Applications of Calculus

ME-C3 is worth about 12 marks out of 100 in recent HSC Mathematics Extension 1 papers. Practise 13 exam-style questions (numerical answer, algebraic answer, multi-part, multiple choice) with instant marking and a worked solution for every question.

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Example questions

Example 1 · 1 mark · multiple choice

The line $y = 2$ for $0 \leq x \leq 3$ is rotated about the $x$ -axis. What is the volume of the solid formed?

A $12$
B $12 π$
C $18 π$
D $6 π$

Example 2 · 1 mark · multiple choice

A slope field has all slopes equal to zero along the line $y = 2$ , positive below it and negative above it. Which differential equation could it represent?

A $\frac{d y}{d x} = y - 2$
B $\frac{d y}{d x} = x - 2$
C $\frac{d y}{d x} = 2 y$
D $\frac{d y}{d x} = 2 - y$

Example 3 · 3 marks · numerical answer

Air is pumped into a spherical balloon at a rate of 100 cm³/s. Find the rate at which the radius is increasing when the radius is 10 cm. ( $V = \frac{4}{3} π r^{3}$ )

Answers and worked solutions appear when you practise these questions.

Applications of Calculus

Example questions

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