| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2013 |
| Session | November |
| Topic | Tangents, normals and gradients |
| Type | Find tangent at given point (polynomial/algebraic) |
| Difficulty | Moderate -0.3 This is a straightforward two-variable simultaneous equations problem. Students substitute the point into the curve equation and the gradient into the derivative, then solve. While it requires careful algebraic manipulation, it's a standard textbook exercise with no conceptual difficulty beyond basic differentiation and simultaneous equations—slightly easier than average. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations |
6 The curve $y = x ^ { 3 } + a x ^ { 2 } + b x + 1$ has a gradient of 11 at the point $( 1,7 )$. Find the values of $a$ and $b$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2013 Q6}}