Pre-U Pre-U 9794/2 2013 November — Question 6

Exam BoardPre-U
ModulePre-U 9794/2 (Pre-U Mathematics Paper 2)
Year2013
SessionNovember
TopicTangents, normals and gradients
TypeFind tangent at given point (polynomial/algebraic)
DifficultyModerate -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.
Spec1.07i 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 \(b\).

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 $b$.

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