Mochi does Maths!

Ms Carolina's Math class

AI Topic 5 - Calculus

Lesson 1 - Introduction to limits Sl 5.1

In this lesson you will learn:


- To understand the concept of a limit

- To calculate limits using tables

- To interpret the limit in relation to the graph of a function


INSTRUCTIONS

1. Read: Pearson: Mathematics Applications and Interpretation SL. Page 298 - 308

2. Read: Oxford: Mathematics Applications and interpretation SL. Page 522 - 526

3. Watch: AI Calculus - Lesson 1 - Introduction to limits I.

4. Watch: AI Calculus - Lesson 1 - Introduction to limits II.

5. Formative assessment: Self Study - Calculus - Lesson 1 (available in our Google classroom)


Additional resources:

Finding limits using graphs Practice (IXL)

Determine if a limit exists (IXL)

Limits [Up to Quiz 1] (Khan Academy) ** Recommended **


Recommended practice:

Lesson 2 - Derivatives of polynomials SL 5.3

In this lesson you will learn:

- to identify the derivative as the value of the slope/gradient of a tangent line to a function f(x) at the point x.

- to evaluate the derivative for polynomial functions.

- to find the derivative of a function at x=a using your GDC.


INSTRUCTIONS

1. Read:  Pearson: Applications and Interpretation SL pages 309 - 311, 317 - 321

2. Read: Oxford: Mathematics Applications and Interpretation SL pages 527 - 528

3. Watch: AI Calculus - Lesson 2 - Derivatives of polynomials I

4. Watch: AI Calculus - Lesson 2 - Derivatives of polynomials II

5. Formative assessment: Self-study - Calculus Lesson 2 (Available at Google classroom)


Additional resources:

Power Rule I (IXL)

Power Rule II (IXL)


Recommended Practice:

Lesson 3 - Tangent and Normal lines SL 5.4

In this lesson you will learn: 

- to find the equation of a line tangent to a curve f(x) at a given point x=a.

- to find the equation of a line normal to a curve f(x) at a given point x=a.


INSTRUCTIONS

1. Read:  Pearson: Mathematics Applications and Interpretation SL pages 336 - 342

2. Read: Oxford: Mathematics Applications and interpretation SL pages 531 - 536


Additional resources:

Slope of a tangent line (IXL)

Equation of a tangent line (IXL)


Recommended Practice:


Lesson 4 - Increasing and decreasing functions SL 5.2

In this lesson you will learn:


INSTRUCTIONS:


Additional resources:


Recommended Practice:

Lesson 5 - Maximum and minimum points (Optimization I) SL 5.6

In this lesson you will learn:


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Additional resources:


Recommended Practice:

Lesson 6 - Optimization II SL 5.7

In this lesson you will learn:


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Additional resources:


Recommended Practice:

Lesson 7 - Introduction to antidifferentiation with and without boundary conditions SL 5.5

In this lesson you will learn:


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Additional resources:


Recommended Practice:

Lesson 8 - Definite integrals and area under the curve SL 5.5

In this lesson you will learn:


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Recommended Practice:

Lesson 9 - Approximating areas using the trapezoid rule SL 5.8

In this lesson you will learn:


INSTRUCTIONS:


Additional resources:


Recommended Practice: