Lesson Category: Grade 12 Lessons

2. Sigma notation
3. Derivation and application of the formulae for the sum of arithmetic:
   3.1 𝑆𝑛 = 𝑛/2 [2𝑎 + (𝑛 − 1)𝑑];
   𝑆𝑛 = 𝑛/2 (𝑎 + 𝑙)

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

1. Definition of a function.

2. General concept of the inverse of a
function and how the domain of the
function may need to be restricted (in
order to obtain a one-to-one function)
to ensure that the inverse is a function.

3. Determine and sketch graphs of the
inverses of the functions defined by
𝑦 = 𝑎𝑥 + 𝑞;

Focus on the following characteristics: domain and range intercepts with the axes,
turning points, minima, maxima, asymptotes (horizontal and vertical), shape and
symmetry, 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.

1. Compound angle identities:

Converting from LOGARITHMIC form to exponential form

2. Revise the proof of the sine, cosine, and area rules.

You are Doing Well. Go ahead and click the Next Topic button.

We are Now Moving to Euclidean Geometry. Good Luck.

3. Solve problems in two and three
   dimensions applying the sine, cosine
   and area rules.