Applications of Differentiation practice questions

Secondary 4 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise applications of differentiation free

What this topic covers

Worked examples

Example 1

Find the yy-intercept of the tangent to y=2x3−3x+4y = 2x^{3} - 3x + 4 at x=−1x = -1.
Show the worked solution
  • $y = 2x^{3} - 3x + 4$
  • $\frac{dy}{dx} = 6x^{2} - 3$
  • $\text{At } x = -1: \quad m = 6(-1)^2 - 3$
  • $m = 3$
  • $y(-1) = 2(-1)^3 - 3(-1) + 4$
  • $y(-1) = 5$
  • $\text{Tangent: } y - 5 = 3(x + 1)$
  • $\text{Set } x = 0: \quad y = 5 + 3$

Answer: 88

Example 2

The side of a square increases at 3 cm/s. Find the rate of change of its area when the side is 10 cm.
Show the worked solution
  • $A = s^2$
  • $\frac{dA}{ds} = 2s$
  • $\text{At } s = 10: \quad \frac{dA}{ds} = 20$
  • $\frac{dA}{dt} = \frac{dA}{ds} \times \frac{ds}{dt}$
  • $= 20 \times 3$
  • $= 60 \text{ cm}^2\text{/s}$

Answer: 6060

Example 3

Find the maximum value of y=2x3−3x2−12x+1y = 2x^{3} - 3x^{2} - 12x + 1.
Show the worked solution
  • $y = 2x^{3} - 3x^{2} - 12x + 1$
  • $\frac{dy}{dx} = 6x^{2} - 6x - 12$
  • $\text{Set } \frac{dy}{dx} = 0: \quad x = -1 \text{ or } x = 2$
  • $\frac{d^2y}{dx^2} = 12x - 6$
  • $\text{At } x = -1: \quad \frac{d^2y}{dx^2} = -18 \quad (< 0 \Rightarrow \text{maximum})$
  • $y(-1) = 8$

Answer: 88

Questions parents ask

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Which syllabus does this follow?

Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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