functions

15. Graphing Reciprocal Functions

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3. Vectors in 3D

3. Dot (Scalar) Product

4. Unit Vector, Scalar Projection, and Vector Projection

5. Cross (Vector) Product

9. Closest Approach and Collision

10. Angle Between Lines and Planes

11. Angle Between Two Planes

12. Shortest Distance Between Point and Line

13. Shortest Distance Between Point and Plane

14. Intersections

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4. Vector Calculus

1. Vector Functions

2. Calculus of Vector Functions

3. Displacement, Velocity, and Acceleration

4. Limits, Continuity, and Differentiability

5. Curvilinear Motion

6. Graphing Curvilinear Motion

7. Equations for Curvilinear Motion

8. Projectile Motion

9. Shortest Distance and Collisions

10. Maximum Height

12. Circular and Elliptical Motion

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5. Differential Equations and Rates of Change

1. First Principles Differentiation

2. Rules for Differentiation

3. Equations of Tangent Lines

4. Implicit Differentiation

5. Differentiation Involving Parametric Equations

6. Simple Harmonic Motion

7. Rectilinear Motion

8. Related Rates

9. Logarithmic Differentiation

10. Separation of Variables

11. Solving Logistic Equations

12. Slope Fields

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6. Integration and Applications of Integration

1. Limit Theorems

2. Differentiation of Trigonometric Functions

3. Integration and Substitution

4. Fundamental Theorem of Calculus

5. Integration of Trigonometric Functions

6. Inverse Functions

7. Inverse Trigonometric Functions and Graphing

8. Calculus of Inverse Trigonometric Functions

9. Exponential Functions

10. Logarithmic Functions

11. Total Change

12. Area Between Curves

13. Volume of Solid of Revolution

14. Integration by Parts

15. Partial Fractions

16. Numerical Integration

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7. Statistical Interence

1. Probability Density Function (PDF)

2. Uniform Distributionubution

3. Exponential Distribution

4. Normal Distribution

5. Population, Samples, and Properties of Samples

6. Distribution of Sample Means

7. Central Limit Theorem

8. Confidence Intervals

9. Confidence Intervals for Population Means

10. Sample Size and Margin of Error

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8. Systems of Linear Equations

1. Three Planes Intersecting

2. Augmented Matrix

3. Gaussian Elimination Row Operations

4. Row Echelon Form and Reduced Row Echelon Form

5. Unique Solutions

6. Infinite Solutions

7. No Solutions

8. Existence of Solutions and Plane Orientation

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