Interactive Coursebook (Online) of C24 Coordinate Geometry (II)
C24 Coordinate Geometry (II)
What’s on the Specification
[TMUA]
| MM6.1 | The derivative of \(f(x)\) as the gradient of the tangent to the graph \(y=f(x)\) at a point.
Differentiation from first principles is excluded. |
| MM6.2 | Differentiation of \( x^n \) for rational \( n \), and related sums and differences. This might require some simplification before differentiating.
For example, the ability to differentiate an expression such as \( \frac{(3x+2)^2}{x^{\frac{1}{2}}} \). |
| MM7.3 | An understanding of the Fundamental Theorem of Calculus and its significance to integration. Simple examples of its use may be required in the forms:
|
[MAT]
| Differentiation: Derivative of \(x^a\), including for fractional exponents. Derivative of \(e^{kx}\). Derivative of a sum of functions. Tangents and normals to graphs. Turning points. Second order derivatives. Maxima and minima. Increasing and decreasing functions. Differentiation from first principles. |
Learning Objectives
- Understand the derivative as the gradient of a tangent and as a rate of change.
- Differentiate functions of the form (for rational ), , and sums/differences of such functions.
- Apply differentiation rules (including product, quotient, and chain rules for more complex functions if encountered).
- Calculate and interpret second-order derivatives.
- Find equations of tangents and normals to curves.
- Locate stationary points (maxima, minima) and determine their nature using first or second derivatives.
- Identify intervals where a function is increasing or decreasing.
- Understand the relationship between differentiation and integration via the Fundamental Theorem of Calculus.
- (MAT only) Understand the concept of differentiation from first principles.
Suggested Time
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 12 | 210 min |
| Quiz | 8 | 20 min |
| Practice A | 16 | 30 min |
| Practice B | 14 | 40 min |
| Total | 50 | 4-5hrs |
None
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