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Circular Functions Graphs Learning Objects

Unit circle

A graphical representation of sin, cos & tan values around the circle.

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Calculus Differentiation Unit 2 Unit 4

First principles of calculus

Move the first point “a” and change the value of “h” that determines the location of the second point. Bring h towards point a.

f(x) must defined as increasing function for the points x=a and x=a+h.

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Calculus Graphs Integration Learning Objects Unit 2 Unit 4

Integration – Area under the curve

Investigate finding the area under a curve – integration. Use the sliders to change the boundaries. You can also modify the function being graphed.

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Calculus Differentiation Graphs Learning Objects Unit 2 Unit 4

Gradient from first principles

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Calculus Integration Podcast Unit 2 Unit 4

Approximating areas under curves

  • Area under curves
  • Left end-point approximation
  • Right end-point approximation
  • Improvements to rectangle approximations
  • Find the total from a rate

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Calculus Integration Podcast Unit 2 Unit 4

Integration

  • Find the total from a rate
  • Anti-differentiation
  • Rules for anti-differentiation
  • Examples of anti-derivative functions
  • Finding the original function
  • Area under a curve – integration
  • Signed area

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Circular Functions Podcast Unit 2

Graphs of circular functions

  • Values of sin x , cos x & tan x,
  • Graphs of sin x & cos x,
  • Transformations of sin graphs,
  • Solving circular function equations,
  • Graphs of tan x

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Calculus Differentiation Podcast Unit 2 Unit 4

Differentiation

  • Differentiation by first principles
  • Differentiation of polynomials
  • Examples of derivative functions & gradients
  • Graphs of derivative functions
  • Tangents
  • Normal lines
  • Finding stationary points

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Probability Probability distributions Unit 4

Six Dice One-Roll Yahtzee (in super slow motion) – Numberphile

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Circular Functions Graphs Learning Objects Unit 2

Sin graph

Investigate changes to the amplitude, dilation, horizontal and vertical translation of a sin graph.