| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2020 |
| Session | October |
| Marks | 6 |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Reverse chain rule with linear composite |
| Difficulty | Easy -1.3 Three straightforward integration exercises requiring standard techniques: (a) substitution with u=x²+1, (b) reverse chain rule for a polynomial, (c) rewriting as exponential then integrating. Each is a 2-mark routine application with no problem-solving or conceptual challenge—typical of easier A-level pure maths questions testing basic integration fluency. |
| Spec | 1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)1.08h Integration by substitution |
\begin{enumerate}[label=(\alph*)]
\item Find
$$\int \frac{x}{x^2 + 1} dx$$
[2]
\item Find.
$$\int 2\pi(4x + 3)^{10} dx$$
[2]
\item Find.
$$\int \frac{2}{e^{4x}} dx$$
[2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2020 Q1 [6]}}