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Differentiation from first principles, rules of differentiation and applications including optimisation and rates of change.
Watch the full lesson before attempting practice questions.
Master these ideas before attempting exam questions.
f'(x) = lim[h→0] [f(x+h) − f(x)] / h. Used when the question specifically asks for it.
Power rule: d/dx[xⁿ] = nxⁿ⁻¹. Constant rule: d/dx[k] = 0. Sum/difference rules apply term by term.
Use f'(x) = 0 to find turning points. f''(x) to classify them. Use f''(x) = 0 for point of inflection.
Set up a primary equation, express in one variable using a constraint, differentiate and solve f'(x) = 0.
f'(x) gives the instantaneous rate of change. Identify what each variable represents in the context.
Commit these to memory — they appear in almost every exam.
These are your learning targets for Calculus.
Avoid these errors — they cost marks every year.
Expand brackets and simplify fractions before applying differentiation rules.
Finding where f'(x) = 0 only locates turning points — you must still classify them.
f'(x) = 0 gives turning points; f''(x) = 0 gives the point of inflection.
Request CAPS-aligned study materials for Calculus.
Comprehensive CAPS-aligned notes covering all key concepts, theorems, and worked examples for Calculus.
NSC-style exam questions with full memorandum. Ideal for timed practice and self-assessment before exams.
Graded practice questions organised by difficulty. Perfect for building confidence before Paper 1.
Straight answers to common Grade 12 CAPS questions about Calculus.
Calculus in Grade 12 CAPS focuses on differentiation and its applications. You learn rules for finding derivatives, then use them for gradient, turning points, optimisation, and curve sketching.
Practise the differentiation rules until they feel automatic, then work on application questions step by step. Many learners improve quickly when they separate basic derivative skills from interpretation questions.
Common mistakes include differentiating powers incorrectly, dropping signs, confusing stationary points with turning points, and not interpreting the question fully after finding the derivative.
CAPS exams usually test differentiation rules, tangent gradients, stationary points, maxima and minima, and optimisation. Calculus is a high-value Paper 1 topic and often appears in structured multi-part questions.
Book a focused session with Chris Khomo and work through this topic step by step — at your own pace, online, from anywhere in South Africa.