Recently two supplements have appeared on the Folens website regarding extra material which they say can be examined in 2015 .
One supplement involves Implicit Differentiation and gives the impression that differentiation of Implicit functions can be examined .
Projectmaths.com has been in contact with the NCCA
This is their reply “It’s worth noting that the syllabus dos not specifically mention implicit differentiation. Thus, it cannot be assumed that students have studied this approach (but may of course use it validly) and an exam question would be set or scaffolded in such a way that the student is able to apply the required differentiation. The specific learning outcome relates to finding the slope of a tangent to a circle, and the type of representation of a circle that is relevant is stated in Section 2.2 (co-ordinate geometry). In a follow up question to clarify the previous answer we received the following”
”Since implicit differentiation is not specified in the learning outcome, the student will not be asked to differentiate x^2 + y^2 + 2gx + 2fy + c. ”
Message: Implicit differentiation cannot be asked.
Regarding the Binomial Theorem
Here are the replies :The application of the binomial theorem follows on from the outcome requiring students to be able to perform the arithmetic operations of addition, subtraction, multiplication and division on polynomials and rational algebraic expressions... and in that context it would apply to n being a natural number rather than a rational number
The two learning outcomes related to the binomial theorem are to ‘compute binomial coefficients’ and ‘apply the binomial theorem’. Thus, they should be able to find the coefficient associated with any particular term. They should also recognise the pattern of these coefficients, particularly in the context of Sections 1.1 and 1.3 of the syllabus.