Introduction to Differentiation

MA-C1 is worth about 1 marks out of 100 in recent HSC Mathematics Advanced papers. Practise 8 exam-style questions (multiple choice, multi-part, numerical answer) with instant marking and a worked solution for every question.

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Example questions

Example 1 · 1 mark · multiple choice

Which expression gives $f^{'} (x)$ from first principles when $f (x) = x^{2}$ ?

A $h \to 0 lim \frac{( x + h ) ^{2} - x ^{2}}{h}$
B $h \to 0 lim ((x + h)^{2} - x^{2})$
C $h \to 0 lim \frac{x ^{2} + h - x ^{2}}{h}$
D $h \to 0 lim \frac{( x + h ) ^{2} + x ^{2}}{h}$

Example 2 · 1 mark · multiple choice

The points $P (2, 4)$ and $Q (2 + h, (2 + h)^{2})$ lie on $y = x^{2}$ , where $h \neq = 0$ . What is the gradient of the secant $P Q$ ?

A $4 + h$
B $4$
C $4 + 2 h$
D $2 + h$

Example 3 · 2 marks · multi-part

Let $f (x) = 3 x^{2} - x$ . Use $f^{'} (x) = h \to 0 lim \frac{f ( x + h ) - f ( x )}{h}$ .

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Introduction to Differentiation

Example questions

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