Differential Calculus Including Polynomials

Patterns: Revise number patterns leading to those where there is a constant second difference betweenconsecutive terms and the general term is therefore quadratic.

Differential Calculus Including Polynomials Generalise to find the derivative of f at any point x in the domain of f , i.e., define the derivative function f ‘(x) of the function f (x) . Understand intuitively that f ‘(a) is the gradient of the tangent to thegraph of f at the point with x -coordinate a.

Number patterns, including arithmetic and geometric sequences and series

3. Derivation and application of the formulae for the sum of geometric series: 3.2 𝑆𝑛 = 𝑎(𝑟 𝑛−1) 𝑟−1 ; (𝑟 ≠ 1); and 3.3 𝑆𝑛 = 𝑎 1−𝑟 ; (−1 < 𝑟 < 1), (𝑟 ≠ 1)

Functions: Formal Definition , Inverse, exponential and logarithmic 2. General concept of the inverse of afunction and how the domain of thefunction may need to be restricted (inorder to obtain a one-to-one function)to ensure that the inverse is a function. 3. Determine and sketch graphs of theinverses of the functions defined by𝑦 = 𝑎𝑥 + 𝑞; Focus on the following characteristics: domain and range intercepts with the axes,turning points, minima, maxima, asymptotes (horizontal and vertical), shape andsymmetry, average gradient (average rate of change), intervals on which the function increases /decreases.

5. Revision of the exponential function and the exponential laws and graph of the function defined by y = b x where b > 0 and b ≠ 0 6. Understand the definition of a logarithm: y = logb x ⇔ x = b y where b > 0 and b ≠ 1 7. The graph of the function, 𝑦 = 𝑙𝑜𝑔𝑏 𝑥 for both the cases 0 < 𝑏 < 1 and 𝑏 > 1.

Converting from LOGARITHMIC form to exponential form