| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2015 |
| Session | June |
| Marks | 4 |
| Topic | Indefinite & Definite Integrals |
| Type | Find curve from gradient |
| Difficulty | Easy -1.2 This is a straightforward integration question requiring only basic polynomial integration and using one point to find the constant of integration. It's a standard textbook exercise with no problem-solving required—just direct application of the power rule and substitution, making it easier than average. |
| Spec | 1.08a Fundamental theorem of calculus: integration as reverse of differentiation |
**Question 2:** $\int 6x^2 + 2\,dx = 2x^3 + 2x\,(+c)$
$3 = 2 + 2 + c$ so $c = -1$
$y = 2x^3 + 2x - 1$
- **M1***: Attempt to integrate at least one term – increase in power by 1
- **A1**: Obtain correct integral (allow no $+c$)
- **M1d***: Substitute $(1,3)$ to find $c$
- **A1**: Correct equation, including $y=$
**Total: [4]**2 The gradient of a curve is given by $\frac { \mathrm { d } y } { \mathrm {~d} x } = 6 x ^ { 2 } + 2$. The curve passes through the point $( 1,3 )$. Find the equation of the curve.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2015 Q2 [4]}}