0606.14.2: Use the notations R V dy d2 y S d JKdyNOW f′(x), f″(x), , dx dx2 SS dx KdxOWW = T L PX … — IGCSE Additional Mathematics 0606 past paper questions

Real questions on 0606.14.2: use the notations r v dy d2 y s d jkdynow f′(x), f″(x), , dx dx2 ss dx kdxoww = t l px …

The newest 20 of 21 written questions. Open one to see it on the real paper.

0606/11 · May/June 2025 · Q6a[5]
A curve has equation $y = (\frac{x ^{2} - 1}{x ^{2} + 1})^{4}$ . (a) Show that $\frac{d y}{d x}$ can be written as $\frac{A x ( x ^{2} - 1 ) ^{3}}{( x ^{2} + 1 ) ^{5}}$ , where $A$ is a positive integer to be found.See it on the paper →
0606/22 · May/June 2025 · Q6[2]
6 The volume, $V$ , of a sphere is increasing at the constant rate of $2 π cm^{3} s^{- 1}$ . Find the rate of change of the surface area, $S$ , of this sphere when the volume of the sphere is $36 π cm^{3}$ .See it on the paper →
0606/23 · May/June 2025 · Q2[3]
Given that $y = \frac{4 x ^{3} - 5}{x ^{2}}$ , show that $\frac{d y}{d x}$ can be written as $\frac{2 ( 2 x ^{3} + 5 )}{x ^{3}}$ .See it on the paper →
0606/11 · October/November 2024 · Q9a[5]
The equation of a curve is $y = \frac{e ^{- 3 x + 2}}{x + 1}$ where $x < - 1$ . (a) Show that $\frac{d y}{d x} = \frac{e ^{- 3 x + 2}}{( x + 1 ) ^{2}} (A x + B)$ where $A$ and $B$ are integers to be found.See it on the paper →
0606/12 · February/March 2023 · Q2a[4]
A curve has equation $y = (5 - x) (x + 2)^{2}$ . (a) Find the $x$ -coordinates of the stationary points on the curve.See it on the paper →
0606/13 · October/November 2022 · Q12a[5]
It is given that $y = \frac{( 3 x ^{2} - 2 ) ^{\frac{2}{3}}}{x - 1}$ , for $x > 1$ . (a) Write $\frac{d y}{d x}$ in the form $\frac{( 3 x ^{2} - 2 ) ^{- \frac{1}{3}}}{( x - 1 ) ^{2}} (x^{2} + A x + B)$ , where $A$ and $B$ are integers.See it on the paper →
0606/13 · October/November 2022 · Q12b[2]
It is given that $y = \frac{( 3 x ^{2} - 2 ) ^{\frac{2}{3}}}{x - 1}$ , for $x > 1$ . (b) Find the approximate increase in $y$ as $x$ increases from $2$ to $2 + p$ , where $p$ is small.See it on the paper →
0606/23 · October/November 2022 · Q2[5]
The tangent to the curve $y = a x^{2} - 5 x + 2$ at the point where $x = 2$ has equation $y = 7 x + b$ . Find the values of the constants $a$ and $b$ .See it on the paper →
0606/23 · October/November 2021 · Q6b[1]
It is given that $x = 2 + sec θ$ and $y = 5 + tan^{2} θ$ . (b) Find $\frac{d y}{d x}$ in terms of $x$ .See it on the paper →
0606/23 · October/November 2021 · Q10a[5]
It is given that $f (x) = 4 x^{3} - 4 x^{2} - 15 x + 18$ . Find the equation of the normal to the curve $y = f (x)$ at the point where $x = 1$ .See it on the paper →
0606/13 · May/June 2021 · Q2a[3]
(a) Find $\frac{d}{d x} (x^{2} e^{3 x})$ .See it on the paper →
0606/13 · May/June 2021 · Q2b(i)[2]
(b) (i) Find $\frac{d}{d x} (3 x^{2} + 4)^{\frac{1}{3}}$ .See it on the paper →
0606/22 · February/March 2021 · Q11a(i)[2]
11 (a) (i) Find $\int \frac{1}{( 10 x - 1 ) ^{6}} d x$ .See it on the paper →
0606/22 · February/March 2021 · Q11a(ii)[3]
(ii) Find \int \frac{(2x^3+5)^2}{x} \, \mathrm{d}x.See it on the paper →
0606/22 · February/March 2021 · Q11b(i)[2]
(b) (i) Differentiate $y = tan (3 x + 1)$ with respect to $x .$ See it on the paper →
0606/21 · October/November 2020 · Q9a[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
0606/21 · October/November 2020 · Q9b[3]
3-mark “Find” question — its maths and diagrams are best seen on the paper.
See it on the paper →
0606/21 · October/November 2020 · Q9c[2]
A particle moves in a straight line such that, $t$ seconds after passing a fixed point $O$ , its displacement from $O$ is $s$ m, where $s = e^{2 t} - 10 e^{t} - 12 t + 9$ . (c) Find the acceleration at this time.See it on the paper →
0606/23 · May/June 2020 · Q8a[2]
Differentiate $y = tan (x + 4) - 3 sin x$ with respect to $x$ .See it on the paper →
0606/23 · May/June 2020 · Q8b[6]
(b) Variables $x$ and $y$ are such that $y = \frac{l n ( 2 x + 5 )}{2 e ^{3 x}}$ . Use differentiation to find the approximate change in $y$ as $x$ increases from $1$ to $1 + h$ , where $h$ is small.See it on the paper →

What examiners said

Most candidates made a good attempt at this part, with many earning 4 or 5 marks. Almost all successful solutions applied the quotient rule rather than the product rule. There were two main approaches: either differentiating the algebraic fraction within the brackets and combining this with the outer differential, or directly differentiating the numerator and denominator and applying the quotient...
— Examiner report, May/June 2025, 0606/11 Q6(a) (Cambridge)

Candidates found this connected rates of change problem to be somewhat challenging. A reasonable number of candidates offered fully correct solutions. There were various different approaches, and some were far more complicated than others. Methods which involved, for example, differentiating an expression for V in terms of S or S in terms of V were generally unsuccessful due to their complexity....
— Examiner report, May/June 2025, 0606/22 Q6 (Cambridge)

The simplest method of solution was to start by writing the expression for y as 4x – 5x –2 and then differentiate. This approach resulted in a much simpler derivative to be manipulated into the given form. Very few candidates chose this method. Those who did were often successful. The majority of candidates chose to use the quotient rule, with a very small number applying the product rule to (4x3...
— Examiner report, May/June 2025, 0606/23 Q2 (Cambridge)