Grade 12 Differential Calculus
Categories: Differential Calculus, Grade 12 Maths
What Will You Learn?
- Learn and apply your knowledge to all topics and concepts in the Grade 12 Differential Calculus syllabus. Students will learn to derive polynomials, determine the equation, sketching & graph interpretation of cubic functions. By the end of this lesson students will have a full knowledge of how to interpret tangents to a function.
Course Content
Limits
Learn and apply your knowledge to Limits in Differential Calculus
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Limits Theory
03:45 -
Limits Part 1
01:22 -
Limits and Factorisation Part 1
01:51 -
Limits and Factorisation Part 2
01:32 -
Limits and Fractions
02:28 -
Limits and First Principles
04:22
Using the Definition (First Principle), Find the Derivatives
In this topic, students will learn how to use the Definition (First Principle, Find the Derivatives for constants
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First Principles Theory
04:50 -
Finding Gradient Using First Principles
02:03 -
Finding the Derivative and Gradient at a Point Using First Principles
06:02
Find Equations of Tangents to Graphs of Functions
In this lesson, students will learn how to answer questions relating to graphs of functions
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Average Gradient Theory
06:39 -
Finding Average Gradient
01:54 -
Finding Average Gradient Using the First Principles Formula
04:54 -
Finding the Equation of a Tangent to a Function Theory
02:56 -
Finding the Equation of a Tangent to a Function Given the X-Value
05:23 -
Finding the Equation of a Tangent to an Hyperbola Given the x-value
05:01 -
Graph Interpretation with Tangents and Parallel Lines Part 1
06:00 -
Graph Interpretation with Tangents and Parallel Lines Part 2
06:15 -
Finding the Equation of a Straight Line Given One Point and the Gradient
02:59 -
Showing that Two Functions Intersect at 90 Degrees
06:55 -
Increasing and Decreasing Functions Part 1
07:31 -
Increasing and Decreasing Functions Part 2
05:04
Graph Sketching and Interpretation
Learn how to sketch all types of graphs
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Graph Interpretation with Gradient and Tangents
01:59 -
Graph Interpretation and a Cubic Function and First Principles
06:49 -
Graph Interpretation and a Cubic Function, Parabola and Straight Line
12:45 -
Graph Interpretation and a Cubic Function
12:04 -
Showing that a Graph has no Stationary Point
03:50 -
Graph Interpretation and Cubic Functions with a Parabola
10:02 -
Consolidated Example on Graph Interpretation with Cubic Function
15:38 -
Interpreting f(x).f^’ (x)<0
03:12
Sketch Graphs of Cubic Polynomial Functions
Learn how to sketch graphs of cubic polynomial functions
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The Remainder and Factor Theorem and Factors
02:53 -
The Remainder and Factor Theorem: Finding the Remainder Part 1
04:18 -
The Remainder and Factor Theorem: Finding the Remainder Part 2
01:54 -
The Remainder and Factor Theorem: Finding the Remainder Part 3
01:52 -
Given a Factor, Finding a Variable with the Remainder and Factor Theorem
02:13 -
Given the Remainder, finding the value of a variable in the remainder and factor theorem
02:18 -
The Remainder and Factor Theorem and Simultaneous Equations
06:36 -
Factorising a Cubic Function Part 1
10:35 -
Factorising a Cubic Function Part 2
06:40 -
Solving for x in a Cubic Function
05:17 -
Solving for x in a Cubic Function and Using the Formula
07:26 -
Finding the Stationary Points of a Cubic Function
04:07 -
Sketching a Cubic Function and the Relationship Between other Functions
07:01 -
Differentiating a Cubic Function
10:17 -
Deriving a Cubic Function Twice
03:57 -
Steps to Sketching a Cubic Function Theory
04:07 -
Sketching a Cubic Function Part 1
12:04 -
Sketching a Cubic Function Part 2
09:42 -
Sketching a Cubic Function Part 3
15:41 -
Sketching a Cubic Function Part 4
11:40 -
Sketching a Cubic Function with a Point of Inflection
07:01 -
Sketching a Cubic Function with Different Type of Information
04:33 -
Sketching a Cubic Function with Different Type of Information Part 2**
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Graph Interpretation and Concavity
05:39 -
Finding the Equation of a Cubic Function when Given 3 x-Intercepts Part 1
04:45 -
Finding the Equation of a Cubic Function When Given 3 x-Intercepts Part 2
04:22 -
Finding the Equation of a Cubic Function When Given an x-Intercept and a Stationary Point
05:17 -
Finding the Equation of a Cubic Function When Given Only a Stationary Point
09:17 -
Translating a Cubic Function Part 1
04:49 -
Translating a Cubic Function Part 2
04:54 -
Finding a Cubic Function When Given 2 Stationary Points
08:41
Finding the Derivative
Use forumulas together with rules to find and answer questions relating to derivatives
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Rules of Differentiation
04:27 -
Notations a Differentiation
04:27 -
Differentiate a Number
00:47 -
Finding the Derivative at a Point Using First Principles Part 1
06:03 -
Finding the Derivative at a Point Using First Principles Part 2
06:13 -
Finding the Derivative at a Point Using First Principles Part 3
05:20 -
Differentiating with Different Variables Part 1
01:16 -
Differentiating with Different Variables Part 2
01:16 -
Differentiating with Different Variables Part 3
01:25 -
Differentiating with Different Variables Part 4
02:23 -
Differentiating with Different Variables Part 5
02:23 -
Differentiating with Different Variables Part 6
04:01 -
Differentiating an Exponent Part 1
00:51 -
Differentiating an Exponent Part 2
00:52 -
Differentiating an Expression with Two Exponents
01:19 -
Differentiating an Expression with Two Terms
01:12 -
Differentiating an Expression with Three Terms
01:01 -
Differentiating the Product of Two
02:10 -
Differentiating a Fraction with Quadratic Term in Numerator and Linear Term in Denominator
02:45 -
Differentiating Two Fractions Added Together
02:28 -
Differentiating a Fraction with Cubic Term in Numerator and Linear Term in Denominator
03:03 -
Differentiating a Fraction and a Surd
02:10 -
Differentiating Three Terms Including a Fraction and a Surd
03:06 -
Differentiating a Fraction with a Cube and Surd
04:49 -
Differentiating a Bracket Squared
03:18 -
Differentiating the Addition of Two Functions
01:26 -
Differentiating a Cubic Function
10:17 -
Stationary Points and Points of Inflection Theory
06:18 -
Concavity Theory
02:03 -
Proving the Existence of a Point of Inflection at a Point
04:35