Edexcel C1 — Question 6 7 marks

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTangents, normals and gradients
TypeFind tangent at given point (polynomial/algebraic)
DifficultyEasy -1.2 This is a straightforward C1 differentiation question requiring only basic power rule differentiation (rewriting √(8x) as (8x)^(1/2)), substitution to find the gradient at x=2, and using y-y₁=m(x-x₁). It's simpler than average A-level questions as it involves a single standard technique with no problem-solving or conceptual challenges.
Spec1.07i Differentiate x^n: for rational n and sums1.07m Tangents and normals: gradient and equations
6. The curve with equation \(y = \sqrt { 8 x }\) passes through the point \(A\) with \(x\)-coordinate 2. Find an equation for the tangent to the curve at \(A\).
AnswerMarks Guidance
\(x = 2 \Rightarrow y = \sqrt{16} = 4\)B1
\(y = \sqrt{8}\sqrt{x} = 2\sqrt{2} \cdot x^{\frac{1}{2}}\)B1
\(\frac{dy}{dx} = \sqrt{2} x^{-\frac{1}{2}}\)M1 A1
\(\text{grad} = \frac{\sqrt{2}}{\sqrt{2}} = 1\)M1
\(\therefore y - 4 = 1(x - 2)\) \([y = x + 2]\)M1 A1 (7) 
$x = 2 \Rightarrow y = \sqrt{16} = 4$ | B1 |
$y = \sqrt{8}\sqrt{x} = 2\sqrt{2} \cdot x^{\frac{1}{2}}$ | B1 |
$\frac{dy}{dx} = \sqrt{2} x^{-\frac{1}{2}}$ | M1 A1 |
$\text{grad} = \frac{\sqrt{2}}{\sqrt{2}} = 1$ | M1 |
$\therefore y - 4 = 1(x - 2)$ $[y = x + 2]$ | M1 A1 | (7)
6. The curve with equation $y = \sqrt { 8 x }$ passes through the point $A$ with $x$-coordinate 2.

Find an equation for the tangent to the curve at $A$.\\

\hfill \mbox{\textit{Edexcel C1  Q6 [7]}}
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