SPS SPS SM Pure 2021 June — Question 1 5 marks

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2021
SessionJune
Marks5
TopicTangents, normals and gradients
TypeFind tangent at given point (polynomial/algebraic)
DifficultyModerate -0.8 This is a straightforward differentiation and tangent line question requiring only basic calculus techniques: differentiate a polynomial, substitute x=2 to find the gradient, then use y-y₁=m(x-x₁). It's simpler than average A-level questions as it involves no problem-solving or conceptual challenges, just routine application of standard methods.
Spec1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations

A curve has equation $$y = 2x^3 - 4x + 5$$ Find the equation of the tangent to the curve at the point \(P(2, 13)\). Write your answer in the form \(y = mx + c\), where \(m\) and \(c\) are integers to be found. Solutions relying on calculator technology are not acceptable. [5]

A curve has equation
$$y = 2x^3 - 4x + 5$$

Find the equation of the tangent to the curve at the point $P(2, 13)$.

Write your answer in the form $y = mx + c$, where $m$ and $c$ are integers to be found.

Solutions relying on calculator technology are not acceptable.
[5]

\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q1 [5]}}