# Difficult Topics

The National Senior Certificate (NSC) is the school leaving certificate in South Africa and is based on the results from examinations in at least 7 subjects, 4 compulsory and at least 3 electives. In order to ensure that the topics chosen for the toolkit will potentially improve learner performance in the NSC as well as in their current grade, the 2013 NSC Examination Diagnostic Report  was used to identify topics of concern.

The report gives a detailed analysis of the final school leaving examination for all subjects. For Mathematics students write two papers, the first focuses more on algebra, functions and calculus while the second one focuses on trigonometry, geometry and data handling.

From the tables below it is clear that most students can be categorised as low achievers and emphasizes why, in the South African toolkit, there is not a specific focus on low achievers.

## Paper 2

Although the question in Paper 1 on equations, inequalities and algebraic manipulations was the second best answered question, a closer read of the report shows that learners struggle with applying exponential laws:

Question 1: Algebra

Common errors and misconceptions:
(d)  There is a definite lack of understanding of and ability to apply exponential laws.

Question 2: Patterns

Common errors and misconceptions:
(c)  The law of exponents is still a challenge for some learners . The rules of exponents were applied incorrectly.

Question 8: Calculus

Common errors and misconceptions:
(d)  Learners made many algebraic mistakes in the simplification part.

Suggestions for improvement:
(d)  Fractions and exponential laws must be emphasised when working with Calculus.
(f)  When differentiating by rules, learners need to understand what the original expression consists of . Identify the fractions, exponents and in the original expression. Make sure that learners KNOW how to simplify before differentiation.
(g) For fractions, it is always better for the learners to do the following to simplify:

Question 10: Calculus (Application)

Suggestions for improvement:
(b)  Application and/or word problems involving differentiation need to be taught with a positive approach and be introduced as early as possible so that learners have a good grasp of the language involved.